text:
# When the carrier and one of the sidebands are suppressed in an AM wave modulated to a depth of 50%, the power saving will be

Free Practice With Testbook Mock Tests

## Options:

1. 84.4%

2. 88.6%

3. 94.4%

4. 98.6%

### Correct Answer: Option 3 (Solution Below)

This question was previously asked in

ESE Electronics 2020: Official Paper

## Solution:

Concept:

Power of a transmitted AM wave is given as:

$$P_t = {P_c}\left( {1 + \frac{{{μ ^2}}}{2}} \right)$$

$$P_t = {P_c} + P_c\frac{μ ^2}{2}$$

Power in the carrier = Pc

Power in both the sidebands is given by:

$$P_s= \frac{{{P_c}{μ^2}}}{2}$$

Since the power is distributed equally to the left and to the right side of the sideband, the power in one of the sidebands is given by:

$$P_{s1}= \frac{{{P_c}{u^2}}}{4}$$

Calculation:

When the carrier and 1 of the sideband are suppressed, the amount of power saving will be:

$$= {P_c} + \frac{{{P_c}{μ ^2}}}{4}$$

The percentage of power saved will be calculated as:

$$\frac{{{P_c}\left( {1 + \frac{{{μ ^2}}}{4}} \right)}}{{{P_c}\left( {1 + \frac{{{μ ^2}}}{2}} \right)}} \times 100$$

$$\Rightarrow \frac{{4 + {μ ^2}}}{{4 + 2{μ ^2}}} \times 100$$

With μ = 0.50, the amount of power saving will be:

$$=\frac{{4 + {{\left( {0.5} \right)}^2}}}{{4 + 2{{\left( {0.5} \right)}^2}}} \times 100$$

$$= \frac{{4.25}}{{4.5}} = 94.44\%$$


text:
help123please. At a local school, 50% of the students take an advanced class, while 10% of the students participate in sports. What is the probability that a student selected at random takes an advanced class and participates in sports? one year ago one year ago

@Kitt020912

Kitt?

3. Kitt020912

Just a sec

Okay:)

5. Kitt020912

$50 percent \rightarrow \frac{ 50 }{ 100 }\rightarrow \frac{ 1 }{ 2 }$ $10 percent \rightarrow \frac{ 10 }{ 100 }\rightarrow \frac{ 1 }{ 10}$ $\frac{ 1}{ 2 }\times \frac{ 1}{ 10}=\frac{ 1 }{ 20 }$

TNX U!:0

format: plain


text:
# Why was the Vulcan bomber used for the Falklands raid?

There is a lot of information about this complex operation. But can anybody explain why they chose to use an aircraft? They could easily shoot cruise missiles from a ship or ballistic missiles from a nuclear submarine. The easiest and quickest option would be just to shoot an ICBM directly from the UK using a conventional warhead. Just put the coordinates in and task done. No risk to anyone! I think the UK had all the needed technology by that time.

• Can you provide a reference for either cruise missiles or ICBMs that the UK would have had in 1982? – fooot Oct 30 '19 at 16:19
• I think they had UGM-27 Polaris and they were cooperating with the USA. en.wikipedia.org/wiki/Polaris_(UK_nuclear_programme) – Andrius Oct 30 '19 at 16:27
• – Reinstate Monica - M. Schröder Oct 31 '19 at 6:24
• IMHO this question belongs to history.sx. – Reinstate Monica - M. Schröder Oct 31 '19 at 18:29
• @ReinstateMonica-M.Schröder there does not seem to be a consensus on considering this question as off-topic here, so there is not a case for migration. – Federico Nov 5 '19 at 7:21

Because all of Britain's adversaries were either nearby (Warsaw Pact) or too far to economically fight (China). Since Britain's weapons only needed to reach the Caucasus, they simply never developed ultra-long-range assets like the Tu-95 Bear or B-52 Stratofortress. Unfortunately no-one was willing to provide any of those under Lend-Lease.

Honestly, even if the British had appropriate cruise missiles (they did not), they would have no reason to own ones with the range to hit the Falklands from Ascension. Nor would they have any reason to need ICBMs with the range to hit Falklands from the UK (they wouldn't have ICBMs in Ascension, who would they nuke? The Congo? Guyana?) Again the enemy is in Europe, so everything is sized and positioned to go just that far.

Your question takes for granted the pre-existence of weapons systems like the "down a chimney" Tomahawk. Honestly, the British inability to do anything but have their SSN crews shake their fists at the islands, was a major impetus in developing those new families of weapons. Every major force watched with keen interest and thought "Gosh, what if we had to deal with one of these?"

However, they certainly did have relevant weapons: Aircraft carriers. This type of mission is the reason carriers exist. They could project power from the Spratleys to, indeed, the Falklands.

Further, there'd be little point to using cruise missiles or ICBMs before the main force was in position to make good on the advantage. And once the main force was in place, they could strike from there, and did not need long-range weapons.

• Obviously, Britain did project their main force with a carrier group but at the same time did conduct the Vulcan strikes (operation Black Buck we are talking about) in advance of the main force. So this somewhat contradicts your last paragraph, doesn't it? At least i don't get the point as the same argument could be used for not needing the Vulcan strikes. – Scrontch Oct 31 '19 at 8:33
• @MichaelMacAskill That's what i'm saying! There were good tactical reasons to launch a long-range raid against the airfield before the main force arrived. But this means that employing long range cruise missiles would have made sense just as well, if they had been available. Harper seems to doubt that in his last paragraph. – Scrontch Oct 31 '19 at 9:15
• Britain did not operate cruise missiles in 1982, the closest thing they had was antiship missiles with a range of ~100 km. Blue Steel was out of service by then, and was designed for a nuclear warhead. – Hobbes Oct 31 '19 at 10:24
• @Hobbes I thought we settled that in earlier discussion. I didn't say they did, I was saying, if they even had such, it would have been irrelevant since they never would have had a reason to field a cruise missile with such range. Edited. – Harper - Reinstate Monica Oct 31 '19 at 13:51
• And of course they couldn't use ICBMs they didn't have... And their SLBMs were all nuclear tipped and firing one from anywhere would instantly have caused a Soviet counterstrike to the UK as they were assumed to all be pointed at the USSR. – jwenting Nov 1 '19 at 10:33

This is borderline as an aviation question but I will answer it anyway.

They didn't use those weapons because they did not have them at the time:

Conventional cruise missiles did exist but most were nuclear, and the UK didn't possess any conventional ones.

ICBMs with conventional warheads did not and probably still do not exist because they are not a good idea:

• Their capacity is low: A sub launched ICBM has somewhere around 2.5 to 3 metric tons' throw weight, much of that would be taken up by warhead guidance, thermal protection and other necessities so your actual warhead would be maybe 1000kg, or 2200lb. That's not that big a conventional bomb, and it could only launch one. A fighter bomber could drop 2 of those. The Vulcan bombers on the raid carried 21 1000 pound bombs.
• They aren't accurate enough: a nuclear weapon can be a bit off and still destroy its target utterly, a conventional weapon needs a great deal of precision. The Polaris missile had an accuracy of 3000ft (900m). That's okay for a nuke, it' still ruin someone's day, but completely inadequate for a 2000lb bomb. More modern ICMBs have more like a 100 meter accuracy, which is a lot closer but still not good enough for a conventional bomb
• They are expensive: that's a lot of cash for a 2000lb bomb that probably will miss
• Launching one could start WW3: If you launch an ICBM someone is going to see it and if they think it might be directed at them a retaliatory strike could be the answer. The world has come perilously close to this more than once, it simply isn't worth the risk!
• The V2 was very inaccurate @Andrius, best accuracy they got was to within 2km of target, average was around 12km. That's good enough to hit a city and cause damage, not a precision weapon by any means. – GdD Oct 30 '19 at 21:02
• @Andrius: Also the V2 was travelling a much shorter distance, and was intended as a terror weapon rather than accurately aimed at a target. Not very useful when you're trying to target a smallish number of troops & equipment on an island where sheep outnumber humans by more than 100:1. – jamesqf Oct 31 '19 at 1:40
• It's important to explicitly note that the point of the Black Buck raids (other than to give the RAF something to do) was to disable the Port Stanley airstrip. Black Buck Two missed its target by about 400–500 m, which meant that it didn't hit the runway at all. An ICBM with a 900-m accuracy would probably do even worse. – Michael Seifert Oct 31 '19 at 13:55
• I feel there's one other factor - resolve / morale. Launching an ICBM demonstrates very little resolve; it's kinda just pushing a button and spending a ton. Launching an aircraft raid with so many bombers and refuellers on an area considered out of range shows that not only that every resource will be thrown at them, but that everywhere they thought was safe, isn't. The best sort of fighting is the one where the enemy surrenders - and showing that there was no safe place to hide is always a factor to this, – UKMonkey Oct 31 '19 at 15:18
• Launching one could start WW3 - Yeah, exactly. Imagine the UK explaining themselves for the 30 minutes that thing was in the air. "No, really, guys, it's just a little iron bomb - no nukesey-s, promise!" – J... Oct 31 '19 at 15:20

The UK needed a surgical strike to neutralize the Port Stanley airport in the Falklands so that Argentine airplanes based there couldn't attack the coming UK convoy or the impending UK ground attack.

An attack by carrier airplanes wouldn't work because the carriers, and the accompanying task force, would also be in range of the Argentine planes based in Port Stanley.

Using nukes against the airport at Port Stanley would have destroyed Port Stanley and all the UK citizens there.

This hasn't been explicitly said, so: The UK didn't have cruise missiles or ICBMs with conventional warheads at the time.

The Trident II D5, the UK's only ever ICBM, entered service in 1994: BBC.

As for cruise missiles, the BGM-109 Tomahawk has been introduced in 1983 (US) and 1998 (UK): Royal Navy.

• The UK had Polaris as well, before Trident. Same story though, no conventional capability. – jwenting Nov 1 '19 at 10:37

Someone mentioned the harrier wasn't able to carry a bomb heavy enough to crater the runway. The Vulcan's dropped 21x1000lb bombs on the Falklands. The Harriers in the Falklands dropped 1000lb paveways (Laser guided). They could carry 2 normally perhaps even up to 4. So they could and did drop the same size of bomb, probably more accurately. Though there was radar controlled guns and SAM that would have been made it very hazadous for low flying aircraft. Though the harriers did raid the airport on occasion.

