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version 1.5, 2015/08/18 16:43:19
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<title>IMaCh Cov biaspar-cov.htm</title></head> |
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<body><font size="2">Imach version 0.98q5, August 2015,INED-EUROREVES-Institut de longevite-Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research 25293121), Intel Software 2015 <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 (-0.338), 70 (-0.360), 75 (-0.404), 80 (-0.456), 85 (-0.418), 90 (-0.359), 95 (-0.341), |
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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 (0.333), 70 (0.332), 75 (0.326), 80 (0.304), 85 (0.276), 90 (0.289), 95 (0.302), |
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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 (0.364), 70 (0.388), 75 (0.423), 80 (0.449), 85 (0.356), 90 (0.255), 95 (0.238), |
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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 (0.047), 70 (0.037), 75 (0.024), 80 (0.024), 85 (0.078), 90 (0.100), 95 (0.097), |
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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 (-0.409), 70 (-0.453), 75 (-0.528), 80 (-0.585), 85 (-0.513), 90 (-0.434), 95 (-0.363), |
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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 (-0.015), 70 (-0.013), 75 (-0.014), 80 (-0.029), 85 (-0.061), 90 (-0.062), 95 (-0.040),<br>Local time at start Tue Aug 18 18:20:44 2015 |
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<br>Local time at end Tue Aug 18 18:26:33 2015 |
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