On the relationship between item response theory and factor analysis of discretized variables

Abstract

marginal maximum likelihood estimation, dichotomous data, ordered and unordered categorical data, pair comparison data,

Trust and the Choice Between Housing and Financial Assets: Evidence from Spanish Households*

“…9 Takane and de Leeuw (1987) show, under specific assumptions, the formal equivalence between the marginal likelihood of an item response model and the likelihood of a confirmatory factor analysis. In that case, the parameters obtained using the item response model are equivalent, under some transformation, to the ones obtained using confirmatory factor analysis.…”

Marginal Maximum Likelihood Analyses of Individual Differences in Additivity and Judgmental Criteria for Categorical Rating Data and Decision Making Data

“…This has made me feel that the MML method will have a wide applicability in psychological researches as a technique to incorporate individual differences into the psychological models in which representation of individual differences are critical. As suggested in Takane and de Leeuw (1987), for exam ple, individual differences multidimensional scaling (Carroll & Chang, 1970) is another potential area for MML to be applied. I am now preparing a paper to propose a MML estimation procedure for the vector model to deal with individual preferences.…”

“…Since there is almost always some degree of individual difference in every psy chological phenomenon, it is almost impossible to develop realistic models without incorporating an individual differences component into the models (Takane & de Leeuw, 1987). However, incorporation of an individual differences component into the models causes some difficulties in parameter estimation from a statistical viewpoint.…”

A New Method for Multidimensional Unfolding

“…However, there arises a problem that since the subject parameters ({xzu}) are incidental to the subjects, the number of parameters to be estimated usually increases with the number of observations, and consequently the asymptotic properties of maximum likelihood estimators never hold. Marginalization of the subject parameters and latent structure analysis are two major possible techniques to deal with this problem (Takane & de Leeuw, 1987;Croon, 1989;Hojo, 1992). These approaches to unfolding, however, would not be capable of geometrically representing all individual differences in a joint space of subject and stimulus points as in the MDU RANK model.…”