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      <img src="../logo.png" class="logo" alt=""><h1>Mean Values-at-age from an age-length key</h1>
      <small class="dont-index">Source: <a href="https://github.com/fishR-Core-Team/FSA/blob/HEAD/R/alkSummaries.R" class="external-link"><code>R/alkSummaries.R</code></a></small>
      <div class="d-none name"><code>alkMeanVar.Rd</code></div>
    </div>

    <div class="ref-description section level2">
    <p>Computes the mean value-at-age in a larger sample based on an age-length-key created from a subsample of ages through a two-stage random sampling design. The mean values could be mean length-, weight-, or fecundity-at-age, for example. The methods of Bettoli and Miranda (2001) or Quinn and Deriso (1999) are used. A standard deviation is computed for the Bettoli and Miranda (2001) method and standard error for the Quinn and Deriso (1999) method. See the testing section notes.</p>
    </div>

    <div class="section level2">
    <h2 id="ref-usage">Usage<a class="anchor" aria-label="anchor" href="#ref-usage"></a></h2>
    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">alkMeanVar</span><span class="op">(</span></span>
<span>  <span class="va">key</span>,</span>
<span>  <span class="va">formula</span>,</span>
<span>  <span class="va">data</span>,</span>
<span>  <span class="va">len.n</span>,</span>
<span>  method <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"BettoliMiranda"</span>, <span class="st">"QuinnDeriso"</span><span class="op">)</span></span>
<span><span class="op">)</span></span></code></pre></div>
    </div>

    <div class="section level2">
    <h2 id="arguments">Arguments<a class="anchor" aria-label="anchor" href="#arguments"></a></h2>
    <dl><dt>key</dt>
<dd><p>A numeric matrix that contains the age-length key. See details.</p></dd>


<dt>formula</dt>
<dd><p>A formula of the form <code>var~lencat+age</code> where <code>var</code> generically represents the variable to be summarized (e.g., length, weight, fecundity), <code>lencat</code> generically represents the variable that contains the length intervals, and <code>age</code> generically represents the variable that contains the assigned ages.</p></dd>


<dt>data</dt>
<dd><p>A data.frame that minimally contains the length intervals, assessed ages, and the variable to be summarized (i.e., this should be the aged sample) as given in <code>formula</code>.</p></dd>


<dt>len.n</dt>
<dd><p>A vector of sample sizes for each length interval in the <em>complete sample</em> (i.e., all fish regardless of whether they were aged or not).</p></dd>


<dt>method</dt>
<dd><p>A string that indicates which method of calculation should be used. See details.</p></dd>

</dl></div>
    <div class="section level2">
    <h2 id="value">Value<a class="anchor" aria-label="anchor" href="#value"></a></h2>
    

