Research Seminar
How the Empirical Meaning of a Statistical Model can be Verified?Ernesto San MartinDepartment of Statistics & Measurement Center MIDE UC, Santiago de Chile | |
| Abstract: | It is well known that, in a pure sampling theory framework, parameter identifiability is not only a necessary condition for the existence of a consistent estimator, but also that it ensures a statistical interpretation of the corresponding parameter. Taking into account that, in general, it is difficult to verify parameter identification, it seems reasonable to look for a framework leading to handle unidentified parameters. In 1971, in a footnote (sic!) of a lecture, Lindley asserted "that unidentifiability causes no real difficulty in the Bayesian approach". This statement has been very well received by the Bayesian literature. It is behind Dawid's (1979) definition of unidentified parameter; it justifies Bayesian inference of unidentified parameters in econometrics (Poirier, 1998), in GLMM (Gelfand and Sahu, 1999), even in Rasch model when analyzing the behavior of the posterior distribution in the presence of unidentified parameters (Ghosh, Ghosh, Chen and Aggresti, 2000). Recently, Gustafson (2005) defended the importance of unidentified parameters, arguing that they capture relevant information. The good reception of Lindley's statement is due to the fact that, in a Bayesian theory framework, it is always possible to compute the posterior probability of an unidentified parameter. The scope of this talk is twofold. First, we will discuss, through a simple example, conceptual issues related with identification. A critical examination of the Bayesian statements concerning unidentifiability will be discussed. In particular, we argue that when a Bayesian inference is performed on an unidentified parameter, is rather easy produce an illusion. The second part of this talk is concerned with the identification of Latent Class Models (LCM). After discussing and illustrating the general result, the identification sterategy will be applied for studying the identification of the Multuiple Classification Latent Class Models (MCLCLM) and of Mixture Rasch models. As a consequence of the identification analysis, it will be shown that MCLCM is a particular case of the LCM, and not the converse as widely stated in the literature. |
| Date: | Tue Oct 7, 12:15 pm - 1:15 pm |
| Place: | room 00.60 (Department of Psychology, Tiensestraat 102, 3000 Leuven) |