Résumé
Factor models were first developed and dealt with in the case where observations are assumed to be normally distributed. Estimation is then carried out using the Expectation-Maximization (EM) algorithm based on the fact that the expectation of the completed log-likelihood conditional to the data is available in such a case. More recently, a less restrictive framework has been considered, in which the distribution of the observations is assumed to belong to the exponential family. We call these models Generalized Linear Factor Models (GLFM). For want of an explicit expression of the expectation of the completed log-likelihood conditional to the data, estimation of a GLFM is currently carried out using Monte-Carlo methods, which are computationally intensive. Here, we propose a quicker estimation technique, based on the fact that the estimation of a Generalized Linear Model can be achieved using the Fisher's Score Algorithm (FSA), that iterates GLS on a locally linearized model. The linearized model mimicking a classical normal factor model, it can be estimated with the EM algorithm. So, our technique consists in nesting an EM algorithm within each iteration of the FSA. Extensive Monte Carlo simulations show promising results of the algorithm.