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 <title>IMaCh Cov rbiaspar.txt</title>  <title>IMaCh Cov biaspar-cov.htm</title></head>
  <font size="2">Imach version 0.98, September 2005, INED-EUROREVES  <br> $Revision$ $Date$</font> <hr size="2" color="#EC5E5E">    <body><font size="2">0.99r19 <br> $Revision$ $Date$</font> <hr size="2" color="#EC5E5E"> 
 Title=1st_example <br>Datafile=data1.txt Firstpass=1 Lastpass=4 Stepm=1 Weight=0 Model=.<br>  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>  <h4>Matrix of variance-covariance of pairs of step probabilities</h4>
   file biaspar-cov.htm<br>  
   
 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>  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>   <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> 
   
 <br>Ellipsoids of confidence cov(p13,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar113-12.png">biaspar/varpijgrbiaspar113-12.png</A>,   
 <br><img src="biaspar/varpijgrbiaspar113-12.png">   
 <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),  
 <br>Ellipsoids of confidence cov(p21,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar121-12.png">biaspar/varpijgrbiaspar121-12.png</A>,   
 <br><img src="biaspar/varpijgrbiaspar121-12.png">   
 <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),  
 <br>Ellipsoids of confidence cov(p23,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-12.png">biaspar/varpijgrbiaspar123-12.png</A>,   
 <br><img src="biaspar/varpijgrbiaspar123-12.png">   
 <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),  
 <br>Ellipsoids of confidence cov(p21,p13) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar121-13.png">biaspar/varpijgrbiaspar121-13.png</A>,   
 <br><img src="biaspar/varpijgrbiaspar121-13.png">   
 <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),  
 <br>Ellipsoids of confidence cov(p23,p13) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-13.png">biaspar/varpijgrbiaspar123-13.png</A>,   
 <br><img src="biaspar/varpijgrbiaspar123-13.png">   
 <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),  
 <br>Ellipsoids of confidence cov(p23,p21) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-21.png">biaspar/varpijgrbiaspar123-21.png</A>,   
 <br><img src="biaspar/varpijgrbiaspar123-21.png">   
 <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),  
   
   <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 Wed May 22 22:32:36 2019
   <br>Local time at end   Wed May 22 22:34:09 2019
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