The formulation of log-linear models within the framework of Generalized Linear Models offers new possibilities in modeling categorical data. The resulting models are not restricted to the analysis of contingency tables in terms of ordinary hierarchical interactions. Such models are considered as the family of nonstandard log-linear models. The problem that can arise is an ambiguous interpretation of parameters. In the current paper this problem is solved by looking at the effects coded in the design matrix and determining the numerical contribution of single effects. Based on these results, stepwise approaches are proposed in order to achieve parsimonious models. In addition, some testing strategies are presented to test such (eventually non-nested) models against each other. As a result, a whole interpretation framework is elaborated to examine nonstandard log-linear models in depth.

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The trait complex approach (Ackerman&Heggestad, 1997) makes it possible to study the individual holistically by taking account of various individual differences at the same time, such as abilities, personality, motivation, and vocational preferences. Recently, Kanfer, Wolf, Kantrowitz, and Ackerman (2010) provided support for taking a whole-person approach in predicting academic performance. They also showed the incremental role of non-ability predictors over the role of ability predictors. Objectives of the present study were to further explore the non-ability variables of the science/math trait complex. Identifying the personality correlates of the science/math trait complex was the first objective. Investigation results yielded four personality factors as correlates of the complex, which play important roles for engineers and scientists at different stages of the vocational track: toughmindedness was the personality marker of the science/math trait complex and was associated with intending to pursue a STEM career; achievement and control were associated with academic success in STEM majors; and cognitively-oriented behavior was associated with more cognitively challenging pursuits, such as attending STEM competitions and planning to go on to graduate school. The second purpose was to revisit the vocational interests associated with the science/math trait complex and the Science, Technology, Engineering, and Mathematics (STEM) groups. A new measure was introduced, referred to as STEM Interest Complexity, which measures interests towards engaging in increasingly complex tasks in the Numerical, Symbolic, Spatial, and STEM-related Ideas domains. It was developed to assess the level of vocational interests, in addition to the traditionally assessed direction of vocational interests (Holland, 1985). Validation of the new STEM Interest Complexity measure showed adequate construct and concurrent criterion-related validities. Construct validity was established by demonstrating associations between the new measure and measures of the direction of interests, cognitive abilities, intelligence as personality, and learning goal orientations. Support for the new measure's criterion-related validity was found by demonstrating that the measure discriminates between majors, and predicts vocational criteria (i.e., college achievement in STEM, attachment to STEM fields, major satisfaction, and one's intentions to chose a complex STEM career). With dominance analyses, it was shown that STEM Interest Complexity was the most important vocational assessment in the prediction of criteria. Results support the assertion that vocational interest inventories can be improved by incorporating the level of complexity dimension. Finally, a science/math trait complex composite score, including the personality factors and STEM Interest Complexity, in addition to the previously determined ability, interest, and self-concept associates, showed moderate associations with STEM-related vocational criteria. The non-ability individual differences, which were the focus of the present study, added to the conceptualization and predictive utility of the science/math trait complex.

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