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

123 Numerous theories within the social and behavioral sciences 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 example, Ganzach (1997) studies the relationship between parents’ educational level and child’s educational expectations. He hypothesizes and finds a simultaneous interactive and quadratic relationship: If at least one parent’s education level 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 compensatory hypothesis is represented by two positive quadratic effects (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 regression model (see Aiken & West, 1991): CEE = β0 + β1ME + β2FE +ω12ME•FE + ω11ME 2 + ω22FE 2 + ε (1)