Summary. In problems with missing or latent data, a standard approach is to first impute the unobserved data, then perform all statistical analyses on the completed dataset-corresponding to the observed data and imputed unobserved data-using standard procedures for complete-data inference. Here, we extend this approach to model checking by demonstrating the advantages of the use of completed-data model diagnostics on imputed completed datasets. The approach is set in the theoretical framework of Bayesian posterior predictive checks (but, as with missing-data imputation, our methods of missing-data model checking can also be interpreted as "predictive inference" in a non-Bayesian context). We consider the graphical diagnostics within this framework. Advantages of the completed-data approach include: (1) One can often check model fit in terms of quantities that are of key substantive interest in a natural way, which is not always possible using observed data alone. (2) In problems with missing data, checks may be devised that do not require to model the missingness or inclusion mechanism; the latter is useful for the analysis of ignorable but unknown data collection mechanisms, such as are often assumed in the analysis of sample surveys and observational studies. (3) In many problems with latent data, it is possible to check qualitative features of the model (for example, independence of two variables) that can be naturally formalized with the help of the latent data. We illustrate with several applied examples.

In IRT models, responses are explained on the basis of person and item effects. Person effects are usually defined as a random sample from a population distribution. Regular IRT models therefore can be formulated as multilevel models, including a within-person part and a between-person part. In a similar way, the effects of the items can be studied as random parameters, yielding multilevel models with a within-item part and a between-item part. The combination of a multilevel model with random person effects and one with random item effects leads to a cross-classification multilevel model, which can be of interest for IRT applications. The use of cross-classification multilevel logistic models will be illustrated with an educational measurement application.Suppose that a set of items is presented to a group of persons and that for each person the correctness of the responses is recorded. These responses will usually vary, partly at random, partly in a systematic way because of differences in person ability and in item difficulty. An item response theory (IRT) defines the probability of responses of persons to items as a function of person and item characteristics. It has been shown earlier that regular IRT models can be formulated as multilevel logistic models (Adams, Wilson, & Wu, 1997;Kamata, 2001). Making use of this reformulation, we will present a type of IRT model that is based on the principle of cross-classification multilevel models. We will first explain how this principle can be of interest for IRT applications, and we will then discuss the estimation of the unknown parameters of these models. We continue with a discussion of a range of cross-classification logistic models, some of which will be illustrated using an example in which for a group of pupils the attainment targets for reading comprehension are evaluated. We end with a discussion and some conclusions. Although in the following we will consider only dichotomous responses (e.g., correct/incorrect), also categorical responses (e.g., yes/no/perhaps) can be modeled in the way we present.

Two studies examined the effect of status and liking of the anger target on anger behavior and individual differences in anger-related behavior. Participants recalled anger instances in which the anger target was of higher/equal/lower status and/or liked/ unfamiliar/disliked; subsequently, they indicated which behaviors they had displayed. In both studies, anger behaviors could be grouped into behaviors that imply approaching the target (anger-out, assertion, reconciliation) and behaviors that reflect avoidance/anger-in or social sharing. The results demonstrated that approach behaviors more likely occur toward lower status or liked targets; avoidance behaviors and social sharing more likely occur when the target is of higher status or disliked. On an individual differences level, an approach and an avoid/social sharing person class were identified. The findings suggest that anger may motivate prosocial behavior or social sharing, depending on the individual and type of relation with the target. Only few gender differences were found.

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Avoidance is considered a key contributor to the development and maintenance of chronic pain disability, likely through its excessive generalization. This study investigated whether acquired avoidance behavior generalizes to novel but similar movements. Using a robotic arm, participants moved their arm from a starting to a target location via one of three possible movement trajectories. For the Experimental Group, the shortest, easiest trajectory was always paired with pain (T1 = 100% reinforcement/no resistance and deviation). Pain could be partly or completely avoided by choosing increasingly effortful movements (T2 = 50% reinforcement, moderate resistance/deviation; T3 = 0% reinforcement, strongest resistance/largest deviation). A Yoked Group received the same number of painful stimuli irrespective of their own behavior. Outcomes were self-reported fear of movement-related pain, pain-expectancy, avoidance behavior, (maximal deviation from the shortest trajectory), and trajectory choice behavior. We tested generalization to three novel trajectories (G1-3) positioned between the acquisition trajectories. Whereas acquired fear of movement-related pain and pain-expectancy generalized in the Experimental Group, avoidance behavior did not, suggesting that threat beliefs and high-cost avoidance may not be directly related. The lack of avoidance generalization may be due to a perceived context-switch in the configurations of the acquisition and the generalization phases.