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		<pubDate>Mon, 10 Oct 2011 13:49:24 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[Statistics]]></category>
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		<guid isPermaLink="false">http://www.fernandohrosa.com.br/en/?p=161</guid>
		<description><![CDATA[Today I was invited by Tal Galili, to join the great www.R-bloggers.com network of R blogs. Now all my posts categorized under Statistics/R, will be automagically published to www.R-bloggers.com. In case you don&#8217;t know R-bloggers yet, I highly encourage you to visit it. It&#8217;s an amazing resource, serving as a hub for hundreds of different [...]]]></description>
			<content:encoded><![CDATA[<p>Today I was invited by Tal Galili, to join the great <a href="http://www.R-bloggers.com">www.R-bloggers.com</a> network of R blogs. Now all my posts categorized under Statistics/R, will be automagically published to www.R-bloggers.com. </p>
<p>In case you don&#8217;t know R-bloggers yet, I highly encourage you to visit it. It&#8217;s an amazing resource, serving as a hub for hundreds of different bloggers about R. I&#8217;ve found some true gems there over the years.</p>
<p>Thank you!</p>
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		<title>Equality of Covariances Matrices Test in R (varcomp)</title>
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		<pubDate>Mon, 10 Oct 2011 01:19:28 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[R]]></category>
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		<category><![CDATA[multivariate analysis]]></category>
		<category><![CDATA[multivariate testing]]></category>

		<guid isPermaLink="false">http://www.fernandohrosa.com.br/en/?p=156</guid>
		<description><![CDATA[This is a piece of code I implemented in 2004, which was supposed to be part of an R-package in multivariate testing (to be named, rather creatively, mvttests). Time has flown, I haven&#8217;t still got around to implementing the said package, but people keep asking me for the varcomp function, so here it is, for [...]]]></description>
			<content:encoded><![CDATA[<p>This is a piece of code I implemented in 2004, which was supposed to be part of an R-package in multivariate testing (to be named, rather creatively, mvttests).</p>
<p>Time has flown, I haven&#8217;t still got around to implementing the said package, but people keep asking me for the varcomp function, so here it is, for posterity:</p>

<div class="wp_codebox_msgheader"><span class="right"></span><span class="left2">Download <a href="http://www.fernandohrosa.com.br/en/wp-content/plugins/wp-codebox/wp-codebox.php?p=156&amp;download=varcomp.R">varcomp.R</a></span><div class="codebox_clear"></div></div><div class="wp_codebox"><table><tr id="p1562"><td class="line_numbers"><pre>1
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</pre></td><td class="code" id="p156code2"><pre class="rsplus" style="font-family:monospace;">varcomp <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/function.html"><span style="color: #0000FF; font-weight: bold;">function</span></a><span style="color: #080;">&#40;</span>covmat,n<span style="color: #080;">&#41;</span> <span style="color: #080;">&#123;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/is.list.html"><span style="color: #0000FF; font-weight: bold;">is.<span style="">list</span></span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span> <span style="color: #080;">&#123;</span>
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;</span> <span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/stop.html"><span style="color: #0000FF; font-weight: bold;">stop</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">&quot;covmat must be a list with at least 2 elements&quot;</span><span style="color: #080;">&#41;</span>
    ps <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/as.vector.html"><span style="color: #0000FF; font-weight: bold;">as.<span style="">vector</span></span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sapply.html"><span style="color: #0000FF; font-weight: bold;">sapply</span></a><span style="color: #080;">&#40;</span>covmat,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/dim.html"><span style="color: #0000FF; font-weight: bold;">dim</span></a><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ps<span style="color: #080;">&#91;</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#93;</span> <span style="color: #080;">==</span> ps<span style="color: #080;">&#41;</span> <span style="color: #080;">!=</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>ps<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/stop.html"><span style="color: #0000FF; font-weight: bold;">stop</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">&quot;all covariance matrices must have the same dimension&quot;</span><span style="color: #080;">&#41;</span>
    p <span style="color: #080;">&lt;-</span> ps<span style="color: #080;">&#91;</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#93;</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/q.html"><span style="color: #0000FF; font-weight: bold;">q</span></a> <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>n<span style="color: #080;">&#41;</span> <span style="color: #080;">==</span> <span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span>
        Ng <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/rep.html"><span style="color: #0000FF; font-weight: bold;">rep</span></a><span style="color: #080;">&#40;</span>n,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/q.html"><span style="color: #0000FF; font-weight: bold;">q</span></a><span style="color: #080;">&#41;</span>
    <span style="color: #0000FF; font-weight: bold;">else</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>n<span style="color: #080;">&#41;</span> <span style="color: #080;">==</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/q.html"><span style="color: #0000FF; font-weight: bold;">q</span></a><span style="color: #080;">&#41;</span>
        Ng <span style="color: #080;">&lt;-</span> n
    <span style="color: #0000FF; font-weight: bold;">else</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/stop.html"><span style="color: #0000FF; font-weight: bold;">stop</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">&quot;n must be equal length(covmat) or 1&quot;</span><span style="color: #080;">&#41;</span>
&nbsp;
    DNAME <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/deparse.html"><span style="color: #0000FF; font-weight: bold;">deparse</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/substitute.html"><span style="color: #0000FF; font-weight: bold;">substitute</span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
   <span style="color: #080;">&#125;</span>
&nbsp;
   <span style="color: #0000FF; font-weight: bold;">else</span>
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/stop.html"><span style="color: #0000FF; font-weight: bold;">stop</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">&quot;covmat must be a list&quot;</span><span style="color: #080;">&#41;</span>
&nbsp;
   ng <span style="color: #080;">&lt;-</span> Ng <span style="color: #080;">-</span> <span style="color: #ff0000;">1</span>
   Ag <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/lapply.html"><span style="color: #0000FF; font-weight: bold;">lapply</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">:</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span>,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/function.html"><span style="color: #0000FF; font-weight: bold;">function</span></a><span style="color: #080;">&#40;</span>i,mat,n<span style="color: #080;">&#41;</span> <span style="color: #080;">&#123;</span> n<span style="color: #080;">&#91;</span>i<span style="color: #080;">&#93;</span> <span style="color: #080;">*</span> mat<span style="color: #080;">&#91;</span><span style="color: #080;">&#91;</span>i<span style="color: #080;">&#93;</span><span style="color: #080;">&#93;</span> <span style="color: #080;">&#125;</span>,mat<span style="color: #080;">=</span>covmat,n<span style="color: #080;">=</span>ng<span style="color: #080;">&#41;</span>
   A <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/matrix.html"><span style="color: #0000FF; font-weight: bold;">matrix</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/colSums.html"><span style="color: #0000FF; font-weight: bold;">colSums</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/matrix.html"><span style="color: #0000FF; font-weight: bold;">matrix</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/unlist.html"><span style="color: #0000FF; font-weight: bold;">unlist</span></a><span style="color: #080;">&#40;</span>Ag<span style="color: #080;">&#41;</span>,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/ncol.html"><span style="color: #0000FF; font-weight: bold;">ncol</span></a><span style="color: #080;">=</span>p<span style="color: #080;">^</span><span style="color: #ff0000;">2</span>,byrow<span style="color: #080;">=</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/T.html"><span style="color: #0000FF; font-weight: bold;">T</span></a><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/ncol.html"><span style="color: #0000FF; font-weight: bold;">ncol</span></a><span style="color: #080;">=</span>p<span style="color: #080;">&#41;</span>
   detAg <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sapply.html"><span style="color: #0000FF; font-weight: bold;">sapply</span></a><span style="color: #080;">&#40;</span>Ag,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/det.html"><span style="color: #0000FF; font-weight: bold;">det</span></a><span style="color: #080;">&#41;</span>
   detA <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/det.html"><span style="color: #0000FF; font-weight: bold;">det</span></a><span style="color: #080;">&#40;</span>A<span style="color: #080;">&#41;</span>
   V1 <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/prod.html"><span style="color: #0000FF; font-weight: bold;">prod</span></a><span style="color: #080;">&#40;</span>detAg<span style="color: #080;">^</span><span style="color: #080;">&#40;</span>ng<span style="color: #080;">/</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #080;">&#40;</span>detA<span style="color: #080;">^</span><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
   kg <span style="color: #080;">&lt;-</span> ng<span style="color: #080;">/</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span>
   l1 <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/prod.html"><span style="color: #0000FF; font-weight: bold;">prod</span></a><span style="color: #080;">&#40;</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">/</span>kg<span style="color: #080;">&#41;</span><span style="color: #080;">^</span>kg<span style="color: #080;">&#41;</span><span style="color: #080;">^</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">*</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">*</span> V1
   rho <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">1</span> <span style="color: #080;">-</span> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">/</span>ng<span style="color: #080;">&#41;</span> <span style="color: #080;">-</span> <span style="color: #ff0000;">1</span><span style="color: #080;">/</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">2</span><span style="color: #080;">*</span>p<span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">+</span><span style="color: #ff0000;">3</span><span style="color: #080;">*</span>p<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">6</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>q<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
   w2 <span style="color: #080;">&lt;-</span> p<span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span> <span style="color: #080;">*</span> <span style="color: #080;">&#40;</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">*</span> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">/</span>ng<span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">-</span> <span style="color: #ff0000;">1</span><span style="color: #080;">/</span><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span><span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span> <span style="color: #080;">-</span> <span style="color: #ff0000;">6</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>q<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">-</span>rho<span style="color: #080;">&#41;</span><span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">/</span> <span style="color: #080;">&#40;</span><span style="color: #ff0000;">48</span><span style="color: #080;">*</span>rho<span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span>
   f <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">0.5</span> <span style="color: #080;">*</span> <span style="color: #080;">&#40;</span>q<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span>p<span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span>
   STATISTIC <span style="color: #080;">&lt;-</span> <span style="color: #080;">-</span><span style="color: #ff0000;">2</span><span style="color: #080;">*</span>rho<span style="color: #080;">*</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/log.html"><span style="color: #0000FF; font-weight: bold;">log</span></a><span style="color: #080;">&#40;</span>l1<span style="color: #080;">&#41;</span>
   PVAL <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">1</span> <span style="color: #080;">-</span> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/pchisq.html"><span style="color: #0000FF; font-weight: bold;">pchisq</span></a><span style="color: #080;">&#40;</span>STATISTIC,f<span style="color: #080;">&#41;</span> <span style="color: #080;">+</span> w2<span style="color: #080;">*</span><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/pchisq.html"><span style="color: #0000FF; font-weight: bold;">pchisq</span></a><span style="color: #080;">&#40;</span>STATISTIC,f<span style="color: #080;">+</span><span style="color: #ff0000;">4</span><span style="color: #080;">&#41;</span> <span style="color: #080;">-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/pchisq.html"><span style="color: #0000FF; font-weight: bold;">pchisq</span></a><span style="color: #080;">&#40;</span>STATISTIC,f<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/names.html"><span style="color: #0000FF; font-weight: bold;">names</span></a><span style="color: #080;">&#40;</span>STATISTIC<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">&quot;corrected lambda*&quot;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/names.html"><span style="color: #0000FF; font-weight: bold;">names</span></a><span style="color: #080;">&#40;</span>f<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">&quot;df&quot;</span>
   RVAL <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/structure.html"><span style="color: #0000FF; font-weight: bold;">structure</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/list.html"><span style="color: #0000FF; font-weight: bold;">list</span></a><span style="color: #080;">&#40;</span>statistic <span style="color: #080;">=</span> STATISTIC, parameter <span style="color: #080;">=</span> f,p.<span style="">value</span> <span style="color: #080;">=</span> PVAL, data.<span style="">name</span> <span style="color: #080;">=</span> DNAME, method <span style="color: #080;">=</span> <span style="color: #ff0000;">&quot;Equality of Covariances Matrices Test&quot;</span><span style="color: #080;">&#41;</span>,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/class.html"><span style="color: #0000FF; font-weight: bold;">class</span></a><span style="color: #080;">=</span><span style="color: #ff0000;">&quot;htest&quot;</span><span style="color: #080;">&#41;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/return.html"><span style="color: #0000FF; font-weight: bold;">return</span></a><span style="color: #080;">&#40;</span>RVAL<span style="color: #080;">&#41;</span>
<span style="color: #080;">&#125;</span></pre></td></tr></table></div>

