Let's do it: Response times in Mental Paper Folding and its execution

Action imagery is the ability to mentally simulate the execution of an action without physically performing it. Action imagery is assumed to rely at least partly on similar mechanisms as action execution. Therefore, we expected that imagery and execution durations would be constrained by the number of folds in a Paper Folding Task. Analogously, individual differences in execution durations were expected to be reflected in imagery durations. Twenty-eight participants performed two imagery conditions (computer vs. paper) and one execution condition (paper) where two-dimensional grids of a three-dimensional cube were (mentally) folded to determine whether two selected edges overlapped or not. As expected, imagery performance and execution performance were strongly correlated and decreased with the number of folds. Further, the number of folds influenced imagery durations even more than execution durations. This may be due to the additional cognitive load in imagery that emerges when tracking the folds to follow up with the next ones. The results indicate that Mental Paper Folding predominantly involves dynamic visual representations that are not functionally associated with one's own movements as in action imagery.

Testing measurement invariance in a conditional likelihood framework by considering multiple covariates simultaneously

This article addresses the problem of measurement invariance in psychometrics. In particular, its focus is on the invariance assumption of item parameters in a class of models known as Rasch models. It suggests a mixed-effects or random intercept model for binary data together with a conditional likelihood approach of both estimating and testing the effects of multiple covariates simultaneously. The procedure can also be viewed as a multivariate multiple regression analysis which can be applied in longitudinal designs to investigate effects of covariates over time or different experimental conditions. This work also derives four statistical tests based on asymptotic theory and a parameter-free test suitable in small sample size scenarios. Finally, it outlines generalizations for categorical data in more than two categories. All procedures are illustrated on real-data examples from behavioral research and on a hypothetical data example related to clinical research in a longitudinal design.

Penalization approaches in the conditional maximum likelihood and Rasch modelling context

Recent detection methods for Differential Item Functioning (DIF) include approaches like Rasch Trees, DIFlasso, GPCMlasso and Item Focussed Trees, all of which - in contrast to well established methods - can handle metric covariates inducing DIF. A new estimation method shall address their downsides by mainly aiming at combining three central virtues: the use of conditional likelihood for estimation, the incorporation of linear influence of metric covariates on item difficulty and the possibility to detect different DIF types: certain items showing DIF, certain covariates inducing DIF, or certain covariates inducing DIF in certain items. Each of the approaches mentioned lacks in two of these aspects. We introduce a method for DIF detection, which firstly utilizes the conditional likelihood for estimation combined with group Lasso-penalization for item or variable selection and L1-penalization for interaction selection, secondly incorporates linear effects instead of approximation through step functions, and thirdly provides the possibility to investigate any of the three DIF types. The method is described theoretically, challenges in implementation are discussed. A dataset is analysed for all DIF types and shows comparable results between methods. Simulation studies per DIF type reveal competitive performance of cmlDIFlasso, particularly when selecting interactions in case of large sample sizes and numbers of parameters. Coupled with low computation times, cmlDIFlasso seems a worthwhile option for applied DIF detection.

Mental Paper Folding Revisited: The Involvement of Visual Action Imagery

Action imagery describes a mental representation of an action and its consequences. Although it is widely recognized that people differ in their ability to imagine actions, objective validated tests to measure such differences are scarce. In search of an objective testing method for action imagery ability, the present study investigated whether solving mental paper-folding tasks involves action imagery. The stimuli were two-dimensional grids of six squares. A total of 99 participants mentally folded each grid into a three-dimensional cube to judge whether two highlighted lines in the grid overlapped in the imagined cube. This was done in two sessions of 214 judgements each, where the grids differed in overlaps, the least number of imagined folds, and the least number of imagined directional changes. Error rates and reaction times increased with the number of imagined folds and with the number of directional changes. Furthermore, more errors were committed with overlapping lines than with no overlaps. This was not reflected in the reaction times. Hence, the reaction times increased when the stepwise folding process was enlarged, but not when the final selection was more difficult. We concluded that the participants predominantly used action imagery as a task-solving strategy rather than for abstract problem-solving.

Conditional Inference in Small Sample Scenarios Using a Resampling Approach

This paper discusses a non-parametric resampling technique in the context of multidimensional or multiparameter hypothesis testing of assumptions of the Rasch model. It is based on conditional distributions and it is suggested in small sample size scenarios as an alternative to the application of asymptotic or large sample theory. The exact sampling distribution of various well-known chi-square test statistics like Wald, likelihood ratio, score, and gradient tests as well as others can be arbitrarily well approximated in this way. A procedure to compute the power function of the tests is also presented. A number of examples of scenarios are discussed in which the power function of the test does not converge to 1 with an increasing deviation of the true values of the parameters of interest from the values specified in the hypothesis to be tested. Finally, an attempt to modify the critical region of the tests is made aiming at improving the power and an R package is provided.