Tests pour la dépendance entre les sections dans un modèle de Poisson
For panel data, repeated measures over time can challenge the hypothesis of dependence between subjects. Tests were developped in order to assess if some dependence remains among residuals. The three tests we present in this master thesis are from Pesaran (2004), Friedman (1937) and Frees (1995). These three tests, constructed specifically for linear models, are based on the residuals generated from models (and their correlations). We wish to study in this master thesis the performances of these three tests in the case of generalized linear Poisson models. For that goal, we compare them between each other (level, power, etc.) using two linear models, one with an autoregressive term and the other without. Next, inspired by Hsiao, Pesaran and Pick (2007) who adapt the test from Pesaran (2004), we will study their performances in a generalized Poisson model. All of our comparisons are done with simulations by modifying some variables (number of observations, strength of the dependence). We will observe that when the correlation is always of the same sign, Pesaran’s test is the best in most cases, for the linear models and the generalized linear model. Frees’ test will show good performances when the sign of the correlations alternates.
Poisson Test Residuals Regression Linear model Generalized linear model Panel data Dependence