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		<title>Sphericity Test for Covariance Matrices in R (sphericity.test)</title>
		<link>http://www.fernandohrosa.com.br/en/P/sphericity-test-for-covariance-matrices-in-r-sphericity-test/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=sphericity-test-for-covariance-matrices-in-r-sphericity-test</link>
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		<pubDate>Sun, 09 Oct 2011 22:04:51 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[R]]></category>
		<category><![CDATA[Statistics]]></category>
		<category><![CDATA[multivariate testing]]></category>

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		<description><![CDATA[This is a piece of code I implemented in 2004, which was supposed to be part of an R-package in multivariate testing (to be named, rather creatively, mvttests). Time has flown, I haven&#8217;t still got around to implementing the said package, but people keep asking me for the sphericity.test function, so here it is, for [...]]]></description>
			<content:encoded><![CDATA[<p>This is a piece of code I implemented in 2004, which was supposed to be part of an R-package in multivariate testing (to be named, rather creatively, mvttests).</p>
<p>Time has flown, I haven&#8217;t still got around to implementing the said package, but people keep asking me for the sphericity.test function, so here it is, for posterity:</p>

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</pre></td><td class="code" id="p150code5"><pre class="rsplus" style="font-family:monospace;">sphericity.<span style="">test</span><span style="color: #080;">&lt;-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/function.html"><span style="color: #0000FF; font-weight: bold;">function</span></a><span style="color: #080;">&#40;</span>n,s1,s2<span style="color: #080;">=</span>NULL,estsigma<span style="color: #080;">=</span>TRUE<span style="color: #080;">&#41;</span><span style="color: #080;">&#123;</span>
<span style="color: #228B22;">#### Performs a hypothesis test that a covariance matrix is of specified </span>
<span style="color: #228B22;">#### form. Test is of the form H0: S1=sigma^2*S2. n is the number of</span>
<span style="color: #228B22;">#### observations on which the sample covariance matrix is based.</span>
<span style="color: #228B22;">#### If the input parameter estsigma is TRUE: </span>
<span style="color: #228B22;">#### Perform test of the hypothesis that S1=sigma^2 S2, for unknown sigma. </span>
<span style="color: #228B22;">#### If S2 not specified, assumed that S2=I. Reference is Basilevsky, </span>
<span style="color: #228B22;">#### Statistical Factor Analysis and Related Methods, page 191. </span>
<span style="color: #228B22;">#### If the input parameter estsigma is FALSE: </span>
<span style="color: #228B22;">#### Perform test of the hypothesis that S1=S2. If S2 not specified, </span>
<span style="color: #228B22;">#### assumed that S2=I. Reference is Seber, Multivariate Observations, </span>
<span style="color: #228B22;">#### sec 3.5.4 </span>
<span style="color: #228B22;">#### Only the lower triangle+diagonal is required at entry, and the upper </span>
<span style="color: #228B22;">#### triangle is ignored. </span>
<span style="color: #228B22;">#### DAW July 2000</span>
dname <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/paste.html"><span style="color: #0000FF; font-weight: bold;">paste</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/substitute.html"><span style="color: #0000FF; font-weight: bold;">substitute</span></a><span style="color: #080;">&#40;</span>s1<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
p<span style="color: #080;">&lt;-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/nrow.html"><span style="color: #0000FF; font-weight: bold;">nrow</span></a><span style="color: #080;">&#40;</span>s1<span style="color: #080;">&#41;</span>
<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/for.html"><span style="color: #0000FF; font-weight: bold;">for</span></a> <span style="color: #080;">&#40;</span>i <span style="color: #0000FF; font-weight: bold;">in</span> <span style="color: #ff0000;">1</span><span style="color: #080;">:</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#123;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/for.html"><span style="color: #0000FF; font-weight: bold;">for</span></a> <span style="color: #080;">&#40;</span>j <span style="color: #0000FF; font-weight: bold;">in</span> <span style="color: #080;">&#40;</span><span style="color: #080;">&#40;</span>i<span style="color: #080;">+</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">:</span>p<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#123;</span>
    s1<span style="color: #080;">&#91;</span>i,j<span style="color: #080;">&#93;</span><span style="color: #080;">&lt;-</span>s1<span style="color: #080;">&#91;</span>j,i<span style="color: #080;">&#93;</span>
    s2<span style="color: #080;">&#91;</span>i,j<span style="color: #080;">&#93;</span><span style="color: #080;">&lt;-</span>s2<span style="color: #080;">&#91;</span>j,i<span style="color: #080;">&#93;</span> <span style="color: #080;">&#125;</span><span style="color: #080;">&#125;</span>
<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><span style="color: #080;">!</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/is.null.html"><span style="color: #0000FF; font-weight: bold;">is.<span style="">null</span></span></a><span style="color: #080;">&#40;</span>s2<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#123;</span>
    b<span style="color: #080;">&lt;-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/eigen.html"><span style="color: #0000FF; font-weight: bold;">eigen</span></a><span style="color: #080;">&#40;</span>s2,symmetric<span style="color: #080;">=</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/T.html"><span style="color: #0000FF; font-weight: bold;">T</span></a>,only.<span style="">values</span><span style="color: #080;">=</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/F.html"><span style="color: #0000FF; font-weight: bold;">F</span></a><span style="color: #080;">&#41;</span>
    r<span style="color: #080;">&lt;-</span>b$vectors <span style="color: #080;">%*%</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/diag.html"><span style="color: #0000FF; font-weight: bold;">diag</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">/</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sqrt.html"><span style="color: #0000FF; font-weight: bold;">sqrt</span></a><span style="color: #080;">&#40;</span>b$values<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
    s<span style="color: #080;">&lt;-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/t.html"><span style="color: #0000FF; font-weight: bold;">t</span></a><span style="color: #080;">&#40;</span>r<span style="color: #080;">&#41;</span> <span style="color: #080;">%*%</span> s1 <span style="color: #080;">%*%</span> r <span style="color: #080;">&#125;</span>
<span style="color: #0000FF; font-weight: bold;">else</span> <span style="color: #080;">&#123;</span> s<span style="color: #080;">&lt;-</span>s1 <span style="color: #080;">&#125;</span>
&nbsp;
d<span style="color: #080;">&lt;-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/eigen.html"><span style="color: #0000FF; font-weight: bold;">eigen</span></a><span style="color: #080;">&#40;</span>s,symmetric<span style="color: #080;">=</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/T.html"><span style="color: #0000FF; font-weight: bold;">T</span></a>,only.<span style="">values</span><span style="color: #080;">=</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/T.html"><span style="color: #0000FF; font-weight: bold;">T</span></a><span style="color: #080;">&#41;</span>$values
ldet<span style="color: #080;">&lt;-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/log.html"><span style="color: #0000FF; font-weight: bold;">log</span></a><span style="color: #080;">&#40;</span>d<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
tr<span style="color: #080;">&lt;-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>d<span style="color: #080;">&#41;</span>
&nbsp;
<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span>estsigma<span style="color: #080;">==</span>TRUE<span style="color: #080;">&#41;</span><span style="color: #080;">&#123;</span>
    sighat<span style="color: #080;">&lt;-</span>tr<span style="color: #080;">/</span>p
    cc<span style="color: #080;">&lt;--</span><span style="color: #080;">&#40;</span>n<span style="color: #080;">-</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">2</span><span style="color: #080;">*</span>p<span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">+</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">6</span><span style="color: #080;">*</span>p<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>ldet<span style="color: #080;">-</span>p<span style="color: #080;">*</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/log.html"><span style="color: #0000FF; font-weight: bold;">log</span></a><span style="color: #080;">&#40;</span>tr<span style="color: #080;">/</span>p<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
    statistic <span style="color: #080;">&lt;-</span> cc
    sighat<span style="color: #080;">&lt;-</span>sighat
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/names.html"><span style="color: #0000FF; font-weight: bold;">names</span></a><span style="color: #080;">&#40;</span>statistic<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">&quot;L statistic&quot;</span>
    parameter <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">0.5</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span>
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/names.html"><span style="color: #0000FF; font-weight: bold;">names</span></a><span style="color: #080;">&#40;</span>parameter<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">&quot;df&quot;</span>
