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Tue Oct 25 11:53:26 2005 UTC (18 years, 8 months ago) by brouard
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    1: <body>
    2: <title>IMaCh Cov rbiaspar.txt</title>
    3:  <font size="2">Imach version 0.98, September 2005, INED-EUROREVES  <br> $Revision: 1.2 $ $Date: 2005/10/25 11:53:26 $</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 (-0.393), 70 (-0.413), 75 (-0.448), 80 (-0.477), 85 (-0.422), 90 (-0.376), 95 (-0.369),
   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 (0.317), 70 (0.314), 75 (0.307), 80 (0.290), 85 (0.281), 90 (0.298), 95 (0.306),
   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 (0.380), 70 (0.402), 75 (0.435), 80 (0.456), 85 (0.358), 90 (0.266), 95 (0.256),
   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 (0.029), 70 (0.021), 75 (0.010), 80 (0.018), 85 (0.079), 90 (0.099), 95 (0.091),
   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 (-0.473), 70 (-0.506), 75 (-0.561), 80 (-0.595), 85 (-0.519), 90 (-0.461), 95 (-0.418),
   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 (-0.027), 70 (-0.023), 75 (-0.021), 80 (-0.028), 85 (-0.059), 90 (-0.076), 95 (-0.064),
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