<p>A data.frame with as many rows as ages (columns) present in <code>key</code> and the following three variables:</p><ul><li><p>age The ages.</p></li>
<li><p>mean The mean value at each age.</p></li>
<li><p>sd,se The SD if <code>method="BettoliMiranda"</code> or SE of the mean if <code>method="QuinnDeriso"</code> for the value at each age.</p></li>
</ul></div>
    <div class="section level2">
    <h2 id="details">Details<a class="anchor" aria-label="anchor" href="#details"></a></h2>
    <p>The age-length key <code>key</code> must have length intervals as rows and ages as columns. The row names of <code>key</code> (i.e., <code>rownames(key)</code>) must contain the minimum values of each length interval (e.g., if an interval is 100-109, then the corresponding row name must be 100). The column names of <code>key</code> (i.e., <code>colnames(key)</code>) must contain the age values (e.g., the columns can NOT be named with “age.1”, for example).</p>
<p>The length intervals in the rows of <code>key</code> must contain all of the length intervals present in the larger sample. Thus, the length of <code>len.n</code> must, at least, equal the number of rows in <code>key</code>. If this constraint is not met, then the function will stop with an error message.</p>
<p>Note that the function will stop with an error if the formula in <code>formula</code> does not meet the specific criteria outlined in the parameter list above.</p>
    </div>
    <div class="section level2">
    <h2 id="testing">Testing<a class="anchor" aria-label="anchor" href="#testing"></a></h2>
    <p>The results of these functions have not yet been rigorously tested. The Bettoli and Miranda (2001) results appear, at least, approximately correct when compared to the results from <code><a href="alkIndivAge.html">alkIndivAge</a></code>. The Quinn and Deriso (1999) results appear at least approximately correct for the mean values, but do not appear to be correct for the SE values. Thus, a note is returned with the Quinn and Deriso (1999) results that the SE should not be trusted.</p>
    </div>
    <div class="section level2">
    <h2 id="ifar-chapter">IFAR Chapter<a class="anchor" aria-label="anchor" href="#ifar-chapter"></a></h2>
    <p>5-Age-Length Key.</p>
    </div>
    <div class="section level2">
    <h2 id="references">References<a class="anchor" aria-label="anchor" href="#references"></a></h2>
    <p>Ogle, D.H. 2016. <a href="https://fishr-core-team.github.io/fishR/pages/books.html#introductory-fisheries-analyses-with-r" class="external-link">Introductory Fisheries Analyses with R</a>. Chapman &amp; Hall/CRC, Boca Raton, FL.</p>
<p>Bettoli, P. W. and Miranda, L. E. 2001. A cautionary note about estimating mean length at age with subsampled data. North American Journal of Fisheries Management, 21:425-428.</p> 
<p>Quinn, T. J. and R. B. Deriso. 1999. Quantitative Fish Dynamics. Oxford University Press, New York, New York. 542 pages</p>
    </div>
    <div class="section level2">
    <h2 id="see-also">See also<a class="anchor" aria-label="anchor" href="#see-also"></a></h2>
    <div class="dont-index"><p>See <code><a href="alkIndivAge.html">alkIndivAge</a></code> and related functions for a completely different methodology. See <code><a href="alkAgeDist.html">alkAgeDist</a></code> for a related method of determining the proportion of fish at each age. See the <span class="pkg">ALKr</span> package.</p></div>
    </div>
    <div class="section level2">
    <h2 id="author">Author<a class="anchor" aria-label="anchor" href="#author"></a></h2>
    <p>Derek H. Ogle, <a href="mailto:DerekOgle51@gmail.com">DerekOgle51@gmail.com</a></p>
    </div>

