## Simultaneous intervals for derivatives of smooths revisited

#### 21 March 2017 /posted in: R

Eighteen months ago I screwed up! I’d written a post in which I described the use of simulation from the posterior distribution of a fitted GAM to derive simultaneous confidence intervals for the derivatives of a penalized spline. It was a nice post that attracted some interest. It was also wrong. In December I corrected the first part of that mistake by illustrating one approach to compute an actual simultaneous interval, but only for the fitted smoother. At the time I thought that the approach I outlined would translate to the derivatives but I was being lazy then Christmas came and went and I was back to teaching — you know how it goes. Anyway, in this post I hope to finally rectify my past stupidity and show how the approach used to generate simultaneous intervals from the December 2016 post can be applied to the derivatives of a spline.

## Modelling extremes using generalized additive models

#### 25 January 2017 /posted in: R

Quite some years ago, whilst working on the EU Sixth Framework project Euro-limpacs, I organized a workshop on statistical methods for analyzing time series data. One of the sessions was on the analysis of extremes, ably given by Paul Northrop (UCL Department of Statistical Science). That intro certainly whet my appetite but I never quite found the time to dig into the arcane world of extreme value theory. Two recent events rekindled my interest in extremes; Simon Wood quietly introduced into his mgcv package a family function for the generalized extreme value distribution (GEV), and I was asked to review a paper on extremes in time series. Since then I’ve been investigating options for fitting models for extremes to environmental time series, especially those that allow for time-varying effects of covariates on the parameters of the GEV. One of the first things I did was sit down with mgcv to get a feel for the gevlss() family function that Simon had added to the package by repeating an analysis of a classic example data set that had been performed using the VGAM package of Thomas Yee.

## Pangaea and R and open palaeo data (also GAM all the things!)

#### 16 December 2016 /posted in: R

For a while now, I’ve been wanting to experiment with rOpenSci’s pangaear package (Chamberlain et al., 2016), which allows you to search, and download data from, the Pangaea, a major data repository for the earth and environmental sciences. Earlier in the year, as a member of the editorial board of Scientific Data, Springer Nature’s open data journal I was handling a data descriptor submission that described a new 2,200-year foraminiferal δ18O record from the Gulf of Taranto in the Ionian Sea (Taricco et al., 2016). The data descriptor was recently published and as part of the submission Carla Taricco deposited the data set in Pangaea. So, what better opportunity to test out pangaear? (Oh and to fit a GAM to the data while I’m at it!)

Chamberlain, S., Woo, K., MacDonald, A., Zimmerman, N., and Simpson, G. (2016). Pangaear: Client for the ’pangaea’ database. Available at: https://CRAN.R-project.org/package=pangaear.

Taricco, C., Alessio, S., Rubinetti, S., Vivaldo, G., and Mancuso, S. (2016). A foraminiferal ()18O record covering the last 2,200 years. Scientific Data 3, 160042. doi:10.1038/sdata.2016.42.

## Simultaneous intervals for smooths revisited correcting a silly mistake

#### 15 December 2016 /posted in: R

Eighteen months ago I wrote a post in which I described the use of simulation from the posterior distribution of a fitted GAM to derive simultaneous confidence intervals for the derivatives of a penalised spline. It was a nice post that attracted some interest. It was also wrong. I have no idea what I was thinking when I thought the intervals described in that post were simultaneous. Here I hope to rectify that past mistake.

I’ll tackle the issue of simultaneous intervals for the derivatives of penalised spline in a follow-up post. Here, I demonstrate one way to compute a simultaneous interval for a penalised spline in a fitted GAM. As example data, I’ll use the strontium isotope data set included in the SemiPar package, and which is extensively analyzed in the monograph Semiparametric Regression (Ruppert et al., 2003). First, load the packages we’ll need as well as the data, which is data set fossil. If you don’t have SemiPar installed, install it using install.packages(“SemiPar”) before proceeding

Ruppert, D., Wand, M. P., and Carroll, R. J. (2003). Semiparametric regression. Cambridge University Press.

