--- imach/html/doc/biaspar-cov.htm 2015/08/04 07:14:48 1.4 +++ imach/html/doc/biaspar-cov.htm 2015/08/18 16:43:19 1.5 @@ -0,0 +1,33 @@ + +IMaCh Cov biaspar-cov.htm + 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
$Revision: 1.5 $ $Date: 2015/08/18 16:43:19 $
+Title=1st_example
Datafile=data1.txt Firstpass=1 Lastpass=4 Stepm=1 Weight=0 Model=
+ +

Matrix of variance-covariance of pairs of step probabilities

+ file biaspar-cov.htm
+ +Ellipsoids of confidence centered on point (pij, pkl) are estimatedand drawn. It helps understanding how is the covariance between two incidences. They are expressed in year-1 in order to be less dependent of stepm.
+ +
Contour plot corresponding to x'cov-1x = 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.
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.
To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.
+ +
Ellipsoids of confidence cov(p13,p12) expressed in year-1 :biaspar/varpijgrbiaspar113-12.png, +
+
Correlation at age 65 (-0.338), 70 (-0.360), 75 (-0.404), 80 (-0.456), 85 (-0.418), 90 (-0.359), 95 (-0.341), +
Ellipsoids of confidence cov(p21,p12) expressed in year-1 :biaspar/varpijgrbiaspar121-12.png, +
+
Correlation at age 65 (0.333), 70 (0.332), 75 (0.326), 80 (0.304), 85 (0.276), 90 (0.289), 95 (0.302), +
Ellipsoids of confidence cov(p23,p12) expressed in year-1 :biaspar/varpijgrbiaspar123-12.png, +
+
Correlation at age 65 (0.364), 70 (0.388), 75 (0.423), 80 (0.449), 85 (0.356), 90 (0.255), 95 (0.238), +
Ellipsoids of confidence cov(p21,p13) expressed in year-1 :biaspar/varpijgrbiaspar121-13.png, +
+
Correlation at age 65 (0.047), 70 (0.037), 75 (0.024), 80 (0.024), 85 (0.078), 90 (0.100), 95 (0.097), +
Ellipsoids of confidence cov(p23,p13) expressed in year-1 :biaspar/varpijgrbiaspar123-13.png, +
+
Correlation at age 65 (-0.409), 70 (-0.453), 75 (-0.528), 80 (-0.585), 85 (-0.513), 90 (-0.434), 95 (-0.363), +
Ellipsoids of confidence cov(p23,p21) expressed in year-1 :biaspar/varpijgrbiaspar123-21.png, +
+
Correlation at age 65 (-0.015), 70 (-0.013), 75 (-0.014), 80 (-0.029), 85 (-0.061), 90 (-0.062), 95 (-0.040),
Local time at start Tue Aug 18 18:20:44 2015 +
Local time at end Tue Aug 18 18:26:33 2015 +
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