    rval<span style="color: #080;">&lt;-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/list.html"><span style="color: #0000FF; font-weight: bold;">list</span></a><span style="color: #080;">&#40;</span>data.<span style="">name</span><span style="color: #080;">=</span>dname,sighat<span style="color: #080;">=</span>sighat,statistic<span style="color: #080;">=</span>statistic,parameter<span style="color: #080;">=</span>parameter,p.<span style="">value</span><span style="color: #080;">=</span><span style="color: #ff0000;">1</span><span style="color: #080;">-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/pchisq.html"><span style="color: #0000FF; font-weight: bold;">pchisq</span></a><span style="color: #080;">&#40;</span>statistic,parameter<span style="color: #080;">&#41;</span>,method<span style="color: #080;">=</span><span style="color: #ff0000;">&quot;Sphericity test&quot;</span><span style="color: #080;">&#41;</span> <span style="color: #080;">&#125;</span>
<span style="color: #0000FF; font-weight: bold;">else</span> <span style="color: #080;">&#123;</span>
    cc<span style="color: #080;">&lt;--</span>n<span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span>ldet<span style="color: #080;">-</span>tr<span style="color: #080;">&#41;</span>
    statistic <span style="color: #080;">&lt;-</span> cc
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/names.html"><span style="color: #0000FF; font-weight: bold;">names</span></a><span style="color: #080;">&#40;</span>statistic<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">&quot;L statistic&quot;</span>
    parameter <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">0.5</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span>p
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/names.html"><span style="color: #0000FF; font-weight: bold;">names</span></a><span style="color: #080;">&#40;</span>parameter<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">&quot;df&quot;</span>
    rval<span style="color: #080;">&lt;-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/list.html"><span style="color: #0000FF; font-weight: bold;">list</span></a><span style="color: #080;">&#40;</span>data.<span style="">name</span><span style="color: #080;">=</span><span style="color: #ff0000;">&quot;&quot;</span>,statistic<span style="color: #080;">=</span>statistic,parameter<span style="color: #080;">=</span>parameter,p.<span style="">value</span><span style="color: #080;">=</span><span style="color: #ff0000;">1</span><span style="color: #080;">-</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/pchisq.html"><span style="color: #0000FF; font-weight: bold;">pchisq</span></a><span style="color: #080;">&#40;</span>statistic,parameter<span style="color: #080;">&#41;</span>,method<span style="color: #080;">=</span><span style="color: #ff0000;">&quot;Covariance equality test statistic&quot;</span><span style="color: #080;">&#41;</span>
<span style="color: #080;">&#125;</span>
<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/class.html"><span style="color: #0000FF; font-weight: bold;">class</span></a><span style="color: #080;">&#40;</span>rval<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">&quot;htest&quot;</span>
<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/return.html"><span style="color: #0000FF; font-weight: bold;">return</span></a><span style="color: #080;">&#40;</span>rval<span style="color: #080;">&#41;</span>
<span style="color: #080;">&#125;</span>
pw <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/function.html"><span style="color: #0000FF; font-weight: bold;">function</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/q.html"><span style="color: #0000FF; font-weight: bold;">q</span></a>,n<span style="color: #080;">&#41;</span> <span style="color: #080;">&#123;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/grDevices/html/pdf.html"><span style="color: #0000FF; font-weight: bold;">pdf</span></a> <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/function.html"><span style="color: #0000FF; font-weight: bold;">function</span></a><span style="color: #080;">&#40;</span>w<span style="color: #080;">&#41;</span> <span style="color: #080;">&#123;</span> <span style="color: #ff0000;">1</span><span style="color: #080;">/</span><span style="color: #ff0000;">2</span> <span style="color: #080;">*</span> <span style="color: #080;">&#40;</span>n<span style="color: #080;">-</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">*</span> w<span style="color: #080;">^</span><span style="color: #080;">&#40;</span><span style="color: #080;">&#40;</span>n<span style="color: #080;">-</span><span style="color: #ff0000;">3</span><span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">&#125;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/integrate.html"><span style="color: #0000FF; font-weight: bold;">integrate</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/grDevices/html/pdf.html"><span style="color: #0000FF; font-weight: bold;">pdf</span></a>,<span style="color: #ff0000;">0</span>,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/q.html"><span style="color: #0000FF; font-weight: bold;">q</span></a><span style="color: #080;">&#41;</span>
<span style="color: #080;">&#125;</span>
&nbsp;
varcomp <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/function.html"><span style="color: #0000FF; font-weight: bold;">function</span></a><span style="color: #080;">&#40;</span>covmat,n<span style="color: #080;">&#41;</span> <span style="color: #080;">&#123;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/is.list.html"><span style="color: #0000FF; font-weight: bold;">is.<span style="">list</span></span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span> <span style="color: #080;">&#123;</span>
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;</span> <span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/stop.html"><span style="color: #0000FF; font-weight: bold;">stop</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">&quot;covmat must be a list with at least 2 elements&quot;</span><span style="color: #080;">&#41;</span>
    ps <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/as.vector.html"><span style="color: #0000FF; font-weight: bold;">as.<span style="">vector</span></span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sapply.html"><span style="color: #0000FF; font-weight: bold;">sapply</span></a><span style="color: #080;">&#40;</span>covmat,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/dim.html"><span style="color: #0000FF; font-weight: bold;">dim</span></a><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ps<span style="color: #080;">&#91;</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#93;</span> <span style="color: #080;">==</span> ps<span style="color: #080;">&#41;</span> <span style="color: #080;">!=</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>ps<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/stop.html"><span style="color: #0000FF; font-weight: bold;">stop</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">&quot;all covariance matrices must have the same dimension&quot;</span><span style="color: #080;">&#41;</span>
    p <span style="color: #080;">&lt;-</span> ps<span style="color: #080;">&#91;</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#93;</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/q.html"><span style="color: #0000FF; font-weight: bold;">q</span></a> <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>n<span style="color: #080;">&#41;</span> <span style="color: #080;">==</span> <span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span>
        Ng <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/rep.html"><span style="color: #0000FF; font-weight: bold;">rep</span></a><span style="color: #080;">&#40;</span>n,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/q.html"><span style="color: #0000FF; font-weight: bold;">q</span></a><span style="color: #080;">&#41;</span>
    <span style="color: #0000FF; font-weight: bold;">else</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/if.html"><span style="color: #0000FF; font-weight: bold;">if</span></a> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>n<span style="color: #080;">&#41;</span> <span style="color: #080;">==</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/q.html"><span style="color: #0000FF; font-weight: bold;">q</span></a><span style="color: #080;">&#41;</span>
        Ng <span style="color: #080;">&lt;-</span> n
    <span style="color: #0000FF; font-weight: bold;">else</span>
        <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/stop.html"><span style="color: #0000FF; font-weight: bold;">stop</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">&quot;n must be equal length(covmat) or 1&quot;</span><span style="color: #080;">&#41;</span>
&nbsp;
    DNAME <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/deparse.html"><span style="color: #0000FF; font-weight: bold;">deparse</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/substitute.html"><span style="color: #0000FF; font-weight: bold;">substitute</span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
   <span style="color: #080;">&#125;</span>
&nbsp;
   <span style="color: #0000FF; font-weight: bold;">else</span>
    <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/stop.html"><span style="color: #0000FF; font-weight: bold;">stop</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">&quot;covmat must be a list&quot;</span><span style="color: #080;">&#41;</span>
&nbsp;
   ng <span style="color: #080;">&lt;-</span> Ng <span style="color: #080;">-</span> <span style="color: #ff0000;">1</span>
