Estimation of nonlinear latent structural equation models using the extended unconstrained approach

Abstract

Numerous theories within the social and behavioral sci-ences hypothesize interaction, quadratic effects, or both between multiple independent and dependent variables (Ajzen, 1987; Cronbach & Snow, 1977; Karasek, 1979; Lusch & Brown, 1996; Snyder & Tanke, 1976). For exam-ple, Ganzach (1997) studies the relationship between par-ents’ educational level and child’s educational expectations. He hypothesizes and finds a simultaneous interactive and quadratic relationship: If at least one parent’s education lev-el is high, the educational expectations of the child will also be high, even if the level of education of the other parent is quite low. In terms of the statistical model, this compensa-tory hypothesis is represented by two positive quadratic ef-fects (for each parent’s educational level) and one negative interaction effect. Within the measured variable framework, such hypotheses can be tested by specifying a multiple re-gression model (see Aiken & West, 1991):

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