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version 1.1, 2004/06/16 21:44:30
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version 1.2, 2005/10/25 11:53:26
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| <body>
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| <title>IMaCh Cov rbiaspar.txt</title>
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| <font size="2">Imach version 0.07a, May 2004, INED-EUROREVES <br> $Revision$ $Date$</font> <hr size="2" color="#EC5E5E">
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| Title=1st_example <br>Datafile=data1.txt Firstpass=1 Lastpass=4 Stepm=1 Weight=0 Model=.<br>
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| <h4>Matrix of variance-covariance of pairs of step probabilities</h4>
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| file biaspar-cov.htm<br>
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| 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>
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| <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>
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| <br>Ellipsoids of confidence cov(p13,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar113-12.png">biaspar/varpijgrbiaspar113-12.png</A>,
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| <br><img src="biaspar/varpijgrbiaspar113-12.png">
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| <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),
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| <br>Ellipsoids of confidence cov(p21,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar121-12.png">biaspar/varpijgrbiaspar121-12.png</A>,
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| <br><img src="biaspar/varpijgrbiaspar121-12.png">
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| <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),
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| <br>Ellipsoids of confidence cov(p23,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-12.png">biaspar/varpijgrbiaspar123-12.png</A>,
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| <br><img src="biaspar/varpijgrbiaspar123-12.png">
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| <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),
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| <br>Ellipsoids of confidence cov(p21,p13) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar121-13.png">biaspar/varpijgrbiaspar121-13.png</A>,
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| <br><img src="biaspar/varpijgrbiaspar121-13.png">
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| <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),
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| <br>Ellipsoids of confidence cov(p23,p13) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-13.png">biaspar/varpijgrbiaspar123-13.png</A>,
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| <br><img src="biaspar/varpijgrbiaspar123-13.png">
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| <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),
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| <br>Ellipsoids of confidence cov(p23,p21) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-21.png">biaspar/varpijgrbiaspar123-21.png</A>,
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| <br><img src="biaspar/varpijgrbiaspar123-21.png">
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| <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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<body> |
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<title>IMaCh Cov rbiaspar.txt</title> |
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<font size="2">Imach version 0.98, September 2005, INED-EUROREVES <br> $Revision$ $Date$</font> <hr size="2" color="#EC5E5E"> |
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Title=1st_example <br>Datafile=data1.txt Firstpass=1 Lastpass=4 Stepm=1 Weight=0 Model=.<br> |
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<h4>Matrix of variance-covariance of pairs of step probabilities</h4> |
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file biaspar-cov.htm<br> |
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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> |
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<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> |
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<br>Ellipsoids of confidence cov(p13,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar113-12.png">biaspar/varpijgrbiaspar113-12.png</A>, |
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<br><img src="biaspar/varpijgrbiaspar113-12.png"> |
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<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), |
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<br>Ellipsoids of confidence cov(p21,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar121-12.png">biaspar/varpijgrbiaspar121-12.png</A>, |
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<br><img src="biaspar/varpijgrbiaspar121-12.png"> |
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<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), |
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<br>Ellipsoids of confidence cov(p23,p12) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-12.png">biaspar/varpijgrbiaspar123-12.png</A>, |
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<br><img src="biaspar/varpijgrbiaspar123-12.png"> |
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<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), |
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<br>Ellipsoids of confidence cov(p21,p13) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar121-13.png">biaspar/varpijgrbiaspar121-13.png</A>, |
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<br><img src="biaspar/varpijgrbiaspar121-13.png"> |
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<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), |
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<br>Ellipsoids of confidence cov(p23,p13) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-13.png">biaspar/varpijgrbiaspar123-13.png</A>, |
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<br><img src="biaspar/varpijgrbiaspar123-13.png"> |
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<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), |
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<br>Ellipsoids of confidence cov(p23,p21) expressed in year<sup>-1</sup> :<a href="biaspar/varpijgrbiaspar123-21.png">biaspar/varpijgrbiaspar123-21.png</A>, |
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<br><img src="biaspar/varpijgrbiaspar123-21.png"> |
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<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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