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version 1.7, 2022/03/15 18:43:13
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| <body>
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| <title>IMaCh Cov rbiaspar.txt</title>
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| <font size="2">Imach version 0.98b, January 2006, 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 (-0.367), 70 (-0.389), 75 (-0.431), 80 (-0.474), 85 (-0.418), 90 (-0.361), 95 (-0.348),
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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 (0.332), 70 (0.327), 75 (0.317), 80 (0.292), 85 (0.282), 90 (0.309), 95 (0.322),
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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 (0.370), 70 (0.393), 75 (0.427), 80 (0.453), 85 (0.359), 90 (0.260), 95 (0.246),
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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 (0.050), 70 (0.040), 75 (0.025), 80 (0.023), 85 (0.081), 90 (0.109), 95 (0.105),
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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 (-0.471), 70 (-0.504), 75 (-0.560), 80 (-0.594), 85 (-0.519), 90 (-0.462), 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 (-0.044), 70 (-0.040), 75 (-0.035), 80 (-0.035), 85 (-0.059), 90 (-0.083), 95 (-0.079), |
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<html><head> |
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<title>IMaCh Cov biaspar-cov.htm</title></head> |
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<body><font size="2">0.99r24 <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=1+age+<br> |
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Current page is file <a href="biaspar-cov.htm">biaspar-cov.htm</a><br> |
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<h4>Matrix of variance-covariance of pairs of step probabilities</h4> |
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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> |
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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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<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>, |
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<br><img src="biaspar/VARPIJGR_biaspar_113-12.svg"> |
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<br> Correlation at age 70 (-0.351), 75 (-0.393), 80 (-0.446), 85 (-0.413), 90 (-0.358), 95 (-0.340), |
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<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>, |
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<br><img src="biaspar/VARPIJGR_biaspar_121-12.svg"> |
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<br> Correlation at age 70 (0.342), 75 (0.332), 80 (0.305), 85 (0.283), 90 (0.307), 95 (0.322), |
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<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>, |
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<br><img src="biaspar/VARPIJGR_biaspar_123-12.svg"> |
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<br> Correlation at age 70 (0.368), 75 (0.405), 80 (0.436), 85 (0.352), 90 (0.249), 95 (0.226), |
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<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>, |
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<br><img src="biaspar/VARPIJGR_biaspar_121-13.svg"> |
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<br> Correlation at age 70 (0.029), 75 (0.021), 80 (0.028), 85 (0.070), 90 (0.082), 95 (0.076), |
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<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>, |
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<br><img src="biaspar/VARPIJGR_biaspar_123-13.svg"> |
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<br> Correlation at age 70 (-0.461), 75 (-0.531), 80 (-0.579), 85 (-0.506), 90 (-0.442), 95 (-0.379), |
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<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>, |
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<br><img src="biaspar/VARPIJGR_biaspar_123-21.svg"> |
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<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 Thu May 20 15:42:13 2021 |
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<br>Local time at end Thu May 20 15:43:12 2021 |
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