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1.5     ! brouard     1: <html><head>
        !             2: <title>IMaCh Cov biaspar-cov.htm</title></head>
        !             3:  <body><font size="2">Imach version 0.98q5, August 2015,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121), Intel Software 2015 <br> $Revision: 1.194 $ $Date: 2015/08/18 13:32:00 $</font> <hr size="2" color="#EC5E5E"> 
        !             4: Title=1st_example <br>Datafile=data1.txt Firstpass=1 Lastpass=4 Stepm=1 Weight=0 Model=<br>
        !             5: 
        !             6: <h4>Matrix of variance-covariance of pairs of step probabilities</h4>
        !             7:   file biaspar-cov.htm<br>
        !             8: 
        !             9: Ellipsoids of confidence centered on point (p<inf>ij</inf>, p<inf>kl</inf>) are estimatedand 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>
        !            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: 
        !            13: <br>Ellipsoids of confidence cov(p13,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar113-12.png">biaspar/varpijgrbiaspar113-12.png</A>, 
        !            14: <br><img src="biaspar/varpijgrbiaspar113-12.png"> 
        !            15: <br> Correlation at age 65 (-0.338), 70 (-0.360), 75 (-0.404), 80 (-0.456), 85 (-0.418), 90 (-0.359), 95 (-0.341),
        !            16: <br>Ellipsoids of confidence cov(p21,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar121-12.png">biaspar/varpijgrbiaspar121-12.png</A>, 
        !            17: <br><img src="biaspar/varpijgrbiaspar121-12.png"> 
        !            18: <br> Correlation at age 65 (0.333), 70 (0.332), 75 (0.326), 80 (0.304), 85 (0.276), 90 (0.289), 95 (0.302),
        !            19: <br>Ellipsoids of confidence cov(p23,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-12.png">biaspar/varpijgrbiaspar123-12.png</A>, 
        !            20: <br><img src="biaspar/varpijgrbiaspar123-12.png"> 
        !            21: <br> Correlation at age 65 (0.364), 70 (0.388), 75 (0.423), 80 (0.449), 85 (0.356), 90 (0.255), 95 (0.238),
        !            22: <br>Ellipsoids of confidence cov(p21,p13) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar121-13.png">biaspar/varpijgrbiaspar121-13.png</A>, 
        !            23: <br><img src="biaspar/varpijgrbiaspar121-13.png"> 
        !            24: <br> Correlation at age 65 (0.047), 70 (0.037), 75 (0.024), 80 (0.024), 85 (0.078), 90 (0.100), 95 (0.097),
        !            25: <br>Ellipsoids of confidence cov(p23,p13) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-13.png">biaspar/varpijgrbiaspar123-13.png</A>, 
        !            26: <br><img src="biaspar/varpijgrbiaspar123-13.png"> 
        !            27: <br> Correlation at age 65 (-0.409), 70 (-0.453), 75 (-0.528), 80 (-0.585), 85 (-0.513), 90 (-0.434), 95 (-0.363),
        !            28: <br>Ellipsoids of confidence cov(p23,p21) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-21.png">biaspar/varpijgrbiaspar123-21.png</A>, 
        !            29: <br><img src="biaspar/varpijgrbiaspar123-21.png"> 
        !            30: <br> Correlation at age 65 (-0.015), 70 (-0.013), 75 (-0.014), 80 (-0.029), 85 (-0.061), 90 (-0.062), 95 (-0.040),<br>Local time at start Tue Aug 18 18:20:44 2015
        !            31: <br>Local time at end   Tue Aug 18 18:26:33 2015
        !            32: <br>
        !            33: </body></html>
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