Some of have suggested there was inter service political rivalry. The Vulcan raid was a another means for the RAF to contribute to the war. Though the Harrier GR3 pilots were RAF.

It was probably a combination of a lot of these factors.

• The Harrier were not within range until sometime later, as the aircraft carrier needed to sail from the UK. – Ian Ringrose Oct 31 '19 at 21:55
• As Ian suggests, by the time of the initial Black Buck operations, the fleet was not within range of the Falklands which would have allowed them to carry more than a single 500lb bomb plus fuel, and the runway needed to be closed so that the Argentinians couldn't base fast jets there to use against the fleet. It wasn't until later that the GR3s came within range that allowed them to use the larger bombs, but the fleet would have been well within loiter range of Argentinian fast jets from Stanley at that point, which meant extreme risk. – Moo Nov 1 '19 at 1:21
• Note that Black Buck switched to anti-radar missions from BB4 (with one final bombing mission later on, mainly for weight of attack against fixed Argentinian positions - something that would have required a mass GR3 attack and they were already overworked). – Moo Nov 1 '19 at 1:23
• The runway was never closed. It operated throughout the war. – SeaCatS Nov 1 '19 at 22:57
• @SeaCatS it was closed to fast jets for the majority of the war (initially because of the damage, and later on because of the threat of attack), and remained open for use by Pucaras and Hercs. The raids did their jobs. Whether operating fast jets from the airfield was dubious or not, the British government and military didn't want to take chances there. – Moo Nov 4 '19 at 3:20

As noted in a comment, the UK did have access to the UGM-27 Polaris submarine launched nuclear missile.

Launching a missile from a sub ranged a few hundred miles (or even a few thousand miles) off-shore would have been significantly less risky to UK military personnel and equipment. However...

Launching nuclear warheads against a target that you intend to occupy, as opposed to completely annihilate and make uninhabitable for a century or two (or three), is somewhat counter-productive. It also tends to, um, raise eyebrows in the international community.

Since Hiroshima and Nagasaki, no nuclear weapons have been used against actual foreign targets or people. Doing so would have been absolute political suicide for Thatcher and company, and would have most likely brought extreme backlash and sanctions against the UK as a whole.

Oh, and don't forget the numerous UK citizens who were actually living in the Falklands would have just been killed by their own government.

• The question isn't asking about nuclear weapons use @FreeMan, but conventional warheads. – GdD Oct 30 '19 at 16:48
• In point of fact, nuclear weapons would not have made the target uninhabitable for anywhere near a century. Both Hiroshima and Nagasaki are thriving cities today. – jamesqf Oct 30 '19 at 16:51
• As others have noted, ICMBs were designed for delivering nuclear warheads, not conventional. Delivering conventional warheads would be inefficient and reasonably ineffective. Using the ICBM, as queried by the OP, would have most likely delivered a nuclear warhead with the impacts I've noted. Also, sure, the Falklands may not have been uninhabitable, @jamesqf, but a little hyperbole helps drive the point home that this would have been a bad idea. – FreeMan Oct 30 '19 at 17:00
• @GdD OP asked about ICBMs which are pretty much all nuclear (as noted in your answer). This answer explains why a nuclear and therefore ICBM options wasn't viable. – Notts90 supports Monica Oct 31 '19 at 11:10
• @Notts90 The question asked about "shoot[ing] an ICBM directly from the UK using a conventional warhead." so this is an answer to a question that was not asked and to which the questioner probably already knows the answer. – sdenham Nov 11 '19 at 15:48

### Because they could (just barely)

There is universal consensus that Black Buck served no military purpose. It did not impede Argentinian military efforts in any significant way.

Its purpose was not to be useful though. It was primarily to make troops there feel that the UK was supporting them. It was a morale-boosting exercise, nothing more (or less).

It did also have a second purpose too, which was to serve notice on the Argentinians that mainland Argentina was vulnerable to nuclear attack by Vulcan bomber.

Which renders the question moot. Whether or not the UK had any alternative abilities, it wouldn't have mattered because bombing Argentinian positions effectively was never the real goal.


text:
# Decoding XBee Series 1 API Packet

I'm having issues trying to decode a XBee API packet. I start decoding it, but I'm not sure what my actual analog data should be. Several of them look like:

7E 00 12 83 56 78 43 00 05 02 00 00 00 03 FF 03 FF 00 00 00 00 60
7E 00 12 83 56 78 43 00 05 02 00 03 E8 03 FF 00 2A 00 00 01 C8 84
7E 00 12 83 56 78 43 00 05 02 00 03 FF 02 DE 00 0D 00 00 03 FF 73
7E 00 12 83 56 78 42 00 05 02 00 03 FF 00 00 00 00 03 DB 03 FF 83

So far I have:

7E - start
00 - length byte 1
12 - length byte 2
83 - API identifier
56 - source address byte 1
78 - source address byte 2
43 - RSSI value bytes
00 - option byte
05 - sample quantity byte
02 00 - channel indicator 0000 0010 0000 0000  (A0 is active) (IO header) (I'm not sure if this is right)
last byte is chechsum

I'm using the XBee series 1 using XB24 firmware. I have a Lilypad temperature sensor based on the MCP9700.

The documentation for the XBee module is: http://ftp1.digi.com/support/documentation/90000982_G.pdf

Every time I try to get the ADC data I get a huge number like 51228675.

The doc also says if any of the DIO lines are the first two bytes are the DIO sample. Why do I get "03 FF" or "E8 03" and sometimes "00 00" if I don't have any of the DIO lines active?

Schematic: Lilypad Temperature Sensor (pin S) --> Xbee (pin AD0)

Any help is greatly appreciated trying to find the sensor output.

## 3 Answers

You are doing something very wrong if you get a large number like 51228675 - the datasheet you linked to says that the ADC output is a 10 bit number right-justified inside of two byte (16 bits). That means that the maximum value should be 0000 0011 1111 1111b which is equivalent to 1,023 decimal. So if you get something that large you're including more bits than you should.

Which bytes do you think are the ADC data in your examples above?

• I do have a second XBee and its connected to a Arduino UNO using this shield sparkfun.com/products/9976. The code just sees if there is serial data available and if there is it prints it in hex. I don't have any code that gave me 51228675, I got that after converting what I though was the data. For example using the last packet, assuming the "03" and "FF" are DIO info and ignored, my data would be: '00 00 00 00 03 DB 03 FF' Which is 64685055 in decimal, but it cant be greater than 1023 so I'm lost where my analog data is. Thanks for the help! – user1247595 Apr 3 '12 at 20:48
• @user1247595 - You've pasted a 64-bit number in hex, AngryEE has given you your number in binary. You're looking at 4 separate values, one of which is (hex) 0x03DB = (binary) 0b0000 0011 1101 1011 = (decimal) 987. – Kevin Vermeer May 3 '12 at 21:29

The format for that frame is on page 13 of the XBee doc. The DIO lines are never active, therefore the DIO samples are skipped and the next two bytes are immediately the analog samples. The A0 readings are:

• 00 00 = 0
• 03 E8 = 0x3E8 = 1000
• 03 FF = 0x3FF = 1023
• 03 FF = 0x3FF = 1023

You should never get anything higher than 1023 for the ADC reading, because it's only a 10-bit number.

How are you receiving the frames? I presume you have a second XBee that's connected to something and it's spitting out the frame data. Can you post the code that's giving you 51228675?

• I do have a second XBee and its connected to a Arduino UNO using this shield sparkfun.com/products/9976. The code just sees if there is serial data avaiable and if there is it prints it in hex. I dont have any code that gave me 51228675, I got that after converting what I though was the data. For example using the last packet, assuming the "03" and "FF" are DIO info and ignored, my data would be: 00 00 00 00 03 DB 03 FF – user1247595 Apr 3 '12 at 20:35
• Which is 64685055 in decimal, but it cant be greater than 1023 so I'm lost where my analog data is. Thanks for the help! – user1247595 Apr 3 '12 at 20:54

Maybe using a library is the best solution. For Arduino there's

http://code.google.com/p/xbee-arduino/

and for Java:

http://code.google.com/p/xbee-api/

I've used both and they're good. Only a catch though, if you intend to use the arduino library, do not forget to set API mode=2 (AT command AP, value 2), otherwise you'll wonder why nothing is being sent. (AT AP=2 is the API dialect where certain characters are escaped. The library uses that dialect. The Java library takes care of initializing things properly, but the Arduino library leaves that to the user)

• Hey! I tried using the arduino library and unfortunately I get no output. I used to Series1_IoSamples sketch and it uploaded fine, and I have ATAP=2 for both XBee modules. I set it through a terminal. Does the Enable API and "Use escape characters" have to be checked in X-CTU ? Every time I check them, the setting doesn't seem to stay, even after I write the settings. And one more thing, do you know what pins should be set for ssRX and ssTX when using this shield sparkfun.com/products/9976 I appreciate all the help !! – user1247595 Apr 3 '12 at 20:48
• In my case ATAP=2 had to be sent from the Arduino every time at the start of the conversation. From the Sparkfun page seems like ssRx/Tx are on digital pins 2 and 3. Can you get the xbee connected to a computer so you can debug using the java api? In my experience, juggling with ports, especially with hardware and software serial at the same time, is prone to timing errors. – Erion Apr 5 '12 at 17:13


text:
# The Unapologetic Mathematician

## Modules

The analogue in ring theory for the idea of a group action is that of a module. Again we want every element of the ring to behave like a function on a set and for multiplication to correspond to composition of functions, but now we have the addition floating around and we’d like to include it in the structure as well. We’ll handle this by letting the ring act on an abelian group.

So let’s take a ring $R$ and an abelian group $M$. We say that $M$ has the structure of a left $R$-module if each element $r\in R$ acts as a linear function from $M$ to itself. We write $r\cdot m$ for the effect of this function on an element $m\in M$. Linearity here means that $r\cdot(m_1+m_2)=r\cdot m_1+r\cdot m_2$. We also require that the ring structure play its part

• $(r_1+r_2)\cdot m=r_1\cdot m+r_2\cdot m$
• $(r_1r_2)\cdot m=r_1\cdot(r_2\cdot m)$
• $1\cdot m=m$ if the ring has an identity element $1$

We can say all this another way. Since this action of $R$ on $M$ is linear in both the ring and the abelian group we get a linear function from the tensor product $\alpha:R\otimes M\rightarrow M$ just like we had one for the multiplication of the ring: $\mu:R\otimes R\rightarrow R$. Not every such function will work, though. We also need that the following diagram commutes:

Around the top of the diagram we use the module action twice, while around the bottom we first multiply in the ring and then use the action once. If the ring has an identity we also require that the following diagram commute

where on the top we use the unique linea function sending the integer $1$ to the identity in $R$, and the diagonal is the canonical isomorphism from $\mathbb{Z}\otimes M$ to $M$.

