IMaCh Cov rbiaspar.txt Imach version 0.98b, January 2006, INED-EUROREVES
$Revision: 1.3 $ $Date: 2006/02/09 15:20:33 $
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 (-0.367), 70 (-0.389), 75 (-0.431), 80 (-0.474), 85 (-0.418), 90 (-0.361), 95 (-0.348),
Ellipsoids of confidence cov(p21,p12) expressed in year-1 :biaspar/varpijgrbiaspar121-12.png,

Correlation at age 65 (0.332), 70 (0.327), 75 (0.317), 80 (0.292), 85 (0.282), 90 (0.309), 95 (0.322),
Ellipsoids of confidence cov(p23,p12) expressed in year-1 :biaspar/varpijgrbiaspar123-12.png,

Correlation at age 65 (0.370), 70 (0.393), 75 (0.427), 80 (0.453), 85 (0.359), 90 (0.260), 95 (0.246),
Ellipsoids of confidence cov(p21,p13) expressed in year-1 :biaspar/varpijgrbiaspar121-13.png,

Correlation at age 65 (0.050), 70 (0.040), 75 (0.025), 80 (0.023), 85 (0.081), 90 (0.109), 95 (0.105),
Ellipsoids of confidence cov(p23,p13) expressed in year-1 :biaspar/varpijgrbiaspar123-13.png,

Correlation at age 65 (-0.471), 70 (-0.504), 75 (-0.560), 80 (-0.594), 85 (-0.519), 90 (-0.462), 95 (-0.418),
Ellipsoids of confidence cov(p23,p21) expressed in year-1 :biaspar/varpijgrbiaspar123-21.png,

Correlation at age 65 (-0.044), 70 (-0.040), 75 (-0.035), 80 (-0.035), 85 (-0.059), 90 (-0.083), 95 (-0.079),