Interaction effects and group comparisons in nonlinear models
|Convenor||Mr Heinz Leitgöb (University of Linz, Austria )|
|Coordinator 1||Professor Stefanie Eifler (University of Eichstätt-Ingolstadt, Germany)|
The present study discusses the usage of non-linear constraints in multivariate regression models with categorical outcomes. With this approach, effect differences between equations are made accessible to statistical tests while potential differences in residual variation are explicitly taken into account. In this context, it can be shown that the techniques reviewed by Williams (2010) are conjointly equivalent to the specification of non-linear constraints in multivariate regression models. However, the application of non-linear constraints extends these approaches into a structural equation modeling framework, which allows the researcher to address a broader range of research questions.
Researchers are often interested in comparing the effects of variables across groups. However, Williams has shown that, when residual variability differs across groups, the use of interaction effects with nonlinear models can be problematic. In this paper we combine features of heterogeneous choice models for the analysis of dichotomies with fractional response models for the analysis of proportions. We examine whether heterogeneous choice models with proportions produce more stable coefficients and superior estimates of interactions than such models do with dichotomous dependent variables. Real data sets, Monte Carlo simulations, and the Stata user-written routine fracglm are employed.
Interaction effects are allowed to vary across individuals in nonlinear models. Further, even the nonlinear main effects model contains an interaction effect if both covariates contribute to the explanation of the outcome. The presence of the model-inherent interaction is owed to the restricted range of the outcome variable. We will develop a general perspective on the idea and meaning of interaction in nonlinear models and target at developing an application scheme guiding researchers to the appropriate concept of interaction – either including the model-inherent interaction or separating it from the total interaction effect.
Situational Action Theory (SAT) states that the interaction of propensity and exposure determines delinquency. Criminal acts are the result of a perception-choice-process, which can be explained by the interaction of criminal propensity and criminogenic conditions. Dealing with non-normal data, the identification of interaction effects faces a number of challenges. Using the data of the German study “Chances and Risks in the Life Course”, two methods for the exploration of interaction effects, both embedded within the structural equation approach, will be compared for the explanation of juvenile delinquency in context of SAT.