   Ag <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/lapply.html"><span style="color: #0000FF; font-weight: bold;">lapply</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">:</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/length.html"><span style="color: #0000FF; font-weight: bold;">length</span></a><span style="color: #080;">&#40;</span>covmat<span style="color: #080;">&#41;</span>,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/function.html"><span style="color: #0000FF; font-weight: bold;">function</span></a><span style="color: #080;">&#40;</span>i,mat,n<span style="color: #080;">&#41;</span> <span style="color: #080;">&#123;</span> n<span style="color: #080;">&#91;</span>i<span style="color: #080;">&#93;</span> <span style="color: #080;">*</span> mat<span style="color: #080;">&#91;</span><span style="color: #080;">&#91;</span>i<span style="color: #080;">&#93;</span><span style="color: #080;">&#93;</span> <span style="color: #080;">&#125;</span>,mat<span style="color: #080;">=</span>covmat,n<span style="color: #080;">=</span>ng<span style="color: #080;">&#41;</span>
   A <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/matrix.html"><span style="color: #0000FF; font-weight: bold;">matrix</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/colSums.html"><span style="color: #0000FF; font-weight: bold;">colSums</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/matrix.html"><span style="color: #0000FF; font-weight: bold;">matrix</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/unlist.html"><span style="color: #0000FF; font-weight: bold;">unlist</span></a><span style="color: #080;">&#40;</span>Ag<span style="color: #080;">&#41;</span>,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/ncol.html"><span style="color: #0000FF; font-weight: bold;">ncol</span></a><span style="color: #080;">=</span>p<span style="color: #080;">^</span><span style="color: #ff0000;">2</span>,byrow<span style="color: #080;">=</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/T.html"><span style="color: #0000FF; font-weight: bold;">T</span></a><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/ncol.html"><span style="color: #0000FF; font-weight: bold;">ncol</span></a><span style="color: #080;">=</span>p<span style="color: #080;">&#41;</span>
   detAg <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sapply.html"><span style="color: #0000FF; font-weight: bold;">sapply</span></a><span style="color: #080;">&#40;</span>Ag,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/det.html"><span style="color: #0000FF; font-weight: bold;">det</span></a><span style="color: #080;">&#41;</span>
   detA <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/det.html"><span style="color: #0000FF; font-weight: bold;">det</span></a><span style="color: #080;">&#40;</span>A<span style="color: #080;">&#41;</span>
   V1 <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/prod.html"><span style="color: #0000FF; font-weight: bold;">prod</span></a><span style="color: #080;">&#40;</span>detAg<span style="color: #080;">^</span><span style="color: #080;">&#40;</span>ng<span style="color: #080;">/</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #080;">&#40;</span>detA<span style="color: #080;">^</span><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
   kg <span style="color: #080;">&lt;-</span> ng<span style="color: #080;">/</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span>
   l1 <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/prod.html"><span style="color: #0000FF; font-weight: bold;">prod</span></a><span style="color: #080;">&#40;</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">/</span>kg<span style="color: #080;">&#41;</span><span style="color: #080;">^</span>kg<span style="color: #080;">&#41;</span><span style="color: #080;">^</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">*</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">*</span> V1
   rho <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">1</span> <span style="color: #080;">-</span> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">/</span>ng<span style="color: #080;">&#41;</span> <span style="color: #080;">-</span> <span style="color: #ff0000;">1</span><span style="color: #080;">/</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">2</span><span style="color: #080;">*</span>p<span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">+</span><span style="color: #ff0000;">3</span><span style="color: #080;">*</span>p<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">/</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">6</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>q<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
   w2 <span style="color: #080;">&lt;-</span> p<span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span> <span style="color: #080;">*</span> <span style="color: #080;">&#40;</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">*</span> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">/</span>ng<span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">-</span> <span style="color: #ff0000;">1</span><span style="color: #080;">/</span><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/sum.html"><span style="color: #0000FF; font-weight: bold;">sum</span></a><span style="color: #080;">&#40;</span>ng<span style="color: #080;">&#41;</span><span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span> <span style="color: #080;">-</span> <span style="color: #ff0000;">6</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span>q<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span><span style="color: #080;">&#40;</span><span style="color: #ff0000;">1</span><span style="color: #080;">-</span>rho<span style="color: #080;">&#41;</span><span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span> <span style="color: #080;">/</span> <span style="color: #080;">&#40;</span><span style="color: #ff0000;">48</span><span style="color: #080;">*</span>rho<span style="color: #080;">^</span><span style="color: #ff0000;">2</span><span style="color: #080;">&#41;</span>
   f <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">0.5</span> <span style="color: #080;">*</span> <span style="color: #080;">&#40;</span>q<span style="color: #080;">-</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span><span style="color: #080;">*</span>p<span style="color: #080;">*</span><span style="color: #080;">&#40;</span>p<span style="color: #080;">+</span><span style="color: #ff0000;">1</span><span style="color: #080;">&#41;</span>
   STATISTIC <span style="color: #080;">&lt;-</span> <span style="color: #080;">-</span><span style="color: #ff0000;">2</span><span style="color: #080;">*</span>rho<span style="color: #080;">*</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/log.html"><span style="color: #0000FF; font-weight: bold;">log</span></a><span style="color: #080;">&#40;</span>l1<span style="color: #080;">&#41;</span>
   PVAL <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">1</span> <span style="color: #080;">-</span> <span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/pchisq.html"><span style="color: #0000FF; font-weight: bold;">pchisq</span></a><span style="color: #080;">&#40;</span>STATISTIC,f<span style="color: #080;">&#41;</span> <span style="color: #080;">+</span> w2<span style="color: #080;">*</span><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/pchisq.html"><span style="color: #0000FF; font-weight: bold;">pchisq</span></a><span style="color: #080;">&#40;</span>STATISTIC,f<span style="color: #080;">+</span><span style="color: #ff0000;">4</span><span style="color: #080;">&#41;</span> <span style="color: #080;">-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/stats/html/pchisq.html"><span style="color: #0000FF; font-weight: bold;">pchisq</span></a><span style="color: #080;">&#40;</span>STATISTIC,f<span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span><span style="color: #080;">&#41;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/names.html"><span style="color: #0000FF; font-weight: bold;">names</span></a><span style="color: #080;">&#40;</span>STATISTIC<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">&quot;corrected lambda*&quot;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/names.html"><span style="color: #0000FF; font-weight: bold;">names</span></a><span style="color: #080;">&#40;</span>f<span style="color: #080;">&#41;</span> <span style="color: #080;">&lt;-</span> <span style="color: #ff0000;">&quot;df&quot;</span>
   RVAL <span style="color: #080;">&lt;-</span> <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/structure.html"><span style="color: #0000FF; font-weight: bold;">structure</span></a><span style="color: #080;">&#40;</span><a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/list.html"><span style="color: #0000FF; font-weight: bold;">list</span></a><span style="color: #080;">&#40;</span>statistic <span style="color: #080;">=</span> STATISTIC, parameter <span style="color: #080;">=</span> f,p.<span style="">value</span> <span style="color: #080;">=</span> PVAL, data.<span style="">name</span> <span style="color: #080;">=</span> DNAME, method <span style="color: #080;">=</span> <span style="color: #ff0000;">&quot;Equality of Covariances Matrices Test&quot;</span><span style="color: #080;">&#41;</span>,<a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/class.html"><span style="color: #0000FF; font-weight: bold;">class</span></a><span style="color: #080;">=</span><span style="color: #ff0000;">&quot;htest&quot;</span><span style="color: #080;">&#41;</span>
   <a href="http://stat.ethz.ch/R-manual/R-devel/library/base/html/return.html"><span style="color: #0000FF; font-weight: bold;">return</span></a><span style="color: #080;">&#40;</span>RVAL<span style="color: #080;">&#41;</span>
<span style="color: #080;">&#125;</span></pre></td></tr></table></div>

