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Tuesday 14th July, 14:00 - 15:30 Room: HT-101

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)

Session Details

In contrast to the linear model, the identification of interaction effects and differences in effects between groups in nonlinear models (e.g. logit, probit, Poisson, negative binomial, PH, AFT) is complicated by link functions deviating from identity form and constraints on the variance of random components. As a consequence, many traditional analytical strategies elaborated within the linear modeling approach proved as not appropriate for the identification of the aforementioned effects in nonlinear models. Thus far, this fact has not received all the attention it deserves.

For this reason we warmly welcome presentations dealing with
(i) the identification of interaction effects in all kinds of nonlinear models,
(ii) the separation of model inherent and product term induced interaction effects,
(iii) the relevance of model inherent interaction from a theoretical point of view,
(iv) the identification of differences in effects between groups in all kinds of nonlinear models, and
(v) the isolation of scaling effects in coefficients between groups.

Further, we highly appreciate presentations containing respective empirical applications.

Paper Details

1. Comparing coefficients of nonlinear multivariate regression models between equations
Mr Christoph Kern (University of Duisburg-Essen)
Mrs Petra Stein (University of Duisburg-Essen)

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.

2. Combining Heterogeneous Choice and Fractional Response Models to Analyze Interaction Effects when the Dependent Variable is a Proportion
Professor Richard Williams (Sociology, University of Notre Dame)

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.

3. Model Inherent and Product Term Induced Interaction Effects in Binary Logit Models
Mr Heinz Leitgöb (Goethe University of Frankfurt)
Mrs Stefanie Eifler (University of Eichstätt-Ingolstadt)

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.

4. Testing interaction hypotheses in Situational Action Theory
Ms Debbie Schepers (Bielefeld University)

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.