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Wed Jun 16 21:44:30 2004 UTC (20 years ago) by brouard
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    1: <body>
    2: <title>IMaCh Cov rbiaspar.txt</title>
    3:  <font size="2">Imach version 0.07a, May 2004, INED-EUROREVES  <br> $Revision: 1.1 $ $Date: 2004/06/16 21:44:30 $</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 (-0.365), 70 (-0.388), 75 (-0.431), 80 (-0.475), 85 (-0.419), 90 (-0.360), 95 (-0.346),
   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 (0.346), 70 (0.341), 75 (0.328), 80 (0.297), 85 (0.283), 90 (0.316), 95 (0.332),
   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 (0.367), 70 (0.390), 75 (0.426), 80 (0.453), 85 (0.359), 90 (0.257), 95 (0.241),
   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 (0.034), 70 (0.024), 75 (0.012), 80 (0.017), 85 (0.080), 90 (0.103), 95 (0.096),
   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 (-0.456), 70 (-0.492), 75 (-0.552), 80 (-0.594), 85 (-0.523), 90 (-0.456), 95 (-0.404),
   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 (-0.025), 70 (-0.022), 75 (-0.020), 80 (-0.027), 85 (-0.060), 90 (-0.077), 95 (-0.065),
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