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		<title>Miracle Fruit Tablets</title>
		<link>http://www.fernandohrosa.com.br/en/P/miracle-fruit-tablets/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=miracle-fruit-tablets</link>
		<comments>http://www.fernandohrosa.com.br/en/P/miracle-fruit-tablets/#comments</comments>
		<pubDate>Fri, 22 Apr 2011 00:05:14 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[Daily Life]]></category>
		<category><![CDATA[miracle fruit]]></category>
		<category><![CDATA[sensory]]></category>

		<guid isPermaLink="false">http://www.fernandohrosa.com.br/en/?p=67</guid>
		<description><![CDATA[The fruit below is called Synsepalum dulcificum, or in common parlance miraculous berry, and was discovered in Africa in 1725, where it was chewed by local tribes before meals. The most interesting aspect of this fruit is that it causes a change in gustatory perception to whoever chews it, making that every sour/citric flavour be [...]]]></description>
			<content:encoded><![CDATA[<p>The fruit below is called <a href="http://en.wikipedia.org/wiki/Synsepalum_dulcificum">Synsepalum dulcificum</a>, or in common parlance miraculous berry, and was discovered in Africa in 1725, where it was chewed by local tribes before meals. The most interesting aspect of this fruit is that it causes a change in gustatory perception to whoever chews it, making that every sour/citric flavour be perceived as sweet instead (for example limes, watercress). The effect lasts usually from 30 minutes to 2 hours in most cases.</p>
<p>Fortunately it is not necessary to go to Africa just to prove the berries, in these modern times you don&#8217;t even have to plant them in your garden. The company <a href="http://www.mymfruit.com/index.html">My M Fruit LLC</a> sells a tablet version, ready (and safe) for consumption. As in every trip to the USA I can&#8217;t help making a online order at <a href="http://www.thinkgeek.com">ThinkGeek.com</a>, last March I couldn&#8217;t miss the chance to buy a few gadgets, the miracle fruit tablets included:</p>
<div id="attachment_180" class="wp-caption aligncenter" style="width: 298px"><a href="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/miraculum.png"><img class="size-full wp-image-180  " title="miraculum" src="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/miraculum.png" alt="" width="288" height="184" /></a><p class="wp-caption-text">Miracle Fruit Tablets</p></div>
<p>The first step was to set an experiment to test the tablets effect. As I did not have any option of citric fruits at hand, we grabbed the next best thing available, so we headed to the pantry and got to our powdered beverages supply:</p>
<div id="attachment_182" class="wp-caption aligncenter" style="width: 394px"><a href="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/estoque-tang.jpg"><img class="size-full wp-image-182  " title="estoque-tang" src="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/estoque-tang.jpg" alt="" width="384" height="216" /></a><p class="wp-caption-text">Depleting the household Tang/Clight supply. (Clight is how Crystal Light is called in Brazil).</p></div>
<p>Final decision was for Clight Tangerine, since it does not have sugar in its formulation and we were trying to rule out this effect. Next step was preparing the drink: we wanted to make the acidity stand out, so we diluted in a concentration 8 times higher than the recommended on the preparing instructions on the packaging (2 pouches of Clight into 1/4 liters of water instead of the regular 1 pouch for 1 liter):</p>
<div id="attachment_185" class="wp-caption aligncenter" style="width: 310px"><a href="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/concentrado.jpg"><img class="size-medium wp-image-185" title="concentrado" src="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/concentrado-300x261.jpg" alt="" width="300" height="261" /></a><p class="wp-caption-text">Super-concentrate of Tangerine</p></div>
<p>As comparison reference, we also prepared according to the recommended dosis (1L, 1 pouch) and put them side by side:</p>
<div id="attachment_186" class="wp-caption aligncenter" style="width: 310px"><a href="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/ladoalado.jpg"><img class="size-medium wp-image-186" title="clight-ladoalado" src="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/ladoalado-300x168.jpg" alt="" width="300" height="168" /></a><p class="wp-caption-text">To the right the 8x concentrate (Power tangerine) and to the left the regular one.</p></div>
<p>We first tasted both drinks before proving the tablets, as a reference before having the &#8216;miraculous&#8217; effect. The regular one was fine, but the super-concentrate was almost impossible to taste. As you can see by the picture, it was really stronger than usual, with acidity topping as far as it can go. One sip on a empty stomach would be like a punch in the belly.</p>
<p>Following this me and the other two human guinea-pigs (my stepson and a friend), dissolved a tablet of the miracle berries each, and waited until it dissolved completely. The tablets taste a little sour themselves, but nothing unordinary. We then went on to prove the super-concentrate, and to our surprise it tasted surprisingly palatable. In fact, it was just a little more consistent than expected, but overall it tasted just like regular Tangerine juice, a little sweeter perhaps. You could drink a whole glass unwittingly. Apparently whatever there was of sour in it was &#8216;converted&#8217; into sweetness. Amazing.</p>
<p>For a comparison, we tasted the regular concentrate and it tasted little different from sugar water, very mild taste. No acidity at all. As an extension, we also tried tasting some watercress:</p>
<div id="attachment_187" class="wp-caption aligncenter" style="width: 310px"><a href="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/agriao.jpg"><img class="size-full wp-image-187" title="agriao" src="http://www.fernandohrosa.com.br/br/wp-content/uploads/2011/04/agriao.jpg" alt="" width="300" height="235" /></a><p class="wp-caption-text">Brazilian watercress</p></div>
<p>We tasted it without any seasoning, and the characteristic bitter taste was gone. It wasn&#8217;t converted into sweetness though, at least with only one tablet of miracle fruit. Perhaps the food you are tasting has to have already some sweet component to it so it can be potentialized. The watercress tasted much like lettuce, without any characteristic taste.</p>
<p>There are still several tablets left for testing, so if we come up with other tasting sessions I&#8217;d updated it here.</p>
<p>&nbsp;</p>
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		<title>Why should you consider using Pinboard?</title>
		<link>http://www.fernandohrosa.com.br/en/P/why_should_you_use_pinboard/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=why_should_you_use_pinboard</link>
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		<pubDate>Wed, 29 Dec 2010 23:11:38 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[Technology]]></category>
		<category><![CDATA[pinboard]]></category>
		<category><![CDATA[tagging]]></category>

