Figure 2: Parameter estimates with varying n for variables under the H1
hypothesis. This figure only concerns estimates for identification sets. Each
of the four panels was obtained with a specific sample size with n={100; 200;
400; 1000}. Whatever the panel, the following distributions were plotted: 1-distribution
of the estimates for the Ωp1 variables computed over 200 identification
sets (grey histogram). 2-distribution of the estimates for the ΩS set of variables
computed over 200 identification sets (histogram with horizontal hatching). The
vertical continuous line indicates 0.2.
With n=100, estimates for Ωp1 are highly fluctuating, as shown by the wide
distribution. Variables are selected in the extreme of the distributions of the
estimates for Ωp1, and these mean estimates are thus far from their true means.
When increasing the sample sizes, the mean distribution of ΩS estimates
tends toward the mean distribution of Ωp1 estimates. This is an illustration of
the regression to the mean phenomenon that leads to over-estimation of the
strength of association for true positives. |
