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How the 2 SLS / IV estimator can handle equality constraints in structural equation models: A system‐of‐equations approach
Author(s) -
Nestler Steffen
Publication year - 2014
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 - 10.1111/bmsp.12023
Subject(s) - estimator , instrumental variable , structural equation modeling , extension (predicate logic) , mathematics , latent variable , estimating equations , least squares function approximation , mathematical optimization , computer science , statistics , programming language
Parameters in structural equation models are typically estimated using the maximum likelihood ( ML ) approach. Bollen (1996) proposed an alternative non‐iterative, equation‐by‐equation estimator that uses instrumental variables. Although this two‐stage least squares/instrumental variables (2 SLS / IV ) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2 SLS / IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2 SLS / IV estimator and allows for the effective handling of equality constraints in structural equation models.