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		<description><![CDATA[As a long-time del.icio.us user I was quite surprised when I first heard about the rumors about its shutdown by Yahoo. As I dug further into it I came across their official blog post dated December 17th, and decided to wait sometime before making a move, figuring Yahoo would not simply shutdown the service without [...]]]></description>
			<content:encoded><![CDATA[<p>As a long-time del.icio.us user I was quite surprised when I first heard about the <a href="http://www.pcmag.com/article2/0,2817,2374446,00.asp">rumors about its shutdown</a> by Yahoo. As I dug further into it I came across their <a href="http://blog.delicious.com/index.htm">official blog post</a> dated December 17th, and decided to wait sometime before making a move, figuring Yahoo would not simply shutdown the service without ample notice. <a href="http://news.slashdot.org/comments.pl?sid=1916104&amp;cid=34599722">This comment</a> on Slashdot was eye-opening though, and after perusing some of the alternatives (Diigo, Historious, Pinboard.In) I settled with <a href="http://www.pinboard.in">Pinboard.In</a> and their <a href="http://pinboard.in/tour/#archive">archiving plan</a>. I&#8217;m pretty happy with the choice and this article aims helping you make an informed decision. If you&#8217;re still not using tagged bookmarks, I&#8217;ll try to explain some of the rationale and why it&#8217;s a good idea to start using them.</p>
<h2>Tags versus folders</h2>
<p>I&#8217;ve lost count of how many different favorite files I had since I started using the web in 1997, across different browsers and operating systems. However, something was constant throughout this time frame: my favorites would inevitably get disorganized, no matter how hard I tried to find a sane folder structure to file them. Then from time to time I&#8217;d find myself refiling &amp; reorganizing, only to have it in a mess a couple of months later. That&#8217;s when del.icio.us came in with the brilliant idea of tagging your links, instead of filing them into folders. Now that eliminates the need for finding a right folder to store that particular link. You just pick as many tags as you want, and when you want to find this link again, you just look for tags you might have applied to it.</p>
<p>Tagging in itself is nowadays a no-brainer, so the basic drill is the same as in delicious. One issue that I had with delicious though, is that a lot of what I bookmark are very specific pages, and in many instances, even with the massive multi-million user base of delicious, no tag suggestions would appear for them. This is generally the case with the bookmarks on statistical science. Sometimes I would tag them as &#8216;stats&#8217;, sometimes as &#8216;stat&#8217;, and when feeling more verbose, &#8216;statistics&#8217; or &#8216;statistic&#8217;. I eventually standardized on plurals, so that reduced the number of tags referring to the same thing as only 2 (stats or statistics) but that was still annoying. Pinboard offers a bulk-edit feature that was perfect to fix this: this allowed me resolve all the tags conflicts I had in my archive.</p>
<h2>Link Rot</h2>
<p>It&#8217;s impressive the amount of link rot that you accumulate over you web life. It&#8217;s very frustrating when you remember you have a solution to a problem in one of your bookmarks, only to find that the bookmark is no longer available. In cases when you spot right away that you will need to revisit it or need to be sure that you will be able to use it as a reference, save an offline copy for safety right away. For all the other cases, Pinboard.In archiving feature is a life saver. For 25$ a year, they will store a full copy of every page you bookmark, together with all the dependencies necessary to render it (such as CSS files, images, flash). This is a clear advantage when compared to Diigo or Historious, as you can see in more details in their blog post: <a href="http://pinboard.in/blog/153">Bookmark Archives That Don&#8217;t</a>.</p>
<h2>Wrap-Up</h2>
<p>I hope you were convinced that tagging is a much better approach than filing into folders for bookmarking. In any case, be it that you decide to use Pinboard.In as well, or keep with delicious or other on-line or offline bookmark archiving solution, remember to regularly <a href="http://www.archiveteam.org/index.php?title=Introduction">back up your data</a>. Currently Pinboard.In does not offer an option to back up the archived pages[1], but you can use the export facility (<a href="http://pinboard.in/howto/#export">http://pinboard.in/howto/#export</a>) to fetch a single file containing all your links, together with tags and notes.</p>
<p>[1]A feature to download archives for local backup is on their <a href="http://pinboard.in/roadmap">road map</a>.</p>
<h2><a name="promo"></a>Instant Promotion</h2>
<p>In the spirit of PinboardIn <a href="http://pinboard.in/blog/161/">Christmas promotion</a>, I&#8217;m offering a similar (albeit humbler one) until January 20th to the first 3 (three) libertarians to comment on this post, with a brief (not smaller than 30 chars, but not larger than 400 chars) description of why they hold this political position. The first three qualifying comments will be published on the website after proper vetting. The authors will receive the activation codes by e-mail. Please note that this promotion is fernandohrosa.com.br&#8217;s responsibility and the founders and maintainers of PinboardIn are not in any way associated with this. In case you have any questions or complaints regarding the promotion you should contact me through the contact section of the site, since PinboardIn won&#8217;t be able to help you with this. In case there are no qualifying comments posted and vetted by January 20th, the promotion will be canceled.</p>
<p>* Please note: LIBERTARIANS, not LIBRARIANS.</p>
 <p><a href="http://www.fernandohrosa.com.br/en/?flattrss_redirect&amp;id=16&amp;md5=f2a1559c81404756c9cbd7d0856b9364" title="Flattr" target="_blank"><img src="http://www.fernandohrosa.com.br/en/wp-content/plugins/flattr/img/flattr-badge-large.png" alt="flattr this!"/></a></p>]]></content:encoded>
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		<title>R2HTML Package</title>
		<link>http://www.fernandohrosa.com.br/en/P/r2html-package/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=r2html-package</link>
		<comments>http://www.fernandohrosa.com.br/en/P/r2html-package/#comments</comments>
		<pubDate>Sun, 01 Aug 2010 23:25:43 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[R]]></category>
		<category><![CDATA[Statistics]]></category>
		<category><![CDATA[development]]></category>
		<category><![CDATA[HTML]]></category>
		<category><![CDATA[Packages]]></category>

