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Genotype by environment interaction in behavioral traits may be assessed by estimating the proportion of variance that is explained by genetic and environmental influencesconditionalon a measured moderating variable, such as a known environmental exposure. Behavioral traits of interest are often measured by questionnaires and analyzed as sum scores on the items. However, statistical results on genotype by environment interaction based on sum scores can be biased due to the properties of a scale. This article presents a method that makes it possible to analyze the actually observed (phenotypic) item data rather than a sum score by simultaneously estimating the genetic model and an item response theory (IRT) model. In the proposed model, the estimation of genotype by environment interaction is based on an alternative parametrization that is uniquely identified and therefore to be preferred over standard parametrizations. A simulation study shows good performance of our method compared to analyzing sum scores in terms of bias. Next, we analyzed data of 2,110 12-year-old Dutch twin pairs on mathematical ability. Genetic models were evaluated and genetic and environmental variance components estimated as a function of a family's socio-economic status (SES). Results suggested that common environmental influences are less important in creating individual differences in mathematical ability in families with a high SES than in creating individual differences in mathematical ability in twin pairs with a low or average SES.

The marketplace has been defined by the interaction between consumers and brands, which has been recognized by the majority of marketing literatures with the exception of the measurement literature. Measurement researchers in marketing have been continuously working on improving the quality of measurement of marketing constructs by applying psychometric theories from the early Classical Test Theory to later generations such as Generalizability Theory and Item Response Theory. But only main effects (normally consumers, sometimes brands) have been focused on, and interactions between them are either ignored or treated as measurement error. This is surprising, given the voluminous literature in other areas of marketing (e.g., marketing segmentation, customer lifetime value, and customer relationship management) that build their entire frameworks on the interpretation and usage of this interaction. In the current research, we propose a new Many Faceted Item Response Theory model to fill this gap in measurement literature. Two sets of indexes describe consumers (and brands); individual main effects (and brand main effects) and brand-specific individual effects (or individual-specific brand effects). Soft drink brand equity data were used for the empirical examination.

AbstractWhen the response pattern in a test item deviates from the deterministic pattern, the percentage of correct answers (p) is shown to be a biased estimator for the latent item difficulty (π). This is specifically true with the items of medium item difficulty. Four elements of impurities in p are formalized in the binary settings and four new estimators of π are proposed and studied. Algebraic reasons and a simulation suggest that, except the case of deterministic item discrimination, the real item difficulty is almost always more extreme than what p indicates. This characteristic of p to be biased toward a medium-leveled item difficulty has a strict consequence to item response theory (IRT) and Rasch modeling. Because the classical estimator of item difficulty p is a biased estimator of the latent difficulty level, the item parameters A and B and the person parameter θ within IRT modeling are, consequently, biased estimators of item discrimination and item difficulty as well as ability levels of the test takers.