    <div class="section level2">
    <h2 id="ref-examples">Examples<a class="anchor" aria-label="anchor" href="#ref-examples"></a></h2>
    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co">## Example -- Even breaks for length categories</span></span></span>
<span class="r-in"><span><span class="va">WR1</span> <span class="op">&lt;-</span> <span class="va">WR79</span></span></span>
<span class="r-in"><span><span class="co"># add length intervals (width=5)</span></span></span>
<span class="r-in"><span><span class="va">WR1</span><span class="op">$</span><span class="va">LCat</span> <span class="op">&lt;-</span> <span class="fu"><a href="lencat.html">lencat</a></span><span class="op">(</span><span class="va">WR1</span><span class="op">$</span><span class="va">len</span>,w<span class="op">=</span><span class="fl">5</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="co"># get number of fish in each length interval in the entire sample</span></span></span>
<span class="r-in"><span><span class="va">len.n</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/xtabs.html" class="external-link">xtabs</a></span><span class="op">(</span><span class="op">~</span><span class="va">LCat</span>,data<span class="op">=</span><span class="va">WR1</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="co"># isolate aged sample</span></span></span>
<span class="r-in"><span><span class="va">WR1.age</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">WR1</span>, <span class="op">!</span><span class="fu"><a href="https://rdrr.io/r/base/NA.html" class="external-link">is.na</a></span><span class="op">(</span><span class="va">age</span><span class="op">)</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="co"># create age-length key</span></span></span>
<span class="r-in"><span><span class="va">raw</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/xtabs.html" class="external-link">xtabs</a></span><span class="op">(</span><span class="op">~</span><span class="va">LCat</span><span class="op">+</span><span class="va">age</span>,data<span class="op">=</span><span class="va">WR1.age</span><span class="op">)</span></span></span>
<span class="r-in"><span><span class="op">(</span> <span class="va">WR1.key</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/proportions.html" class="external-link">prop.table</a></span><span class="op">(</span><span class="va">raw</span>, margin<span class="op">=</span><span class="fl">1</span><span class="op">)</span> <span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#&gt;</span>      age</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> LCat           4          5          6          7          8          9</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   35  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   40  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   45  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   50  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   55  1.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   60  0.60000000 0.40000000 0.00000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   65  0.00000000 1.00000000 0.00000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   70  0.00000000 1.00000000 0.00000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   75  0.00000000 0.88888889 0.11111111 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   80  0.00000000 0.25000000 0.75000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   85  0.00000000 0.00000000 0.90909091 0.09090909 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   90  0.00000000 0.00000000 0.26315789 0.63157895 0.10526316 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   95  0.00000000 0.00000000 0.05882353 0.70588235 0.17647059 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   100 0.00000000 0.00000000 0.00000000 0.55555556 0.16666667 0.27777778</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   105 0.00000000 0.00000000 0.00000000 0.28571429 0.42857143 0.14285714</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   110 0.00000000 0.00000000 0.00000000 0.20000000 0.20000000 0.20000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   115 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>      age</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> LCat          10         11</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   35  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   40  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   45  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   50  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   55  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   60  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   65  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   70  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   75  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   80  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   85  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   90  0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   95  0.05882353 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   100 0.00000000 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   105 0.14285714 0.00000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   110 0.20000000 0.20000000</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   115 1.00000000 0.00000000</span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co">## use age-length key to estimate mean length-at-age of all fish</span></span></span>
<span class="r-in"><span><span class="co"># Bettoli-Miranda method</span></span></span>
<span class="r-in"><span><span class="fu">alkMeanVar</span><span class="op">(</span><span class="va">WR1.key</span>,<span class="va">len</span><span class="op">~</span><span class="va">LCat</span><span class="op">+</span><span class="va">age</span>,<span class="va">WR1.age</span>,<span class="va">len.n</span><span class="op">)</span></span></span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   age      mean       sd</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 1   4  51.95492 5.050430</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 2   5  72.01342 5.519135</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 3   6  86.59311 4.714664</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 4   7  97.45567 5.247117</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 5   8 101.38084 5.576238</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 6   9 103.65599 2.312767</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 7  10 104.86056 7.497515</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 8  11 113.00000 0.000000</span>
<span class="r-in"><span></span></span>
<span class="r-in"><span><span class="co"># Quinn-Deriso method</span></span></span>
<span class="r-in"><span><span class="fu">alkMeanVar</span><span class="op">(</span><span class="va">WR1.key</span>,<span class="va">len</span><span class="op">~</span><span class="va">LCat</span><span class="op">+</span><span class="va">age</span>,<span class="va">WR1.age</span>,<span class="va">len.n</span>,method<span class="op">=</span><span class="st">"QuinnDeriso"</span><span class="op">)</span></span></span>
<span class="r-msg co"><span class="r-pr">#&gt;</span> The 'se' values should not be trusted!</span>
<span class="r-out co"><span class="r-pr">#&gt;</span>   age      mean        se</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 1   4  51.95492 0.3031374</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 2   5  72.01342 0.5018225</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 3   6  86.59311 0.5977608</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 4   7  97.45567 0.4823013</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 5   8 101.38084 1.4384950</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 6   9 103.65599 0.9653842</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 7  10 104.86056 0.6696853</span>
<span class="r-out co"><span class="r-pr">#&gt;</span> 8  11 113.00000 0.0000000</span>
<span class="r-in"><span></span></span>
</code></pre></div>
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