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A method of moments technique for fitting interaction effects in structural equation models
Author(s) -
Wall Melanie M.,
Amemiya Yasuo
Publication year - 2003
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711003321645331
Subject(s) - estimator , structural equation modeling , flexibility (engineering) , product (mathematics) , standard error , mathematics , generalized method of moments , polynomial , computer science , normality , method of moments (probability theory) , econometrics , mathematical optimization , statistics , mathematical analysis , geometry
The desire to fit structural equation models containing an interaction term has received much methodological attention in the social science literature. This paper presents a technique for the cross‐product structural model that utilizes factor score estimates and results in closed‐form moments‐type estimators. The technique, which does not require normality for the underlying factors, was originally introduced in a very general form by Wall and Amemiya (2000) for any polynomial structural model. In this paper, the practical implementation of this method, including standard error estimation, is presented specifically for the cross‐product model. The procedure is applied to an example from social/behavioural epidemiology where the flexibility of the cross‐product model provides a useful description of the underlying theory. A simulation study is also presented comparing the method of moments for the cross‐product model with three other procedures.