Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables

We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency tables. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator. For a widely used item response model, when r is small and multidimensional tables are sparse, the proposed statistics have accurate empirical Type I errors, unlike Pearson's X ². For this model in nonsparse situations, the proposed statistics are also more powerful than X ². In addition, the proposed statistics are asymptotically chi-square when applied to subtables, and can be used for a piecewise goodness-of-fit assessment to determine the source of misfit in poorly fitting models. This research has been supported by the Department of Universities, Research, and Information Society (DURSI) of the Catalan Government, by grant BSO2003-08507 of the Spanish Ministry of Science and Technology, and an NSERC Canada grant. We are grateful to the referees for comments leading to improvements.     

On the asymptotic distribution of Pearson’s X 2 in cross-validation samples

In categorical data analysis, two-sample cross-validation is used not only for model selection but also to obtain a realistic impression of the overall predictive effectiveness of the model. The latter is of particular importance in the case of highly parametrized models capable of capturing every idiosyncracy of the calibrating sample. We show that for maximum likelihood estimators or other asymptotically efficient estimators Pearson's X ² is not asymptotically chi-square in the two-sample cross-validation framework due to extra variability induced by using different samples for estimation and goodness-of-fit testing. We propose an alternative test statistic, X _xval ², obtained as a modification of X ² which is asymptotically chi-square with C−1 degrees of freedom in cross-validation samples. Stochastically, X _xval ² ≤ X ². Furthermore, the use of X ² instead of X _xval ² with a χ _C −1² reference distribution may provide an unduly poor impression of fit of the model in the cross-validation sample. This paper is dedicated to the memory of Michael V. Levine. Requests for reprints should be sent to Albert Maydeu-Olivares, Faculty of Psychology, University of Barcelona, P. Valle de Hebrón, 171, 0835 Barcelona, Spain.     

Comparison of isokinetic peak force and power in adults with partial and total blindness

For many populations the ability to move efficiently is compromised by an impaired muscular functioning. Strength development is necessary to overcome the effects of gravity to maintain posture and generate movement responses for mobility. The strength and power capabilities of individuals with total blindness (n = 12) were compared to those with partial vision (n = 12) to evaluate effects of vision on performance. Results indicate that (1) no significant differences were apparent between total blindness and partial vision, (2) significant sex differences were evident in each group, and (3) better performance was apparent at lower velocities. It was concluded that physical performance in individuals with blindness and partial vision are equally deficient.     

From power to action

Three experiments investigated the hypothesis that power increases an action orientation in the power holder, even in contexts where power is not directly experienced. In Experiment 1, participants who possessed structural power in a group task were more likely to take a card in a simulated game of blackjack than those who lacked power. In Experiment 2, participants primed with high power were more likely to act against an annoying stimulus (a fan) in the environment, suggesting that the experience of power leads to the performance of goal-directed behavior. In Experiment 3, priming high power led to action in a social dilemma regardless of whether that action had prosocial or antisocial consequences. The effects of priming power are discussed in relation to the broader literature on conceptual and mind-set priming.