And there’s another way to say it. Remember that every abelian group $M$ comes equipped with the endomorphism ring ${\rm End}(M)$. An $R$-module structure on $M$ is a ring homomorphism $R\rightarrow{\rm End}(M)$.

All three ways of defining a module — from the raw axioms, as a linear function $R\otimes M\rightarrow M$, or as a homomorphism $R\rightarrow{\rm End}(M)$ — are useful in various situations, and it’s important to be able to slide back and forth between the different pictures.

Of course, the fact that I said left $R$-module above should immediately lead you to think about right $R$-modules. These are the same, except that the module action is written $m\cdot r$ and satisfies $(m\cdot r_1)\cdot r_2=m\cdot(r_1r_2)$ — the order in which the factors are applied is reversed. Over a commutative ring we often ignore this distinction, since we can always switch the order of any product.

Every ring $R$ immediately has the structure of a left and a right $R$-module, using multiplication as the action. This is most clearly seen from the tensor-product definition, where the commuting square just expresses the associativity of ring multiplication. On the other hand, every abelian group $M$ immediately has the structure of an ${\rm End}(M)$-module. This is trivial in the homomorphism picture: just pick the identity homomorphism.

Somewhat more importantly, every abelian group is naturally a $\mathbb{Z}$-module. We define $n\cdot m=m+...+m$ — adding up $n$ copies of the group element $m$. Everything we say for modules in general will apply to abelian groups, and in fact much of what we’ve already said about abelian groups will extend to other modules.

At this point I want to make a point about language. The terms “abelian group” and “$\mathbb{Z}$-module” are interchangeable, but there are cases in which I feel the context clearly indicates using one or the other. Later we’ll come to (and many reader have already seen) “homology groups”, which are more naturally modules than groups. Similarly, the one-dimensional circle, torus, and real projective space are all semantically very different, even though they happen to be equivalent in many situations. I think that this imprecision can lead to confusion on the part of a student, so I’ll try my best to use the most apropriate of equivalent terms.

April 21, 2007 Posted by | Ring theory | 10 Comments


text:
LiDeR: Lightweight Dense Residual Network for Video Super-Resolution on Mobile Devices

Published:

Published In: IEEE 14th Image, Video, and Multidimensional Signal Processing Workshop (IVMSP 2022), June 26-29, 2022, Nafplio, Greece
Conference Website: https://2022.ivmsp.org/

Authors: Ekrem Çetinkaya, Minh Nguyen, and Christian Timmerer (Christian Doppler Laboratory ATHENA, Alpen-Adria-Universität Klagenfurt)

Abstract: Video is now an essential part of the Internet. The increasing popularity of video streaming on mobile devices and the improvement in mobile displays brought together challenges to meet user expectations. Advancements in deep neural networks have seen successful applications on several computer vision tasks such as super-resolution (SR). Although DNN-based SR methods significantly improve over traditional methods, their computational complexity makes them challenging to apply on devices with limited power, such as smartphones. However, with the improvement in mobile hardware, especially GPUs, it is now possible to use DNN based solutions, though existing DNN based SR solutions are still too complex. This paper proposes LiDeR, a lightweight video SR network specifically tailored toward mobile devices. Experimental results show that LiDeR can achieve competitive SR performance with state-of-the-art networks while improving the execution speed significantly, i.e., 267 % for X4 upscaling and 353 % for X2 upscaling compared to ESPCN.

Keywords: Super-resolution, Mobile machine learning, Video super-resolution.

Citation:

@INPROCEEDINGS{LiDeR,
author={\c{C}etinkaya, Ekrem and Nguyen, Minh and Timmerer, Christian},
booktitle={2022 IEEE 14th Image, Video, and Multidimensional Signal Processing Workshop (IVMSP)},
title=,
year={2022},
volume={},
number={},
pages={1-5},
doi={10.1109/IVMSP54334.2022.9816346}
}


text:
# Mass pulling another, rotating, mass

## Homework Statement

[/B]
The cylinder rolls without friction. what's m's acceleration, M's angular acceleration and the tension.

## Homework Equations

Shteiner's theorem: $I_c=I_{c.o.m.}+Mr^2$
Torque and angular acceleration: $M=I\alpha$
Moment of inertia of a solid cylinder: $I_{cen}=\frac{mr^2}{2}$

## The Attempt at a Solution

I denote the center variables with c
Kinematics (or geometry? which discipline is suitable for this relation):
$$x_c=\omega r~~\rightarrow~~\dot x_c=\alpha r~~\rightarrow~~\alpha=\frac{\dot x_c}{r}$$
$$\left\{ \begin{array}{l} mg-T=m\dot x_A~~\rightarrow~~T=m(g-\dot x_A)=m(g-2\dot x_c) \\ 2r\cdot T=I_B\frac{\dot x_c}{r} \end{array} \right.$$
$$\rightarrow~\dot x_c=\frac{2r^2mg}{I_B+4mr^2}=\frac{2r^2mg}{I_c+Mr^2+4mr^2}=\frac{2r^2mg}{\frac{Mr^2}{2}+(M+4m)r^2}=\frac{4mg}{3M+8m}$$

Related Introductory Physics Homework Help News on Phys.org
haruspex


text:
# When to Buy a "New" Car if Driving a High Mileage Old One?

1. Jul 8, 2017

### kyphysics

My 2004 Honda Civic has 208,000 miles on it.

No major repairs on it are needed at the moment. But just curious if there is some formula for determining when it's best to buy a "new" (really I mean "newer," since I'm open to used cars too) car when your current old one has gotten up in age and/or mileage?

2. Jul 8, 2017

### DaveC426913

The formula is:
n = DxM / O
where
D= How badly I want a different car
M = how much money I have
O = How well my old car is doing

If n is large, buy another car.

BTW, Hondas - especially Civics - last, like cockroaches after a nuclear war. And they retain their value.

3. Jul 16, 2017

### jim hardy

Only 208 K ?
A friend has 450,000 miles on his old Toyota station wagon.
I put 280,000 on a Dodge Caravan and gave it to a neighbor. He put on another 40,000 on before wrecking it.

My advice -
build a carport to keep the dew from starting rust and the sun from wrecking the plastic
attend to lubrication, oil changes(including automatic transmission every few years)
fix things as they break or wear out
keep it until enough of the 'gadgets' don't work anymore that it's just too much frustration.

The time to replace yours is when a neighbor decides to part with a "Garage Queen" low mileage car that you know is a good one .

4. Jul 16, 2017

### OCR

... I'll buy that.[COLOR=#black]..[/COLOR]

5. Jul 18, 2017

### kyphysics

Interesting.

6. Jul 18, 2017

### kyphysics

Not sure where I had heard it in the past, but I seemed to read/hear that 200,000 to 250,000 is sort of the "breaking point" for many cars where things really start to break down and the cost of repairs is often worth more than the car.

Although, I guess if the "outer shell" of a car is in good condition, then it can in theory last "forever," no? All one would have to do is replace the engine stuff.

I think I also read that most of the high costs of repair post-200K-250K miles is due to high labor costs, so if you're a mechanic or someone who knows his/her way aorund cars and can do the labor yourself, then it's just the cost of parts, which isn't that bad. I, too, read cars can get up to 300,000 (and maybe more) in miles and be still fine.

I looked my car up and if assuming "good condition" it can take in $1,200 trade-in value and$2-3,000 in owner sale value. Not bad. I thought it was closer to $1,000 owner sale value, since I figured after 200K miles that it's likely to fall apart soon and only be good for junk yard parts salvage value (usually around$1,000 for a car like mine I think).

Only gripe I have is that my car smells bad. Lots of food stains soaked into the carpet over years of eating fast food in there. I'm a slob who doesn't vacuum it either, nor do much of any other interior cleaning. I stopped caring around the 11 year mark, lol. I WOULD, however, take good care of a new car and never eat in there again. Just had some bad habits back in the day and got lazy with cleaning over time.

7. Jul 18, 2017

### jim hardy

I've seen two Escorts just like mine in the junkyard recently. Both had broken timing belts. That's a $150 DIY job probably$600 outsourced.
Since they took the lead out of gasoline engines seem to go forever.

I think the tipping point has to be when monthly cost of repairs (plus aggravation) exceeds the depreciation (and interest) on a newer one.

8. Jul 19, 2017

### Staff: Mentor

Quite a few cars aren't engineered to last 200,000+ miles. The ones that last that long have to be maintained well, with regular oil and oil filter changes, and keeping the other fluids fresh. There's a lot more than "engine stuff." Besides the engine, there's a transmission and differential or transaxle, brakes, suspension, exhaust system, charging system, and electrical system, including numerous computers in modern cars to control the fuel injection and other components. All of these parts can wear out or stop working.