		<guid isPermaLink="false">http://www.fernandohrosa.com.br/en/?p=183</guid>
		<description><![CDATA[Introduction R2HTML is an R package, written and maintained by Eric Lecoutre currently maintained by me. It provides functions and methods to output different R objects to HTML files. It also has a Sweave driver to allow parsing of HTML files containing R code and automatically write the corresponding outputs. Current released version: 1.59 Download [...]]]></description>
			<content:encoded><![CDATA[<div class='et-box et-info'>
					<div class='et-box-content'>Update: I maintained R2HTML from the original pub date of this post (2005) up until version 1.59, but no longer maintain it. Maintenance is now back to the author of the package (Eric Lecoutre). Keeping this page just for posterity.</div></div>
<h2>Introduction</h2>
<p>R2HTML is an <a href="http://www.R-project.org">R</a> package, written and maintained by Eric Lecoutre <del datetime="2011-10-15T23:25:44+00:00"> currently maintained by me</del>. It provides functions and methods to output different R objects to HTML files. It also has a Sweave driver to allow parsing of HTML files containing R code and automatically write the corresponding outputs.</p>
<h2>Current released version: <del datetime="2011-10-15T23:25:44+00:00">1.59</del></h2>
<p>Download source from CRAN: <a href="http://cran-r.c3sl.ufpr.br/src/contrib/R2HTML_1.59.tar.gz">R2HTML_1.59.tar.gz</a>.</p>
<h2>Latest development snapshot (to be 1.60)</h2>
<p>This package is being maintained on Sourceforge.net now. Please check its project page on <a href="http://sourceforge.net/projects/r2html/">http://sourceforge.net/projects/r2html/</a> for latest development snapshots and package releases.</p>
<h2>Subversion (SVN) Access</h2>
<p>Anonymous SVN access is provided for read-only via Sourceforge.net now. The repository address is: https://r2html.svn.sourceforge.net/svnroot/r2html. To checkout a working copy of the current development version, try:</p>

<div class="wp_codebox_msgheader"><span class="right"></span><span class="left"><a href="javascript:;" onclick="javascript:showCodeTxt('p183code8'); return false;">View Code</a> BASH</span><div class="codebox_clear"></div></div><div class="wp_codebox"><table><tr id="p1838"><td class="line_numbers"><pre>1
</pre></td><td class="code" id="p183code8"><pre class="bash" style="font-family:monospace;"><span style="color: #666666;">$ </span><span style="color: #c20cb9; font-weight: bold;">svn co</span> https:<span style="color: #000000; font-weight: bold;">//</span>r2html.svn.sourceforge.net<span style="color: #000000; font-weight: bold;">/</span>svnroot<span style="color: #000000; font-weight: bold;">/</span>r2html<span style="color: #000000; font-weight: bold;">/</span>trunk</pre></td></tr></table></div>

<h2>Todo List</h2>
<ul>
<li> Add method for printing epitools objects, as suggested by Ulrike Grömping.</li>
<li> Improvement of HTML.matrix(), which currently is generating invalid HTML code.</li>
<li> Overall improvement of CSS used.</li>
<li> As pointed out by Kurt Hornik, HTMLcore.R uses global variables and manipulates the user&#8217;s workspace, which is not a very recommended programming practice on R. A rewrite of the mechanism used to keep track of the .HTMLfile in use is needed, using, as suggested by Hornik, a dynamic variable inside the package.</li>
</ul>
<h2>Documentation</h2>
<p>The following RNews article by Eric Lecoutre is a good introduction to the package capabilities:</p>
<ul>
<li>
		Lecoutre, Eric (2003). <a href="http://cran.r-project.org/doc/Rnews/Rnews_2003-3.pdf">The R2HTML Package</a>. R News, Vol 3. N. 3,<br />
  Vienna, Austria.
		</li>
</ul>
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		<title>Printing to PostScript in Windows 7 (or where did Apple Color LW 12/660 go?)</title>
		<link>http://www.fernandohrosa.com.br/en/P/printing_ps_in_windows_7_or_where_did_apple_ls_12_660_go/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=printing_ps_in_windows_7_or_where_did_apple_ls_12_660_go</link>
		<comments>http://www.fernandohrosa.com.br/en/P/printing_ps_in_windows_7_or_where_did_apple_ls_12_660_go/#comments</comments>
		<pubDate>Sat, 03 Apr 2010 23:59:53 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[Technology]]></category>
		<category><![CDATA[linux]]></category>
		<category><![CDATA[printing]]></category>
		<category><![CDATA[windows]]></category>