## ISEC 2016 Talk

#### 02 July 2016 /posted in: Science

My ISEC 2016 talk, Estimating temporal change in mean and variance of community composition via location, scale additive models, describes some of my recent research into methods to analyse palaeoenvironmental time series from sediment cores.

## Rootograms a new way to assess count models

#### 07 June 2016 /posted in: R

Assessing the fit of a count regression model is not necessarily a straightforward enterprise; often we just look at residuals, which invariably contain patterns of some form due to the discrete nature of the observations, or we plot observed versus fitted values as a scatter plot. Recently, while perusing the latest statistics offerings on ArXiv I came across Kleiber and Zeileis (2016) who propose the rootogram as an improved approach to the assessment of fit of a count regression model. The paper is illustrated using R and the authors’ countreg package (currently on R-Forge only). Here, I thought I’d take a quick look at the rootogram with some simulated species abundance data.

Kleiber, C., and Zeileis, A. (2016). Visualizing count data regressions using rootograms.

## A new default plot for multivariate dispersions tribulations of base graphics programming

#### 17 April 2016 /posted in: R

This weekend, prompted by a pull request from Michael Friendly, I finally got round to improving the plot method for betadisper() in the vegan package. betadisper() is an implementation of Marti Anderson’s Permdisp method, a multivariate analogue of Levene’s test for homogeneity of variances. In improving the default plot and allowing customisation of plot features, I was reminded of how much I dislike programming plot functions that use base graphics. But don’t worry, this isn’t going to degenerate into a ggplot love-in nor a David Robinson-esque dig at Jeff Leek.

## LOESS revisited

#### 10 April 2016 /posted in: Science

It’s fair to say I have gotten a bee1 in my bonnet about how palaeolimnologists handle time. For a group of people for whom time is everything, we sure do a poor job (in general) of dealing with it in when it comes time to analyse our data. In many instances, “poor job” means making no attempt at all to account for the special nature of the time series. LOESS comes in for particular criticism because it is widely used by palaeolimnologists despite not being particularly suited to the task. Why this is so is perhaps due to it’s promotion in influential books, papers, and software. I am far from innocent in this regard having taught LOESS and it’s use for many years on the now-defunct ECRC Numerical Course. Here I want to look at further problems with our use of LOESS, and will argue that we need to resign it to the trash can for all but exploratory analyses. I will begin the case for the prosecution with one of my own transgressions.

1. an entire hive is perhaps more apt!

## Soap-film smoothers & lake bathymetries

#### 27 March 2016 /posted in: R

A number of years ago, whilst I was still working at ENSIS, the consultancy arm of the ECRC at UCL, I worked on a project for the (then) Countryside Council for Wales (CCW; now part of Natural Resources Wales). I don’t recall why they were doing this project, but we were tasked with producing a standardised set of bathymetric maps for Welsh lakes. The brief called for the bathymetries to be provided in standard GIS formats. Either CCW’s project manager or the project lead at ENSIS had proposed to use inverse distance weighting (IWD) to smooth the point bathymetric measurements. This probably stemmed from the person that initiatied our bathymetric programme at ENSIS being a GIS wizard, schooled in the ways of ArcGIS. My involvement was mainly data processing of the IDW results. I was however, at the time, also somewhat familiar with the problem of finite area smoothing1 and had read a paper of Simon Wood’s on his then new soap-film smoother (Wood et al., 2008). So, as well as writing scripts to process and present the IDW-based bathymetry data in the report, I snuck a task into the work programme that allowed me to investigate using soap-film smoothers for modelling lake bathymetric data. The timing was never great to write up this method (two children and a move to Canada have occurred since the end of this project), so I’ve not done anything with the idea. Until now…

Wood, S. N., Bravington, M. V., and Hedley, S. L. (2008). Soap film smoothing. Journal of the Royal Statistical Society. Series B, Statistical methodology 70, 931–955. doi:10.1111/j.1467-9868.2008.00665.x.

1. smoothing over a domain with known boundaries, like a lake