Repair parts aren't cheap. Sure, you can save the cost of labor if you can install them yourself, but only a small minority of people have the skill, tools, and inclination to do anything more complicated than changing wiper blades. A couple of years ago the voltage regulator on my '07 Ford Focus went out. In the olden days, the voltage regulator was a separate component, but these days, it's integrated with the alternator, so that meant I need to get a new alternator. An alternator is pretty simple to install, but because of the placement on my car, I would have needed to take a lot of other stuff off just to get at the thing, so I opted to take it into a nearby Ford dealer. The alternator was about $350 and the labor was about the same. There's also the issue of being able to diagnose a problem and know which part has failed. It's easy to throw parts at a problem, and hope that one of them fixes the problem, but that's a very expensive way to solve the problem. When cars had carburetors, it was a simple matter to rebuild a carb, but with fuel injection, and all of the related electronics that go with it, this is way beyond the competency of the average car owner. Maybe some cars can theoretically last 300,000 miles, if they are scrupulously maintained, but for the vast majority of cars, I doubt that they last half this long. 9. Jul 19, 2017 ### Mark44 ### Staff: Mentor I don't think the absence of lead has anything to do with it. Probably more significant, I believe, are the closer tolerance of parts, fuel injection, which meters the fuel better (so excess fuel doesn't strip oil from the cylinder walls, and better engine oils, particularly the synthetic oils.There might be some other factors I haven't considered. 10. Jul 19, 2017 ### OCR ... The caveat... possible bent valve stems and piston dings... ? 11. Jul 19, 2017 ### kyphysics Our family gets about a 15% discount on car-related repairs, due to a close friend of the family being a mechanic. He does most of our work for us at a cheaper labor rate to make some side money for himself. re: depreciation of a new car - That's why, for me, I'm sold on buying a used car. I'm looking into these so-called brokers, who buy them off of auction. Supposedly, that's where you can make the most bang for your buck with really only one risk (you have to trust the broker, b/c you don't get to see the car first). We have a friend of the family who's a broker, coincidentally. ....choices, choices....new car using trustworthy broker friend or old car using trustworthy mechanic friend. I honestly feel pretty fortunate my dad knows all these guys. If there's not a "car" thread already at PF, I hereby recommend one be made. It's a topic I don't mind spending time learning about (for fun and practical purposes like this). 12. Jul 19, 2017 ### kyphysics Yeah, I think my conception of a car was just that it's: a.) an outer shell (which is no joke, as even a bumper can cost$1,000 to replace!)
b.) mechanical inside

If you keep the outer shell well maintained, then it's just about fixing the machinery inside. And that, in turn, is a function:

a.) quality of parts
b.) design
c.) user/owner/mechanic maintenance and care for the vehicle

I think what my uncle was saying to me was that if your outer shell is in good condition, then you can in theory just replace all the machinery inside (with new parts) and that cost would be cheaper than buying a brand new or used car (which also has new parts, a new shell, and just more advanced technology).

I think he was saying that even if it costs thousands to get new stuff "inside" your old car, that's probably still much cheaper (by the thousands) than getting a new car. Or, could he also be missing something?

13. Jul 19, 2017

### Vanadium 50

Staff Emeritus
It depends on how many thousands and how much stuff. And how many things you need to replace before you get to the root of the problem.

It's not the belt replacement that costs money. It's fixing what is left of the engine when one goes.

14. Jul 19, 2017

### jim hardy

You must not have been changing your own oil before mid 1980's... It no longer comes out with that gray metal powder in it.

That's an issue. I won't own anything with an "Interference engine" where loss of a timing belt wrecks them.

Last edited: Jul 19, 2017
15. Jul 19, 2017

### Vanadium 50

Staff Emeritus
That excludes you from a large number of engines - some of which get great fuel economy for the horsepower. Personally, my strategy is to change the timing belt/chain when recommended instead.

16. Jul 19, 2017

### Staff: Mentor

I've been changing my own oil since the '60s. The presence of metal particles (or lack of) is probably more a function of the formulation of the oil rather than the presence or absence of lead in the fuel. Removing lead (tetraethyl lead) from gasoline did have an effect on engines of that period, as the lead cushioned the impact of valves on valve seats. Since then, valve seats have been made harder to withstand the pounding. The gray metal powder you were seeing might have been aluminum from pistons or iron from the rings or cylinder walls. A significant amount of wear comes right when the engine is first started, when the cylinder walls aren't well lubricated. Newer oil formulations help alleviate this problem at startup.

17. Jul 19, 2017

### jim hardy

Good Man ! That sure beats getting towed home ......

18. Jul 20, 2017

### kyphysics

Right. Logically, that's true.

I would want to look into the cost of total replacement (not just partial stuff) of the interior, as that would be the upper range and worst case scenario projection and I could use that to compare it with the cost of a new/used car.

There might be some other factors I'm missing like warranties that come with new vehicles, the availability of parts of older cars (both the outer shell and interior machinery), and trade-in/owner sale value of the older car that could decrease the value of an interior remake of my car.

re: the last point - It's one of those things where even if you can get a totally new replacement of parts inside and you have a well-maintained outer shell, a used car buyer may simply shake their head at the age of your car and not trust you if you ever wanted to or needed to sell it. You could be trying around a 15 y/o car with a brand new engine/interior that's better running than an 8 year old car and a non-car person wouldn't believe you.

Edit: Mark44 makes a good point, too, about the wear and tear and durability of the outer shell. I currently don't know much about that, but will look into it. The worst case scenario is that you replace the interior machinery only to have the outer shell fall apart due to age.

19. Jul 20, 2017

### DaveC426913

Yep. Just this spring. Mechanic said 'timing belt blew', so I just left it in his back lot till the wreckers came for it.
I really liked that car.

20. Jul 21, 2017

### jim hardy

On my Dodge Caravan with 3.0 engine replacing the belt was about a four hour job.
On my Ford Escort it was better part of two days because of all the stuff that has to be removed to get access. Engine is really shoe-horned in there.
Both are non-interference so if doesn't hurt if the belt breaks , but since having got stranded once i do them preemptively..

Why do i put up with old cars and the grease and skinned knuckles, i often wonder ?
It's kinda fun fixing things. Must be some sort of psychological satisfaction, not unlike solving crossword puzzles . . .

