Information Theoretic Criterion Approach to Dimensionality Reduction in Multinomial Logistic Regression Models: Part II: Some Simulations
Titel:
Information Theoretic Criterion Approach to Dimensionality Reduction in Multinomial Logistic Regression Models: Part II: Some Simulations
Auteur:
Sambamoorthi, N.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 18 (1989) nr. 3 pagina's 897-908
Jaar:
1989
Inhoud:
In Part I, Sambamoorthi(1989), an information theoretic criterion for (1) identification of the rank of the parameter matrix, (2) selection of variables, and (3) collapsibility of response categories in multinomial logistic regression models was proposed. The proposed procedure, a large sample method, gives strongly consistent estimates of the population model for a wide class of criterion functions. In this paper, we report the simulation results of variable selection problem. The criterion functions is a class of functions of the sample size and the number of parameters satisfying some special conditions asymptotically. The simulation results show that extensive search for best criterion function to attain minimum probability of misidentification results in criterion functions for which not only the probability of incorrect identification is almost same as Akaike Information Criterion(AIC) for small sample sizes but also go to zero fast as the sample size increases. This conclusion, probably, upholds the simplicity and optimality of AIC for small sample size even when probability of misidentification is the criterion. More detailed work is needed if minimum probability of misidentification, not just consistency, is to be used as a criterion for practical problems.
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