		<guid isPermaLink="false">http://www.fernandohrosa.com.br/en/?p=8</guid>
		<description><![CDATA[1 &#8211; Windows 7: First Impressions I&#8217;ve recently purchased a copy of Windows 7 for my wife&#8217;s computer, and I have to say that it is indeed a quite nice jump ahead in terms of quality in comparison to Windows XP. After installing it and using it for a while I can certainly vouch that [...]]]></description>
			<content:encoded><![CDATA[<h2>1 &#8211;  Windows 7: First Impressions</h2>
<p>I&#8217;ve recently purchased a copy of Windows 7 for my wife&#8217;s computer, and I have to say that it is indeed a quite nice jump ahead in terms of quality in comparison to Windows XP. After installing it and using it for a while I can certainly vouch that Windows seems to be ready for the Desktop again. Ubuntu for quite sometime was very much ahead of Windows, but now the distance seems to have narrowed. For my own computer I&#8217;d definitely not consider anything but Linux for the moment, but Windows can now be considered seriously again as a desktop OS.</p>
<p>Installation was pretty effortless, asking a couple of questions about my locale and keyboard, and it ran pretty much unattended. Pretty much like installing Ubuntu: no need to download any driver off the internet, it simply worked out of the box after installation. Only one minor nuisance: MS apparently hasn&#8217;t still figured out how to not need to reboot your PC countless times every time you do any system modification. There was a notice to that effect during the setup screens: &#8220;Your computer will need to reboot several times during setup&#8221;. Well, at least it required no attendance from me, but still, you kind of expect Microsoft would have figured a way out of their reset addiction by now.</p>
<h2>2 &#8211; Issues</h2>
<p>The idea was to have this post as a placeholder where I&#8217;d add issues with the migration, but so far the only problem I had was with the printer driver for generating PostScript files. If there are more issues later, I&#8217;ll post them here.</p>
<h3>2.1 &#8211;  Apple Color LW 12/660 PS driver gone missing</h3>
<p>As my main PC runs GNU/Linux, I have set up a SAMBA Share using CUPS, for file and printer sharing. As it happens, when you map such a printer share on Windows, you need to set it up to print to a PostScript file. In Windows XP and earlier you&#8217;d look up Apple on the list of printer makers and choose &#8220;Apple Color LW 12/660 PS&#8221;. This also worked well if you set it up for printing to file and then saving the result as .ps file:</p>
<div class="imgborder"><img class="size-full wp-image-9 aligncenter" title="Printer-WinXP" src="http://www.fernandohrosa.com.br/en/wp-content/uploads/2011/04/Printer-WinXP.png" alt="Install Printer Dialog in Windows XP" width="498" height="387" /></div>
<p>In Windows Vista that option wasn&#8217;t available. Doing a cursory search on the interweb I came across a workaround: using the maker Generic and the printer &#8220;MS Publisher Imagesetter&#8221;. I haven&#8217;t tried writing to a file, but sending it to CUPS via the samba share worked nicely:</p>
<div class="imgborder">
<div id="attachment_10" class="wp-caption aligncenter" style="width: 639px"><img class="size-full wp-image-10" title="Printer-Win7" src="http://www.fernandohrosa.com.br/en/wp-content/uploads/2011/04/Printer-Win7.png" alt="Install Printer Dialog in Windows 7" width="629" height="463" /><p class="wp-caption-text">Install Printer Dialog in Windows 7</p></div>
</div>
<p>That&#8217;s it for now. I&#8217;ll post updates if there are any more issues.</p>
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		<title>South Park strikes again</title>
		<link>http://www.fernandohrosa.com.br/en/P/south-park-strikes-again/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=south-park-strikes-again</link>
		<comments>http://www.fernandohrosa.com.br/en/P/south-park-strikes-again/#comments</comments>
		<pubDate>Fri, 03 Oct 2008 00:49:36 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[Entertainment]]></category>
		<category><![CDATA[South Park]]></category>
		<category><![CDATA[TV]]></category>

		<guid isPermaLink="false">http://www.fernandohrosa.com.br/en/?p=20</guid>
		<description><![CDATA[On Southpark episode &#8216;Le Petit Tourette&#8217;, Cartman decides to appear on Dateline NBC, with Chris Hansen. On the episode we find out that Dateline is a show (which I promptly guessed to be fictional for its exaggeration&#8230;) that portrays a host who sets up dates with men who were trying to have intercourse with girls [...]]]></description>
			<content:encoded><![CDATA[<p>On Southpark episode &#8216;Le Petit Tourette&#8217;, Cartman decides to appear on Dateline NBC, with Chris Hansen. On the episode we find out that Dateline is a show (which I promptly guessed to be fictional for its exaggeration&#8230;) that portrays a host who sets up dates with men who were trying to have intercourse with girls under the age of consent. Guess what? SP strikes again! Dataline To Catch a Predator IS real, and it&#8217;s even more bizarre than depicted in the show. Check these out: <a href="http://www.youtube.com/watch?v=qVLT26CMzk4%20">http://www.youtube.com/watch?v=qVLT26CMzk4</a>, <a href="http://www.youtube.com/watch?v=rE2R_ACw3Rs&amp;feature=related">http://www.youtube.com/watch?v=rE2R_ACw3Rs&amp;feature=related</a> .</p>
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		<title>Digital Art</title>
		<link>http://www.fernandohrosa.com.br/en/P/digital_art/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=digital_art</link>
		<comments>http://www.fernandohrosa.com.br/en/P/digital_art/#comments</comments>
		<pubDate>Tue, 09 Sep 2008 00:52:39 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[Entertainment]]></category>
		<category><![CDATA[photography]]></category>

		<guid isPermaLink="false">http://www.fernandohrosa.com.br/en/?p=22</guid>
		<description><![CDATA[These are some trials I did with digital art around 1999. No definite thematic, just me playing around with some filters]]></description>
			<content:encoded><![CDATA[<p>These are some trials I did with digital art around 1999. No definite thematic, just me playing around with some filters</p>

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		<title>Financial Times on Islamic Finance</title>
		<link>http://www.fernandohrosa.com.br/en/P/islamic_finance/?utm_source=rss&#038;utm_medium=rss&#038;utm_campaign=islamic_finance</link>
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		<pubDate>Wed, 18 Jun 2008 01:34:04 +0000</pubDate>
		<dc:creator>fernandohrosa</dc:creator>
				<category><![CDATA[Finance]]></category>
		<category><![CDATA[finance]]></category>
		<category><![CDATA[religion]]></category>

		<guid isPermaLink="false">http://www.fernandohrosa.com.br/en/?p=30</guid>
		<description><![CDATA[Found a nice article on Financial Times today on Islamic Finance: Grappling with problems of success http://media.ft.com/cms/11cc1304-3c81-11dd-b958-0000779fd2ac.pdf Some interesting points: - &#8216;Yet, an industry where every product needs a religious stamp of approval is also starting to face some vital questions.&#8217; - &#8216;There are perhaps up to 100 religious experts who know enough about finance [...]]]></description>
			<content:encoded><![CDATA[<p>Found a nice article on Financial Times today on Islamic Finance:</p>
<p>Grappling with problems of success<br />
<a href="http://media.ft.com/cms/11cc1304-3c81-11dd-b958-0000779fd2ac.pdf">http://media.ft.com/cms/11cc1304-3c81-11dd-b958-0000779fd2ac.pdf</a></p>
<p>Some interesting points:</p>
<blockquote><p>- &#8216;Yet, an industry where every product needs a religious stamp of approval<br />
is also starting to face some vital questions.&#8217;</p>
<p>- &#8216;There are perhaps up to 100 religious experts who know enough about<br />
finance and much of the industry relies on the top 12 scholars within that<br />
group.&#8217;</p>
<p>- &#8216;Dubai International Financial Centre and Cass Business School are<br />
offering an executive MBA programme in Islamic finance.&#8217;</p></blockquote>
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