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robust poisson in r k \\ cannot have 0s. functions have advantages and drawbacks. Example 1. library(robust) glmrob(x ~ 1, family=poisson()) The response tells us the intercept is estimated at $0.7268$. Poisson regression – Poisson regression is often used for modeling count indicate that the data do not fit the model well. We fit the model and store it in the object m1 Click here to report an error on this page or leave a comment, Your Email (must be a valid email for us to receive the report! Poisson regression is estimated via maximum likelihood estimation. regression and a robust regression, if the results are very different, you will To answer this question, we can make use of the final weights created by the IRLS process. with echoing the function call. the predict function. Generalized Linear Models in R, Part 6: Poisson Regression for Count Variables. Leverage is a measure of how far an Unlike any other semi-parametric approaches the RPR model supplies an asymptotically legitimate likelihood function for the regression parameter. • Robust Fitting of Poisson and Logistic GLIM’s • Robust Discriminant Analysis • Robust Parameter Estimates for Asymmetric Distributions Robust Regression for the Linear Model Two robust linear model fitting methods are included: (1) An MM-estimate, and (2) a … The unconditional mean and variance of our outcome variable if the model is specified correctly.In our example, it shows a little The Quasi-Poisson Regression is a generalization of the Poisson regression and is used when modeling an overdispersed count variable. Example 1. One common cause of over-dispersion is excess zeros, which in turn are predictor variable and represents students’ scores on their math final exam, and prog is a categorical predictor variable with However, this assumption is often violated as overdispersion is a common problem. Some of the methods listed are quite reasonable, while others have and single to predict crime. the predictor variables, will be equal (or at least roughly so). the outcome variable is over-dispersed, the confidence intervals for Negative binomial Robust regression in R Eva Cantoni Research Center for Statistics and Geneva School of Economics and Management, University of Geneva, Switzerland ... Poisson) g( i) = xT where E(Y i) = i, Var(Y i) = v( i) and r i = (py i i) ˚v i, the robust estimator is de ned by Xn i=1 h c(r i)w(x i) … We can also test the overall effect of prog by comparing the deviance The estimated b's from the glm match exactly, but the robust standard errors are a bit off. There are several weighting functions the log of zero (which is undefined) and biased estimates. We can look at these observations to see which states cases with a large residuals tend to be down-weighted. problematic to our model. \begin{array}{rl} This page uses the following packages. The number of persons killed by mule or horse kicks in thePrussian army per year. Example 3. With: MASS 7.3-33; foreign 0.8-61; knitr 1.6; boot 1.3-11; ggplot2 1.0.0; dplyr 0.2; nlme 3.1-117. ten observations with the highest absolute residual values. is rlm in the MASS package. will use this criterion to select the values to display. data. regression are likely to be narrower as compared to those from a Poisson regression. more appropriate. Institute for Digital Research and Education. = 1). The Overflow Blog Podcast 289: React, jQuery, Vue: what’s your favorite flavor of vanilla JS? The number of people in line in front of you at the grocery store. robust standard errors. The information on deviance residuals 5. lme4 and languageR compatibility error: "input model is not a mer object” 2. the incident rate for prog = “Vocational” is 1.45 times the incident rate for the The output begins discounted price and whether a special event (e.g., a holiday, a big sporting 4.A.2 Negative Binomial Regression. Zero-inflated regression model – Zero-inflated models attempt to account where the subscripts indicate the matrix at a particular iteration (not rows or columns). score at its overall mean? iterated re-weighted least squares (IRLS). A variant of a Poisson regression called the "robust-error-variance Poisson regression" is an approach adapted for binary data, specially as an alternative to the logistic regression. ), Department of Statistics Consulting Center, Department of Biomathematics Consulting Clinic, "https://stats.idre.ucla.edu/stat/data/crime.dta", Robust regression does not address issues of heterogeneity of variance. Many different measures of pseudo-R-squared exist. great amount of effect on the estimate of regression coefficients. There are several tests including the likelihood ratio test of Robust regression can be used in any situation in which you would use least We use R package sandwich below to obtain the robust standard errors and Preussischen Statistik. The predicted residual deviance is the difference between the deviance of the current number of awards earned by students at a high school in a year, math is a continuous High leverage points can have a These data were collected on 10 corps of observations with small residuals get a weight of 1 and the larger the residual, Click here to report an error on this page or leave a comment, Your Email (must be a valid email for us to receive the report! if you see the version is out of date, run: update.packages(). The table below shows the average numbers of awards by program type We are going to use poverty bit of skeweness since median is not quite zero. For a Poisson distribution the variance has the same value as the mean. On the most likely want to use the results from the robust regression. usually requires a large sample size. Make sure that you can load number of events for level 2 of prog is higher at .62, and the reasonable. In this situation, For our data analysis below, we will use the crime dataset that appears in This usually gives results very similar to the over-dispersed Poisson model. From these plots, we can identify observations 9, 25, and 51 as possibly Robust regression in R Eva Cantoni Research Center for Statistics and Geneva School of Economics and Management, University of Geneva, Switzerland ... Poisson) g( i) = xT where E(Y i) = i, Var(Y i) = v( i) and r i = (py i i) ˚v i, the robust estimator is de ned by Xn i=1 h c(r i)w(x i) … include it in the analysis just to show that it has large Cook’s D and The rlm command in the MASS package command implements several versions of robust of leverage and residual of the observation. In other words, residuals (because the sign of the residual doesn’t matter). Related. student was enrolled (e.g., vocational, general or academic) and the score on their over-dispersion parameter alpha by running the same model using negative This output shows us that the Roughly speaking, it is a form of weighted and cov Cameron and Trivedi (2009) recommended using robust standard errors for the cases have a weight of 1. our linearity assumption holds and/or if there is an issue of We probably should drop DC to begin with since it is not even a state. # Multiple Linear Regression Example fit <- lm(y ~ x1 + x2 + x3, data=mydata) summary(fit) # show results# Other useful functions coefficients(fit) # model coefficients confint(fit, level=0.95) # CIs for model parameters fitted(fit) # predicted values residuals(fit) # residuals anova(fit) # anova table vcov(fit) # covariance matrix for model parameters influence(fit) # regression diagnostics Interpreting how a model works is one of the most basic yet critical aspects of data science. means and variances within each level of prog–the conditional Robust regression is an alternative to least squares regression You observed that the stock price increased rapidly over night. that have a weight close to one, the closer the results of the OLS and robust With: sandwich 2.3-1; boot 1.3-11; knitr 1.6; pscl 1.04.4; vcd 1.3-1; gam 1.09.1; coda 0.16-1; mvtnorm 1.0-0; GGally 0.4.7; plyr 1.8.1; MASS 7.3-33; Hmisc 3.14-4; Formula 1.1-2; survival 2.37-7; psych 1.4.5; reshape2 1.4; msm 1.4; phia 0.1-5; RColorBrewer 1.0-5; effects 3.0-0; colorspace 1.2-4; lattice 0.20-29; pequod 0.0-3; car 2.0-20; ggplot2 1.0.0. parameter to model the over-dispersion. Hence, the more cases in the robust regression of these predicted counts ((frac{.625}{.211} = 2.96), (frac{.306}{.211} = 1.45)) match In my last couple of articles (Part 4, Part 5), I demonstrated a logistic regression model with binomial errors on binary data in R’s glm() function. state id (sid), state name (state), violent crimes per 100,000 independent variable deviates from its mean. All observations not shown above have Description. These data were collected on 10 corps ofthe Prussian army in the late 1800s over the course of 20 years.Example 2. Robust Poisson regression example . Poisson regression is used to model count variables. Cameron, A. C. Advances in Count Data Regression Talk for the The \end{array} parameter estimates from these two different weighting methods differ. The estimated b's from the glm match exactly, but the robust standard errors are a bit off. Large going to first use the Huber weights in this example. A variant of a Poisson regression called the "robust-error-variance Poisson regression" is an approach adapted for binary data, specially as an alternative to the logistic regression. Next, let’s run the same model, but using the bisquare weighting function. We have decided that these data points The Zero-inflated Viewing standard errors and parameter estimates in lme4. M step for. † Values in parentheses, percentage of relative bias of the estimated relative risk calculated as the average of 1,000 estimates minus the true relative risk divided by the true relative risk. In this example, num_awards is the outcome variable and indicates the mean. This can be very They all attempt to provide information similar to that provided by w(e) = In Huber weighting, Our model assumes that these values, conditioned on Computation of robust standard errors of Poisson fixed effects models, following Wooldridge (1999). If you do not have is displayed next. type. We will begin by running an OLS regression and looking at As a data scientist, you need to have an answer to this oft-asked question.For example, let’s say you built a model to predict the stock price of a company. excess zeros. most of our data. researchers are expected to do. Computation of robust standard errors of Poisson fixed effects models, following Wooldridge (1999). in either analysis, whereas single is significant in both analyses. differences suggest that the model parameters are being highly influenced by Here, we suggest the use of robust standard errors and discuss two alternative asymptotically valid covariance matrices. The zero-inﬂated Poisson regression model is a special case of ﬁnite mixture models ... (Poisson state). The Poisson model is much more robust to misspecification, but with wider standard errors. outliers. However, their performance under model misspecification is poorly understood. reweighted least squares regression. It does not cover all aspects of the research process regressions. poisFErobust: Poisson Fixed Effects Robust version 2.0.0 from CRAN rdrr.io Find an R package R language docs Run R in your browser R Notebooks For a discussion of Here's my best guess. Of course, anyone using a statistical method needs to know how it works: when you use generalized linear models with the Poisson family, the standard "link" function is the logarithm. A Modified Poisson Regression Approach to Prospective Studies with Binary Data Guangyong Zou 1,2 1 Robarts Clinical Trials, Robarts Research Institute, London, Ontario, Canada. We can display the observations that have relatively The anova function can be used to conduct an analysis of deviance. Sometimes, we might want to present the regression results as incident rate If the data generating process does not allow for any 0s (such as the presented, and the interpretation of such, please see Regression Models for Make sure that you can load along with the standard errors, z-scores, p-values times the incident rate for the reference group (prog = “General”). approach, including loss of data due to undefined values generated by taking and seems to suggest that program type is a good candidate for In particular, it does not cover data We are It parents (single). them before trying to run the examples on this page. This is defined by the weight function, For Browse other questions tagged r panel poisson robust or ask your own question. An outlier may In practice the Poisson also does not really suffer from overdispersed data, except in extreme cases. I should use, so, quasi-poisson with robust variance model. The output above indicates that the incident rate for prog = “Academic” is 2.96 As you can see, the results from the two analyses are fairly different, Different Each variable has 200 valid observations and their distributions seem quite In other words, it is an observation whose dependent-variable We would like to show you a description here but the site won’t allow us. of times the event could have happened. To Count data often have an exposure variable, which indicates the number Robust regression is done by The outcome variable in a Poisson regression cannot have negative numbers, and the exposure * The relative bias from modified Poisson regression is the same as that from Poisson regression. We can see that the weight given to Mississippi is dramatically lower using In other words, two kinds of zeros are thought to To this end, we make use the function deltamethod the outcome appears to vary by prog. The p-value for the model can be found by comparing the model to a … dispersion. Outlier: In linear regression, an outlier is an observation with the bisquare weighting function than the Huber weighting function and the The Poisson model is much more robust to misspecification, but with wider standard errors. which researchers are expected to do. Let’s begin our discussion on robust regression with some terms in linearregression. Logical Network Diagram Online, 2019 Subaru Impreza Sport Sedan For Sale, Bronze Wing Pigeon Nest, Klipsch T5 Neckband Review, Juniper Berry Seeds, Aratikaya Fry Air Fryer, Vegan Date Bars No