A generalized rasch model for manifest predictors

A logistic regression model is suggested for estimating the relation between a set of manifest predictors and a latent trait assumed to be measured by a set ofk dichotomous items. Usually the estimated subject parameters of latent trait models are biased, especially for short tests. Therefore, the relation between a latent trait and a set of predictors should not be estimated with a regression model in which the estimated subject parameters are used as a dependent variable. Direct estimation of the relation between the latent trait and one or more independent variables is suggested instead. Estimation methods and test statistics for the Rasch model are discussed and the model is illustrated with simulated and empirical data.     

A general solution for a class of weakly constrained linear regression problems

This paper contains a globally optimal solution for a class of functions composed of a linear regression function and a penalty function for the sum of squared regression weights. Global optimality is obtained from inequalities rather than from partial derivatives of a Lagrangian function. Applications arise in multidimensional scaling of symmetric or rectangular matrices of squared distances, in Procrustes analysis, and in ridge regression analysis. The similarity of existing solutions for these applications is explained by considering them as special cases of the general class of functions addressed.The author is obliged to Henk Kiers and Willem Heiser for helpful comments.     

On the factor score controversy

A summary and interpretation of the recent literature on the indeterminacy of factor scores is given in simple terms. A good index of factor score determinacy is the squared multiple correlation of the factor with the observed variables.     

Some simple procedures for handling missing data in multivariate analysis

For analyses with missing data, some popular procedures delete cases with missing values, perform analysis with missing value correlation or covariance matrices, or estimate missing values by sample means. There are objections to each of these procedures. Several procedures are outlined here for replacing missing values by regression values obtained in various ways, and for adjusting coefficients (such as factor score coefficients) when data are missing. None of the procedures are complex or expensive.This research was supported by NIH Special Research Resources Grant RR-3. The author expresses his gratitude to Robert I. Jennrich and the referees for their suggestions.     

External analyses of preference models

Using Carroll's external analysis, several studies have found that unfolding models account for more, although seldom significantly more, variance in preferences than Tucker's vector model. In studies of sociometric ratings and political preferences, the unfolding model again rarely outpredicted the vector model by a significant amount. Yet on cross-validation, the unfolding model consistently accounted for more variance. Results suggest that sometimes significance tests are less sensitive than cross-validation procedures to the small but consistent superiority of the unfolding model. Future researchers may wish to use significance tests and cross-validation techniques in comparing models.     

Monotonic weighted power transformations to additivity

A class of monotonic transformations which generalize the power transformation is fit to the independent and dependent variables in multiple regression so that the resulting additive relationship is optimized. This is achieved by minimizing a quadratic fitting criterion with linear inequality constraints on the parameters. A quadratic programming technique which works reliably and quickly in this application is outlined. Some examples of the analysis of artificial and real data are offered.This work was supported by National Research Council of Canada Grant APA 320 to the author.     

Component analysis in cross-sectional and longitudinal data

An extension of component analysis to longitudinal or cross-sectional data is presented. In this method, components are derived under the restriction of invariant and/or stationary compositing weights. Optimal compositing weights are found numerically. The method can be generalized to allow differential weighting of the observed variables in deriving the component solution. Some choices of weightings are discussed. An illustration of the method using real data is presented.Preparation of this article was supported in part by PSC-CUNY Grant #665365 to Roger E. Millsap and by National Institute of Aging Grant NIA-AG03164-03 to William Meredith. The authors thank John Nesselroade for permitting the use of the data presented in the article.     

Discriminant validity of the Multiple Affect Adjective Check List - revised

Four groups of patients (depressives, schizophrenics, substance dependents and abusers), a miscellaneous group of other patients, and a group of matched normals from a general population sample were compared on the scales of the Multiple Affect Adjective Check List - Revised (MAACL-R). All scales showed highly significant differentiation among the groups. An index consisting of Depression minus Positive Affect scales was particularly effective in discriminating between depressive and other groups. A discriminant function analysis showed that the depressive could be distinguished from other patient groups and normals with an accuracy of 72% correct. The normals could be distinguished from all of the patient groups with a 60% accuracy, and 87% if the substance abuser group is ignored. The discriminant validity among the nondepressive patient groups was not nearly as good.     

Convergence theory for partial images and revision of the definition of total images

Guttman's assumption underlying his definition of “total images” is rejected: Partial images are not generally convergent everywhere. Even divergence everywhere is shown to be possible. The convergence type always found on partial images is convergence in quadratic mean; hence, total images are redefined as quadratic mean-limits. In determining the convergence type in special situations, the asymptotic properties of certain correlations are important, implying, in some cases, convergence almost everywhere, which is also effected by a countable population or multivariate normality or independent variables. The interpretations of a total image as a predictor, and a “common-factor score”, respectively, are made precise.     

Enumeration versus multiple object tracking: the case of action video game players

Here, we demonstrate that action video game play enhances subjects' ability in two tasks thought to indicate the number of items that can be apprehended. Using an enumeration task, in which participants have to determine the number of quickly flashed squares, accuracy measures showed a near ceiling performance for low numerosities and a sharp drop in performance once a critical number of squares was reached. Importantly, this critical number was higher by about two items in video game players (VGPs) than in non-video game players (NVGPs). A following control study indicated that this improvement was not due to an enhanced ability to instantly apprehend the numerosity of the display, a process known as subitizing, but rather due to an enhancement in the slower more serial process of counting. To confirm that video game play facilitates the processing of multiple objects at once, we compared VGPs and NVGPs on the multiple object tracking task (MOT), which requires the allocation of attention to several items over time. VGPs were able to successfully track approximately two more items than NVGPs. Furthermore, NVGPs trained on an action video game established the causal effect of game playing in the enhanced performance on the two tasks. Together, these studies confirm the view that playing action video games enhances the number of objects that can be apprehended and suggest that this enhancement is mediated by changes in visual short-term memory skills.