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Tue Mar 15 18:43:13 2022 UTC (2 years, 7 months ago) by brouard
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Summary: IMaCh-0.99r24

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<title>IMaCh Cov biaspar-cov.htm</title></head>
 <body><font size="2">0.99r24 <br> $Revision: 1.7 $ $Date: 2022/03/15 18:43:13 $</font> <hr size="2" color="#EC5E5E"> 
Title=1st_example <br>Datafile=data1.txt Firstpass=1 Lastpass=4 Stepm=1 Weight=0 Model=1+age+<br>
Current page is file <a href="biaspar-cov.htm">biaspar-cov.htm</a><br>

<h4>Matrix of variance-covariance of pairs of step probabilities</h4>

Ellipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimated and drawn. It helps understanding how is the covariance between two incidences. They are expressed in year<sup>-1</sup> in order to be less dependent of stepm.<br>

<br> Contour plot corresponding to x'cov<sup>-1</sup>x = 4 (where x is the column vector (pij,pkl)) are drawn. It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 standard deviations wide on each axis. <br> Now, if both incidences are correlated (usual case) we diagonalised the inverse of the covariance matrix and made the appropriate rotation to look at the uncorrelated principal directions.<br>To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.<br> 

<p><br>Ellipsoids of confidence cov(p13,p12) expressed in year<sup>-1</sup> :<a href="biaspar/VARPIJGR_biaspar_113-12.svg">																		biaspar/VARPIJGR_biaspar_113-12.svg</A>, 
<br><img src="biaspar/VARPIJGR_biaspar_113-12.svg"> 
<br> Correlation at age 70 (-0.351), 75 (-0.393), 80 (-0.446), 85 (-0.413), 90 (-0.358), 95 (-0.340),
<p><br>Ellipsoids of confidence cov(p21,p12) expressed in year<sup>-1</sup> :<a href="biaspar/VARPIJGR_biaspar_121-12.svg">																		biaspar/VARPIJGR_biaspar_121-12.svg</A>, 
<br><img src="biaspar/VARPIJGR_biaspar_121-12.svg"> 
<br> Correlation at age 70 (0.342), 75 (0.332), 80 (0.305), 85 (0.283), 90 (0.307), 95 (0.322),
<p><br>Ellipsoids of confidence cov(p23,p12) expressed in year<sup>-1</sup> :<a href="biaspar/VARPIJGR_biaspar_123-12.svg">																		biaspar/VARPIJGR_biaspar_123-12.svg</A>, 
<br><img src="biaspar/VARPIJGR_biaspar_123-12.svg"> 
<br> Correlation at age 70 (0.368), 75 (0.405), 80 (0.436), 85 (0.352), 90 (0.249), 95 (0.226),
<p><br>Ellipsoids of confidence cov(p21,p13) expressed in year<sup>-1</sup> :<a href="biaspar/VARPIJGR_biaspar_121-13.svg">																		biaspar/VARPIJGR_biaspar_121-13.svg</A>, 
<br><img src="biaspar/VARPIJGR_biaspar_121-13.svg"> 
<br> Correlation at age 70 (0.029), 75 (0.021), 80 (0.028), 85 (0.070), 90 (0.082), 95 (0.076),
<p><br>Ellipsoids of confidence cov(p23,p13) expressed in year<sup>-1</sup> :<a href="biaspar/VARPIJGR_biaspar_123-13.svg">																		biaspar/VARPIJGR_biaspar_123-13.svg</A>, 
<br><img src="biaspar/VARPIJGR_biaspar_123-13.svg"> 
<br> Correlation at age 70 (-0.461), 75 (-0.531), 80 (-0.579), 85 (-0.506), 90 (-0.442), 95 (-0.379),
<p><br>Ellipsoids of confidence cov(p23,p21) expressed in year<sup>-1</sup> :<a href="biaspar/VARPIJGR_biaspar_123-21.svg">																		biaspar/VARPIJGR_biaspar_123-21.svg</A>, 
<br><img src="biaspar/VARPIJGR_biaspar_123-21.svg"> 
<br> Correlation at age 70 (-0.033), 75 (-0.032), 80 (-0.038), 85 (-0.055), 90 (-0.060), 95 (-0.050),<br>Local time at start Thu May 20 15:42:13 2021
<br>Local time at end   Thu May 20 15:43:12 2021
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