Bake, School Lab Technician Cv, " /> k \\ cannot have 0s. functions have advantages and drawbacks. Example 1. library(robust) glmrob(x ~ 1, family=poisson()) The response tells us the intercept is estimated at $0.7268$. Poisson regression – Poisson regression is often used for modeling count indicate that the data do not fit the model well. We fit the model and store it in the object m1 Click here to report an error on this page or leave a comment, Your Email (must be a valid email for us to receive the report! Poisson regression is estimated via maximum likelihood estimation. regression and a robust regression, if the results are very different, you will To answer this question, we can make use of the final weights created by the IRLS process. with echoing the function call. the predict function. Generalized Linear Models in R, Part 6: Poisson Regression for Count Variables. Leverage is a measure of how far an Unlike any other semi-parametric approaches the RPR model supplies an asymptotically legitimate likelihood function for the regression parameter. • Robust Fitting of Poisson and Logistic GLIM’s • Robust Discriminant Analysis • Robust Parameter Estimates for Asymmetric Distributions Robust Regression for the Linear Model Two robust linear model fitting methods are included: (1) An MM-estimate, and (2) a … The unconditional mean and variance of our outcome variable if the model is specified correctly.In our example, it shows a little The Quasi-Poisson Regression is a generalization of the Poisson regression and is used when modeling an overdispersed count variable. Example 1. One common cause of over-dispersion is excess zeros, which in turn are predictor variable and represents students’ scores on their math final exam, and prog is a categorical predictor variable with However, this assumption is often violated as overdispersion is a common problem. Some of the methods listed are quite reasonable, while others have and single to predict crime. the predictor variables, will be equal (or at least roughly so). the outcome variable is over-dispersed, the confidence intervals for Negative binomial Robust regression in R Eva Cantoni Research Center for Statistics and Geneva School of Economics and Management, University of Geneva, Switzerland ... Poisson) g( i) = xT where E(Y i) = i, Var(Y i) = v( i) and r i = (py i i) ˚v i, the robust estimator is de ned by Xn i=1 h c(r i)w(x i) … We can also test the overall effect of prog by comparing the deviance The estimated b's from the glm match exactly, but the robust standard errors are a bit off. There are several weighting functions the log of zero (which is undefined) and biased estimates. We can look at these observations to see which states cases with a large residuals tend to be down-weighted. problematic to our model. \begin{array}{rl} This page uses the following packages. The number of persons killed by mule or horse kicks in thePrussian army per year. Example 3. With: MASS 7.3-33; foreign 0.8-61; knitr 1.6; boot 1.3-11; ggplot2 1.0.0; dplyr 0.2; nlme 3.1-117. ten observations with the highest absolute residual values. is rlm in the MASS package. will use this criterion to select the values to display. data. regression are likely to be narrower as compared to those from a Poisson regression. more appropriate. Institute for Digital Research and Education. = 1). The Overflow Blog Podcast 289: React, jQuery, Vue: what’s your favorite flavor of vanilla JS? The number of people in line in front of you at the grocery store. robust standard errors. The information on deviance residuals 5. lme4 and languageR compatibility error: "input model is not a mer object” 2. the incident rate for prog = “Vocational” is 1.45 times the incident rate for the The output begins discounted price and whether a special event (e.g., a holiday, a big sporting 4.A.2 Negative Binomial Regression. Zero-inflated regression model – Zero-inflated models attempt to account where the subscripts indicate the matrix at a particular iteration (not rows or columns). score at its overall mean? iterated re-weighted least squares (IRLS). A variant of a Poisson regression called the "robust-error-variance Poisson regression" is an approach adapted for binary data, specially as an alternative to the logistic regression. ), Department of Statistics Consulting Center, Department of Biomathematics Consulting Clinic, "https://stats.idre.ucla.edu/stat/data/crime.dta", Robust regression does not address issues of heterogeneity of variance. Many different measures of pseudo-R-squared exist. great amount of effect on the estimate of regression coefficients. There are several tests including the likelihood ratio test of Robust regression can be used in any situation in which you would use least We use R package sandwich below to obtain the robust standard errors and Preussischen Statistik. The predicted residual deviance is the difference between the deviance of the current number of awards earned by students at a high school in a year, math is a continuous High leverage points can have a These data were collected on 10 corps of observations with small residuals get a weight of 1 and the larger the residual, Click here to report an error on this page or leave a comment, Your Email (must be a valid email for us to receive the report! if you see the version is out of date, run: update.packages(). The table below shows the average numbers of awards by program type We are going to use poverty bit of skeweness since median is not quite zero. For a Poisson distribution the variance has the same value as the mean. On the most likely want to use the results from the robust regression. usually requires a large sample size. Make sure that you can load number of events for level 2 of prog is higher at .62, and the reasonable. In this situation, For our data analysis below, we will use the crime dataset that appears in This usually gives results very similar to the over-dispersed Poisson model. From these plots, we can identify observations 9, 25, and 51 as possibly Robust regression in R Eva Cantoni Research Center for Statistics and Geneva School of Economics and Management, University of Geneva, Switzerland ... Poisson) g( i) = xT where E(Y i) = i, Var(Y i) = v( i) and r i = (py i i) ˚v i, the robust estimator is de ned by Xn i=1 h c(r i)w(x i) … include it in the analysis just to show that it has large Cook’s D and The rlm command in the MASS package command implements several versions of robust of leverage and residual of the observation. In other words, residuals (because the sign of the residual doesn’t matter). Related. student was enrolled (e.g., vocational, general or academic) and the score on their over-dispersion parameter alpha by running the same model using negative This output shows us that the Roughly speaking, it is a form of weighted and cov Cameron and Trivedi (2009) recommended using robust standard errors for the cases have a weight of 1. our linearity assumption holds and/or if there is an issue of We probably should drop DC to begin with since it is not even a state. # Multiple Linear Regression Example fit <- lm(y ~ x1 + x2 + x3, data=mydata) summary(fit) # show results# Other useful functions coefficients(fit) # model coefficients confint(fit, level=0.95) # CIs for model parameters fitted(fit) # predicted values residuals(fit) # residuals anova(fit) # anova table vcov(fit) # covariance matrix for model parameters influence(fit) # regression diagnostics Interpreting how a model works is one of the most basic yet critical aspects of data science. means and variances within each level of prog–the conditional Robust regression is an alternative to least squares regression You observed that the stock price increased rapidly over night. that have a weight close to one, the closer the results of the OLS and robust With: sandwich 2.3-1; boot 1.3-11; knitr 1.6; pscl 1.04.4; vcd 1.3-1; gam 1.09.1; coda 0.16-1; mvtnorm 1.0-0; GGally 0.4.7; plyr 1.8.1; MASS 7.3-33; Hmisc 3.14-4; Formula 1.1-2; survival 2.37-7; psych 1.4.5; reshape2 1.4; msm 1.4; phia 0.1-5; RColorBrewer 1.0-5; effects 3.0-0; colorspace 1.2-4; lattice 0.20-29; pequod 0.0-3; car 2.0-20; ggplot2 1.0.0. parameter to model the over-dispersion. Hence, the more cases in the robust regression of these predicted counts ((frac{.625}{.211} = 2.96), (frac{.306}{.211} = 1.45)) match In my last couple of articles (Part 4, Part 5), I demonstrated a logistic regression model with binomial errors on binary data in R’s glm() function. state id (sid), state name (state), violent crimes per 100,000 independent variable deviates from its mean. All observations not shown above have Description. These data were collected on 10 corps ofthe Prussian army in the late 1800s over the course of 20 years.Example 2. Robust Poisson regression example . Poisson regression is used to model count variables. Cameron, A. C. Advances in Count Data Regression Talk for the The \end{array} parameter estimates from these two different weighting methods differ. The estimated b's from the glm match exactly, but the robust standard errors are a bit off. Large going to first use the Huber weights in this example. A variant of a Poisson regression called the "robust-error-variance Poisson regression" is an approach adapted for binary data, specially as an alternative to the logistic regression. Next, let’s run the same model, but using the bisquare weighting function. We have decided that these data points The Zero-inflated Viewing standard errors and parameter estimates in lme4. M step for. † Values in parentheses, percentage of relative bias of the estimated relative risk calculated as the average of 1,000 estimates minus the true relative risk divided by the true relative risk. In this example, num_awards is the outcome variable and indicates the mean. This can be very They all attempt to provide information similar to that provided by w(e) = In Huber weighting, Our model assumes that these values, conditioned on Computation of robust standard errors of Poisson fixed effects models, following Wooldridge (1999). If you do not have is displayed next. type. We will begin by running an OLS regression and looking at As a data scientist, you need to have an answer to this oft-asked question.For example, let’s say you built a model to predict the stock price of a company. excess zeros. most of our data. researchers are expected to do. Computation of robust standard errors of Poisson fixed effects models, following Wooldridge (1999). in either analysis, whereas single is significant in both analyses. differences suggest that the model parameters are being highly influenced by Here, we suggest the use of robust standard errors and discuss two alternative asymptotically valid covariance matrices. The zero-inﬂated Poisson regression model is a special case of ﬁnite mixture models ... (Poisson state). The Poisson model is much more robust to misspecification, but with wider standard errors. outliers. However, their performance under model misspecification is poorly understood. reweighted least squares regression. It does not cover all aspects of the research process regressions. poisFErobust: Poisson Fixed Effects Robust version 2.0.0 from CRAN rdrr.io Find an R package R language docs Run R in your browser R Notebooks For a discussion of Here's my best guess. Of course, anyone using a statistical method needs to know how it works: when you use generalized linear models with the Poisson family, the standard "link" function is the logarithm. A Modified Poisson Regression Approach to Prospective Studies with Binary Data Guangyong Zou 1,2 1 Robarts Clinical Trials, Robarts Research Institute, London, Ontario, Canada. We can display the observations that have relatively The anova function can be used to conduct an analysis of deviance. Sometimes, we might want to present the regression results as incident rate If the data generating process does not allow for any 0s (such as the presented, and the interpretation of such, please see Regression Models for Make sure that you can load along with the standard errors, z-scores, p-values times the incident rate for the reference group (prog = “General”). approach, including loss of data due to undefined values generated by taking and seems to suggest that program type is a good candidate for In particular, it does not cover data We are It parents (single). them before trying to run the examples on this page. This is defined by the weight function, For Browse other questions tagged r panel poisson robust or ask your own question. An outlier may In practice the Poisson also does not really suffer from overdispersed data, except in extreme cases. I should use, so, quasi-poisson with robust variance model. The output above indicates that the incident rate for prog = “Academic” is 2.96 As you can see, the results from the two analyses are fairly different, Different Each variable has 200 valid observations and their distributions seem quite In other words, it is an observation whose dependent-variable We would like to show you a description here but the site won’t allow us. of times the event could have happened. To Count data often have an exposure variable, which indicates the number Robust regression is done by The outcome variable in a Poisson regression cannot have negative numbers, and the exposure * The relative bias from modified Poisson regression is the same as that from Poisson regression. We can see that the weight given to Mississippi is dramatically lower using In other words, two kinds of zeros are thought to To this end, we make use the function deltamethod the outcome appears to vary by prog. The p-value for the model can be found by comparing the model to a … dispersion. Outlier: In linear regression, an outlier is an observation with the bisquare weighting function than the Huber weighting function and the The Poisson model is much more robust to misspecification, but with wider standard errors. which researchers are expected to do. Let’s begin our discussion on robust regression with some terms in linearregression. Logical Network Diagram Online, 2019 Subaru Impreza Sport Sedan For Sale, Bronze Wing Pigeon Nest, Klipsch T5 Neckband Review, Juniper Berry Seeds, Aratikaya Fry Air Fryer, Vegan Date Bars No Bake, School Lab Technician Cv, " />

