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1.5       brouard     1: <html><head>
                      2: <title>IMaCh Cov biaspar-cov.htm</title></head>
1.7     ! brouard     3:  <body><font size="2">0.99r24 <br> $Revision: 1.309 $ $Date: 2021/05/20 12:39:14 $</font> <hr size="2" color="#EC5E5E"> 
1.6       brouard     4: Title=1st_example <br>Datafile=data1.txt Firstpass=1 Lastpass=4 Stepm=1 Weight=0 Model=1+age+<br>
                      5: Current page is file <a href="biaspar-cov.htm">biaspar-cov.htm</a><br>
1.5       brouard     6: 
                      7: <h4>Matrix of variance-covariance of pairs of step probabilities</h4>
                      8: 
1.6       brouard     9: 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>
1.5       brouard    10: 
                     11: <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> 
                     12: 
1.6       brouard    13: <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>, 
                     14: <br><img src="biaspar/VARPIJGR_biaspar_113-12.svg"> 
                     15: <br> Correlation at age 70 (-0.351), 75 (-0.393), 80 (-0.446), 85 (-0.413), 90 (-0.358), 95 (-0.340),
                     16: <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>, 
                     17: <br><img src="biaspar/VARPIJGR_biaspar_121-12.svg"> 
                     18: <br> Correlation at age 70 (0.342), 75 (0.332), 80 (0.305), 85 (0.283), 90 (0.307), 95 (0.322),
                     19: <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>, 
                     20: <br><img src="biaspar/VARPIJGR_biaspar_123-12.svg"> 
                     21: <br> Correlation at age 70 (0.368), 75 (0.405), 80 (0.436), 85 (0.352), 90 (0.249), 95 (0.226),
                     22: <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>, 
                     23: <br><img src="biaspar/VARPIJGR_biaspar_121-13.svg"> 
                     24: <br> Correlation at age 70 (0.029), 75 (0.021), 80 (0.028), 85 (0.070), 90 (0.082), 95 (0.076),
                     25: <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>, 
                     26: <br><img src="biaspar/VARPIJGR_biaspar_123-13.svg"> 
                     27: <br> Correlation at age 70 (-0.461), 75 (-0.531), 80 (-0.579), 85 (-0.506), 90 (-0.442), 95 (-0.379),
                     28: <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>, 
                     29: <br><img src="biaspar/VARPIJGR_biaspar_123-21.svg"> 
1.7     ! brouard    30: <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
        !            31: <br>Local time at end   Thu May 20 15:43:12 2021
1.5       brouard    32: <br>
                     33: </body></html>
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