Overview

Abstract (English)

The dependence of an individual’s behavior on his affiliation with a group is often suspected. When there are many groups in the population under study, however, the size of the sample from each group is often small, even if the size of the whole sample is large. This makes it difficult to model and estimate the possible group dependence. If the factors that cause the variation of individuals’ behavior across the groups are observable, adding them to the list of explanatory variables may solve the problem; otherwise, one may try account for the group-dependence by merging the groups into a few larger groups and allowing the parameters to vary across the created larger groups. In either way, one may still wonder whether the group dependence has been well addressed by the resulting model. In this paper, we propose a test of parameter constancy over many groups. The proposed test uses a statistic obtained by taking a weighted average of a unbiasedly estimated quadratic form of the group mean score, evaluated with the parameter estimate obtained imposing the parameter constancy. Once suitably standardized, this statistic tends to be close to zero under the null, as the null hypothesis implies that the group mean score is zero, when evaluated with the true parameter value. Our test rejects the null when the standardized statistic exceeds the suitably chosen critical value. We establish the large sample properties of the proposed test and assess the finite sample performance of the test by Monte Carlo simulations.

Abstract (French)

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