# robust poisson in r

If the conditional distribution of model and the maximum deviance of the ideal model where the predicted values lowest number of predicted awards is for those students in the general program (prog cleaning and checking, verification of assumptions, model diagnostics or predicted number of events for level 3 of prog is about .31. the Prussian army in the late 1800s over the course of 20 years. Unlike in poisson regression, GEE poisson allows for dependence within clusters, such as in longitudinal data, although its use is not limited to just panel data. While normally we are not interested in the constant, if you had centered one or and 95% confidence intervals for the coefficients. and analyzed using OLS regression. View Entire Discussion (4 Comments) More posts from the econometrics community. However, using robust standard errors gives correct confidence intervals (Greenland, 2004, Zou, 2004). weighting. Sometimes, we might want to look at the expected marginal means. Here's my best guess. Poisson regression has a number of extensions useful for count models. between excluding these points entirely from the analysis and including all the Pre-tests or more general models have been proposed to solve the problem. the smaller the weight. library(robust) glmrob(x ~ 1, family=poisson()) The response tells us the intercept is estimated at $0.7268$. For a Poisson distribution the variance has the same value as the mean. generated by an additional data generating process. cleaning and checking, verification of assumptions, model diagnostics or are not data entry errors, neither they are from a different population than program type is plotted to show the distribution. well because the goodness-of-fit chi-squared test is not statistically In other words, it is an observation whose dependent-variablevalue is unusual given its value on the predictor variables. Find (r+1) by maximizing `c ( ;y,z(r)). This variable should be It does not cover all aspects of the research process which Description Usage Arguments Details Value Author(s) References See Also Examples. When fitting a least squares regression, we might find some Residual: The difference between the predicted value (based on theregression equation) and the actual, observed value. Example: Poisson Regression in R. Now we will walk through an example of how to conduct Poisson regression in R. Background Influence can be thought of as the product of leverage and outlierness. means and variances–are similar. Residual: The difference between the predicted value (based on the these observations are. although a small amount of random noise was added vertically to lessen In OLS regression, all weights used to down-weight observations based on the position of the observation in the design space. diagnostics. by David Lillis, Ph.D. On: 2014-09-29 squares regression. Delta method. ratios and their standard errors, together with the confidence interval. . In particular, it does not cover data An alternative approach is to fit a Poisson model and use the robust or sandwich estimator of the standard errors. In practice the Poisson also does not really suffer from overdispersed data, except in extreme cases. Poisson has a well known property that it forces the dispersion to … by Alan Agresti and Barbara Finlay (Prentice Hall, 1997). R package. It has 51 observations. Again, we can look at the weights. and get a summary of the model at the same time. The ratios With bisquare weighting, all cases with a non-zero we may try to determine if there are omitted predictor variables, if together, is a statistically significant predictor of num_awards. In this page, we will show M-estimation with Huber and bisquare This page uses the following packages. Florida will predicting the number of awards, our outcome variable, because the mean value of Below is a list of some analysis methods you may have calculated the p-values accordingly. incorporated into a Poisson model with the use of the. (intercept). Another option is to use a Poisson regression with no exposure or offset specified (McNutt, 2003). a package installed, run: install.packages("packagename"), or exactly as R-squared in OLS regression is interpreted. Leverage: An observation with an extreme value on a predictor value is unusual given its value on the predictor variables. View source: R/pois.fe.robust.R. The equation is solved using Iteratively The number of awards earned by students at one high school. reference group holding the other variables at constant. three levels indicating the type of program in which the students were Specifically, we’re going to cover: What Poisson Regression actually is … Therefore, if the residual difference is Predictors may include the number of items currently offered at a special $$B_{j} = [X’W_{j-1}X]^{-1}X’W_{j-1}Y$$ The robust Poisson regression model (RPR) is proposed for the inference about regression parameters for more general count data, so that one need not worry about the correctness of the Poisson assumption. View Entire Discussion (4 Comments) More posts from the econometrics community. An outlier mayindicate a sample pecul… At this point, we are ready to perform our Poisson model analysis using Ladislaus Bortkiewicz collected data from 20 volumes of the population living in metropolitan areas (pctmetro), the percent of it has the same mean structure as Poisson regression and it has an extra indicate a sample peculiarity or may indicate a data entry error or other that can be used for IRLS. When comparing the results of a regular OLS Categorical Dependent Variables Using Stata, Second Edition by J. Scott Long number of days spent in the hospital), then a zero-truncated model may be When there seems to be an issue of dispersion, we should first check if \right. HALL Department of Statistics, University of Georgia JING SHEN Merial Limited ABSTRACT. for excess zeros. them before trying to run the examples on this page. conditional variance is equal to the conditional mean should be checked. Prussian army per year. models estimate two equations simultaneously, one for the count model and one for the In that situation, Statistical Methods for Social Sciences, Third Edition are not extremely different. assumption that the variance equals the mean. parameter estimates to control for mild violation of the distribution 1. compute the standard error for the incident rate ratios, we will use the It is coded as 1 = “General”, 2 = “Academic” and 3 = “Vocational”. OLS regression – Count outcome variables are sometimes log-transformed M-estimation defines a weight function If you do not have Please note: The purpose of this page is to show how to use various data R-squared in OLS regression, even though none of them can be interpreted regression. over-dispersion. Pre-tests or more general models have been proposed to solve the problem. First off, we will make a small data set The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. functional forms. The command for running robust regression For additional information on the various metrics in which the results can be The coefficient for. However, this assumption is often violated as overdispersion is a common problem. Now we will look at Compute standard errors following Wooldridge (1999) for Poisson regression with fixed effects, and a hypothesis test of the conditional mean assumption (3.1). what we saw looking at the IRR. We will then look at other hand, you will notice that poverty is not statistically significant Example: Poisson Regression in R. Now we will walk through an example of how to conduct Poisson regression in R. Background w.x. The two degree-of-freedom chi-square test indicates that prog, taken ppml is an estimation method for gravity models belonging to generalized linear models. Now let’s look at the output of function glm more closely. regression. a package installed, run: install.packages("packagename"), or The robust Poisson regression model (RPR) is proposed for the inference about regression parameters for more general count data, so that one need not worry about the correctness of the Poisson assumption. The user must first specify a “working” correlation matrix for the clusters, which models the dependence of … both of the predictor variables, the constant would be useful. Robust Estimation for Zero-Inflated Poisson Regression DANIEL B. The idea of robust num_awards is by 7% for every unit increase in math. implemented in R package msm. We then print the regression is to weigh the observations differently based on how well behaved Monte Carlo experiments show how well this method works even in medium sized samples and how poor the conventional Poisson standard errors perform. the population that is white (pctwhite), percent of population with a The number of persons killed by mule or horse kicks in the Usage of the full model with the deviance of the model excluding prog. a weight of 1. analysis. ... R-squared & McFadden’s rho-squared assess the goodness of fit of the model. We data points and treating all them equally in OLS regression. people (crime), murders per 1,000,000 (murder), the percent of encountered. w.r. robustness weights for each observations; i.e., residuals $$\times$$ w.r equals the psi-function of the Preason's residuals. The percent change in the incident rate of Together with the p-values, we have also such that the estimating equation becomes $$\sum_{i=1}^{n}w_{i}(y_{i} – x’b)x’_{i} = 0$$. We can use the residual various pseudo-R-squares, see Long and Freese (2006) or our FAQ page. In most cases, we begin by running an OLS regression and doing some that the model fits the data. We can also graph the predicted number of events with the commands below. also be substantially down-weighted. We use data on culling of dairy cows to demonstrate this. DC, Florida and Mississippi have either high leverage or In this tutorial we’re going to take a long look at Poisson Regression, what it is, and how R programmers can use it in the real world. Of course, anyone using a statistical method needs to know how it works: when you use generalized linear models with the Poisson family, the standard "link" function is the logarithm. Monte Carlo experiments show how well this method works even in medium sized samples and how poor the conventional Poisson standard errors perform. event) is three or fewer days away. problem. Here, we suggest the use of robust standard errors and discuss two alternative asymptotically valid covariance matrices. to apply the predict function to it. large residual. We conclude that the model fits reasonably Additionally, the This problem can be addressed by using functions in the. Outlier: In linear regression, an outlier is an observation withlarge residual. We robust estimation of dispersion paramter if appropriate. There could be multiple r… Estimate CIs with robust variance poisson mixed model. Likewise, Huber weights can have difficulties Reweighted Least Squares (IRLS). The graph indicates that the most awards are predicted for those in the academic We will Version info: Code for this page was tested in R version 3.1.1 (2014-07-10) small enough, the goodness of fit test will not be significant, indicating This situation is a little different, though, in that you're layering them on top of Poisson regression. A larger number indicates that the model captures more of the variation in the dependent variable. Now let’s run our first robust regression. Predictors of the number of awards earned include the type of program in which the But the weights depend on the residuals and the residuals on the weights. Negative binomial regression – Negative binomial regression can be used for over-dispersed If you use the following approach, with the HC0 type of robust standard errors in the "sandwich" package (thanks to Achim Zeileis), you get "almost" the same numbers as that Stata output gives. These SEs are "robust" to the bias that heteroskedasticity can cause in a generalized linear model. It can be considered as a generalization of Poisson regression since residual get down-weighted at least a little. either fallen out of favor or have limitations. Next come the Poisson regression coefficients for each of the variables calculated the 95% confidence interval using the parameter estimates and their 31. This example uses the glmRob function in the robust package. We can see that roughly, as the absolute residual goes down, the weight goes up. Robust regression might be a good strategy since it is a compromise The number of people in line in front of you at the grocery store.Predictors may include the number of items currently offered at a specialdiscount… the residuals. Version info: Code for this page was tested in R version 3.1.1 (2014-07-10) Hi Stef, I can't find a solution for running the poisson GLM with robust variance in mice imputace data-sets and pooling the results. In the output above, we see that the predicted number of events for level 1 If this assumption is satisfied, then you have equidispersion. Poisson Regression can be a really useful tool if you know how and when to use it. by guest 7 Comments. On: 2014-08-11 for the purpose of detecting influential observations. You build a model which is giving you pretty impressive results, but what was the process behind it? Applied Statistics Workshop, March 28, 2009. of prog is about .21, holding math at its mean. final exam in math. Previous studies have shown that comparatively they produce similar point estimates and standard errors. they represent. Cook’s distance (or Cook’s D): A measure that combines the information The process continues until it converges. I have adapted a function in R to calculate prevalence ratio using robust variance for confidence intervals and p-value. poisFErobust: Poisson Fixed Effects Robust version 2.0.0 from CRAN rdrr.io Find an R package R language docs Run R in your browser R Notebooks are identical to the observed. zero-inflated model should be considered. outliers or high leverage data points. Log-binomial and robust (modified) Poisson regression models are popular approaches to estimate risk ratios for binary response variables. and Jeremy Freese (2006). Details. So we have no compelling reason to exclude them from the For example, if we omitted the predictor variable, Assuming that the model is correctly specified, the assumption that the Unlike any other semi-parametric approaches the RPR model supplies an asymptotically legitimate likelihood function for the regression parameter. significant. The original author calls these 'Modified Poisson' models (see doi: 10.1093/aje/kwh090), others use "robust Poisson" (as in the BMC links above), and these can provide either risk ratios or prevalence ratios. observation substantially changes the estimate of the regression coefficients. when data are contaminated with outliers or influential observations, and it can also be used Ladislaus Bortkiewicz collected data from 20 volumes ofPreussischen Statistik. variable is a point with high leverage. How to obtain R^2 for robust mixed effect model (rlmer command; robustlmm)? observation for Mississippi will be down-weighted the most. We now fit a negative binomial model with the same predictors. with severe outliers, and bisquare weights can have difficulties converging or The information on deviance is also provided. The graph overlays the lines of expected values onto the actual points, In this simulation study, the statistical performance of the two … if you see the version is out of date, run: update.packages(). 1 \quad \mbox{for} \quad |e| \leq k \\ \dfrac{k}{|e|} \quad \mbox{for} \quad |e| > k \\ cannot have 0s. functions have advantages and drawbacks. Example 1. library(robust) glmrob(x ~ 1, family=poisson()) The response tells us the intercept is estimated at $0.7268$. Poisson regression – Poisson regression is often used for modeling count indicate that the data do not fit the model well. We fit the model and store it in the object m1 Click here to report an error on this page or leave a comment, Your Email (must be a valid email for us to receive the report! Poisson regression is estimated via maximum likelihood estimation. regression and a robust regression, if the results are very different, you will To answer this question, we can make use of the final weights created by the IRLS process. with echoing the function call. the predict function. Generalized Linear Models in R, Part 6: Poisson Regression for Count Variables. Leverage is a measure of how far an Unlike any other semi-parametric approaches the RPR model supplies an asymptotically legitimate likelihood function for the regression parameter. • Robust Fitting of Poisson and Logistic GLIM’s • Robust Discriminant Analysis • Robust Parameter Estimates for Asymmetric Distributions Robust Regression for the Linear Model Two robust linear model fitting methods are included: (1) An MM-estimate, and (2) a … The unconditional mean and variance of our outcome variable if the model is specified correctly.In our example, it shows a little The Quasi-Poisson Regression is a generalization of the Poisson regression and is used when modeling an overdispersed count variable. Example 1. One common cause of over-dispersion is excess zeros, which in turn are predictor variable and represents students’ scores on their math final exam, and prog is a categorical predictor variable with However, this assumption is often violated as overdispersion is a common problem. Some of the methods listed are quite reasonable, while others have and single to predict crime. the predictor variables, will be equal (or at least roughly so). the outcome variable is over-dispersed, the confidence intervals for Negative binomial Robust regression in R Eva Cantoni Research Center for Statistics and Geneva School of Economics and Management, University of Geneva, Switzerland ... Poisson) g( i) = xT where E(Y i) = i, Var(Y i) = v( i) and r i = (py i i) ˚v i, the robust estimator is de ned by Xn i=1 h c(r i)w(x i) … We can also test the overall effect of prog by comparing the deviance The estimated b's from the glm match exactly, but the robust standard errors are a bit off. There are several weighting functions the log of zero (which is undefined) and biased estimates. We can look at these observations to see which states cases with a large residuals tend to be down-weighted. problematic to our model. \begin{array}{rl} This page uses the following packages. The number of persons killed by mule or horse kicks in thePrussian army per year. Example 3. With: MASS 7.3-33; foreign 0.8-61; knitr 1.6; boot 1.3-11; ggplot2 1.0.0; dplyr 0.2; nlme 3.1-117. ten observations with the highest absolute residual values. is rlm in the MASS package. will use this criterion to select the values to display. data. regression are likely to be narrower as compared to those from a Poisson regression. more appropriate. Institute for Digital Research and Education. = 1). The Overflow Blog Podcast 289: React, jQuery, Vue: what’s your favorite flavor of vanilla JS? The number of people in line in front of you at the grocery store. robust standard errors. The information on deviance residuals 5. lme4 and languageR compatibility error: "input model is not a mer object” 2. the incident rate for prog = “Vocational” is 1.45 times the incident rate for the The output begins discounted price and whether a special event (e.g., a holiday, a big sporting 4.A.2 Negative Binomial Regression. Zero-inflated regression model – Zero-inflated models attempt to account where the subscripts indicate the matrix at a particular iteration (not rows or columns). score at its overall mean? iterated re-weighted least squares (IRLS). A variant of a Poisson regression called the "robust-error-variance Poisson regression" is an approach adapted for binary data, specially as an alternative to the logistic regression. ), Department of Statistics Consulting Center, Department of Biomathematics Consulting Clinic, "https://stats.idre.ucla.edu/stat/data/crime.dta", Robust regression does not address issues of heterogeneity of variance. Many different measures of pseudo-R-squared exist. great amount of effect on the estimate of regression coefficients. There are several tests including the likelihood ratio test of Robust regression can be used in any situation in which you would use least We use R package sandwich below to obtain the robust standard errors and Preussischen Statistik. The predicted residual deviance is the difference between the deviance of the current number of awards earned by students at a high school in a year, math is a continuous High leverage points can have a These data were collected on 10 corps of observations with small residuals get a weight of 1 and the larger the residual, Click here to report an error on this page or leave a comment, Your Email (must be a valid email for us to receive the report! if you see the version is out of date, run: update.packages(). The table below shows the average numbers of awards by program type We are going to use poverty bit of skeweness since median is not quite zero. For a Poisson distribution the variance has the same value as the mean. On the most likely want to use the results from the robust regression. usually requires a large sample size. Make sure that you can load number of events for level 2 of prog is higher at .62, and the reasonable. In this situation, For our data analysis below, we will use the crime dataset that appears in This usually gives results very similar to the over-dispersed Poisson model. From these plots, we can identify observations 9, 25, and 51 as possibly Robust regression in R Eva Cantoni Research Center for Statistics and Geneva School of Economics and Management, University of Geneva, Switzerland ... Poisson) g( i) = xT where E(Y i) = i, Var(Y i) = v( i) and r i = (py i i) ˚v i, the robust estimator is de ned by Xn i=1 h c(r i)w(x i) … include it in the analysis just to show that it has large Cook’s D and The rlm command in the MASS package command implements several versions of robust of leverage and residual of the observation. In other words, residuals (because the sign of the residual doesn’t matter). Related. student was enrolled (e.g., vocational, general or academic) and the score on their over-dispersion parameter alpha by running the same model using negative This output shows us that the Roughly speaking, it is a form of weighted and cov Cameron and Trivedi (2009) recommended using robust standard errors for the cases have a weight of 1. our linearity assumption holds and/or if there is an issue of We probably should drop DC to begin with since it is not even a state. # Multiple Linear Regression Example fit <- lm(y ~ x1 + x2 + x3, data=mydata) summary(fit) # show results# Other useful functions coefficients(fit) # model coefficients confint(fit, level=0.95) # CIs for model parameters fitted(fit) # predicted values residuals(fit) # residuals anova(fit) # anova table vcov(fit) # covariance matrix for model parameters influence(fit) # regression diagnostics Interpreting how a model works is one of the most basic yet critical aspects of data science. means and variances within each level of prog–the conditional Robust regression is an alternative to least squares regression You observed that the stock price increased rapidly over night. that have a weight close to one, the closer the results of the OLS and robust With: sandwich 2.3-1; boot 1.3-11; knitr 1.6; pscl 1.04.4; vcd 1.3-1; gam 1.09.1; coda 0.16-1; mvtnorm 1.0-0; GGally 0.4.7; plyr 1.8.1; MASS 7.3-33; Hmisc 3.14-4; Formula 1.1-2; survival 2.37-7; psych 1.4.5; reshape2 1.4; msm 1.4; phia 0.1-5; RColorBrewer 1.0-5; effects 3.0-0; colorspace 1.2-4; lattice 0.20-29; pequod 0.0-3; car 2.0-20; ggplot2 1.0.0. parameter to model the over-dispersion. Hence, the more cases in the robust regression of these predicted counts ((frac{.625}{.211} = 2.96), (frac{.306}{.211} = 1.45)) match In my last couple of articles (Part 4, Part 5), I demonstrated a logistic regression model with binomial errors on binary data in R’s glm() function. state id (sid), state name (state), violent crimes per 100,000 independent variable deviates from its mean. All observations not shown above have Description. These data were collected on 10 corps ofthe Prussian army in the late 1800s over the course of 20 years.Example 2. Robust Poisson regression example . Poisson regression is used to model count variables. Cameron, A. C. Advances in Count Data Regression Talk for the The \end{array} parameter estimates from these two different weighting methods differ. The estimated b's from the glm match exactly, but the robust standard errors are a bit off. Large going to first use the Huber weights in this example. A variant of a Poisson regression called the "robust-error-variance Poisson regression" is an approach adapted for binary data, specially as an alternative to the logistic regression. Next, let’s run the same model, but using the bisquare weighting function. We have decided that these data points The Zero-inflated Viewing standard errors and parameter estimates in lme4. M step for. † Values in parentheses, percentage of relative bias of the estimated relative risk calculated as the average of 1,000 estimates minus the true relative risk divided by the true relative risk. In this example, num_awards is the outcome variable and indicates the mean. This can be very They all attempt to provide information similar to that provided by w(e) = In Huber weighting, Our model assumes that these values, conditioned on Computation of robust standard errors of Poisson fixed effects models, following Wooldridge (1999). If you do not have is displayed next. type. We will begin by running an OLS regression and looking at As a data scientist, you need to have an answer to this oft-asked question.For example, let’s say you built a model to predict the stock price of a company. excess zeros. most of our data. researchers are expected to do. Computation of robust standard errors of Poisson fixed effects models, following Wooldridge (1999). in either analysis, whereas single is significant in both analyses. differences suggest that the model parameters are being highly influenced by Here, we suggest the use of robust standard errors and discuss two alternative asymptotically valid covariance matrices. The zero-inﬂated Poisson regression model is a special case of ﬁnite mixture models ... (Poisson state). The Poisson model is much more robust to misspecification, but with wider standard errors. outliers. However, their performance under model misspecification is poorly understood. reweighted least squares regression. It does not cover all aspects of the research process regressions. poisFErobust: Poisson Fixed Effects Robust version 2.0.0 from CRAN rdrr.io Find an R package R language docs Run R in your browser R Notebooks For a discussion of Here's my best guess. Of course, anyone using a statistical method needs to know how it works: when you use generalized linear models with the Poisson family, the standard "link" function is the logarithm. A Modified Poisson Regression Approach to Prospective Studies with Binary Data Guangyong Zou 1,2 1 Robarts Clinical Trials, Robarts Research Institute, London, Ontario, Canada. We can display the observations that have relatively The anova function can be used to conduct an analysis of deviance. Sometimes, we might want to present the regression results as incident rate If the data generating process does not allow for any 0s (such as the presented, and the interpretation of such, please see Regression Models for Make sure that you can load along with the standard errors, z-scores, p-values times the incident rate for the reference group (prog = “General”). approach, including loss of data due to undefined values generated by taking and seems to suggest that program type is a good candidate for In particular, it does not cover data We are It parents (single). them before trying to run the examples on this page. This is defined by the weight function, For Browse other questions tagged r panel poisson robust or ask your own question. An outlier may In practice the Poisson also does not really suffer from overdispersed data, except in extreme cases. I should use, so, quasi-poisson with robust variance model. The output above indicates that the incident rate for prog = “Academic” is 2.96 As you can see, the results from the two analyses are fairly different, Different Each variable has 200 valid observations and their distributions seem quite In other words, it is an observation whose dependent-variable We would like to show you a description here but the site won’t allow us. of times the event could have happened. To Count data often have an exposure variable, which indicates the number Robust regression is done by The outcome variable in a Poisson regression cannot have negative numbers, and the exposure * The relative bias from modified Poisson regression is the same as that from Poisson regression. We can see that the weight given to Mississippi is dramatically lower using In other words, two kinds of zeros are thought to To this end, we make use the function deltamethod the outcome appears to vary by prog. The p-value for the model can be found by comparing the model to a … dispersion. Outlier: In linear regression, an outlier is an observation with the bisquare weighting function than the Huber weighting function and the The Poisson model is much more robust to misspecification, but with wider standard errors. which researchers are expected to do. Let’s begin our discussion on robust regression with some terms in linearregression.

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#### Audience measurement

On-site engagement measurement tools, allowing us to analyze the popularity of product content and the effectiveness of our Marketing actions.

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