Stochastic Ordering Of the Latent Trait by the Sum Score Under Various Polytomous IRT Models

The sum score is often used to order respondents on the latent trait measured by the test. Therefore, it is desirable that under the chosen model the sum score stochastically orders the latent trait. It is known that unlike dichotomous item response theory (IRT) models, most polytomous IRT models do not imply stochastic ordering. It is unknown, however, (1) whether stochastic ordering is often or rarely violated and (2) whether violations yield a serious problem for practical data analysis. These are the central issues of this paper. First, some unanswered questions that pertain to polytomous IRT models implying stochastic ordering were investigated. Second, simulation studies were conducted to evaluate stochastic ordering in practical situations. It was found that for most polytomous IRT models that do not imply stochastic ordering, the sum score can be used safely to order respondents on the latent trait.The author would like to thank Klaas Sijtsma for commenting on earlier drafts of this paper.     

The Future of Research on Intimate Partner Violence: Person-Oriented and Variable-Oriented Perspectives

This article uses the distinction between the person and the variable orientations as a frame for structuring (1) research on IPV, (2) results of this research, and (3) an agenda for future research. The main tenet of this agenda is that causes, processes, and effects of IPV are person and context specific; therefore, results that relate variables to each other are of limited value if it can be shown that the processes that take place, the meaning of the variables, the profile of the transgressors and the women who experience IPV depend on time, environment, and research design. Examples of valuable variable-oriented research are given; examples of the growing contribution made by person-oriented research are given as well. Sample theories are sketched out, for the variable-oriented, the person-oriented, and the theoretical research arenas, the need for future research is derived from inconsistencies and shortcomings in both current research and theory. Sample research questions are proposed. The contributions made by the authors of this Special Section are embedded within the discussion of research and theory of IPV. It is shown that each of the contributions is valuable within a particular segment of the research landscape.     

Time ordering in frontal lobe patients: a stochastic model approach

Frontal lobe patients reproduced a sequence of capital letters or abstract shapes. Immediate and delayed reproduction trials allowed the analysis of short- and long-term memory for time order by means of suitable Markov chain stochastic models. Patients were as proficient as healthy subjects on the immediate reproduction trial, thus showing spared encoding and short-term memory. They failed, instead, on the delayed trials with capital letters, but not with random shapes, suggesting that their long-term memory impairment did not depend on primary deficits for ordering, but on inability to benefit from the organisational strategies that improve the retention and retrieval in normal subjects.     

Changing behavior within session: cyclicity and perseverance produced by varying the minimum ratio of a variable-ratio schedule

Four pigeons repeatedly chose between a fixed-ratio (FR) 20 and a variable-ratio (VR) 40 schedule of reinforcement, in which the minimum ratio of the VR cycled within each session. The minimum ratio ascended and descended (ASCDESC), descended and ascended (DESCASC), or remained constant (unchanging). In Phase 1, 2 birds (Group 1) were exposed to ASCDESC series and 2 birds (Group 2) were exposed to the DESCASC series. Choice proportions changed with the cycling minimum ratio for Group 2 but not for Group 1. In Phase 2, Group 1 subjects were exposed to the DESCASC series and Group 2 subjects were exposed to the unchanging condition. Although Group 1's choice proportions appeared to be undifferentiated in Phase 2, Group 2's choice proportions continued to cycle for more than 100 sessions. Group 2 subjects were then moved to the ASCDESC series in the third phase, and choice proportions cycled with the minimum ratio as in the first phase. The descending portion of the series was the more powerful determinant of cyclicity. Response rates also changed with the minimum component ratio, a finding that goes against the claim of universality of a rise-and-fall within-session pattern of responding. That preference varied despite the constancy of the average ratio requirement suggests nonlinear averaging in quantitatively representing a variable schedule's value. The strong perseverance observed also lends support to a growing body of literature on history effects.     

Model Fit and Item Factor Analysis: Overfactoring,Underfactoring, and a Program to Guide Interpretation

In exploratory item factor analysis (IFA), researchers may use model fit statistics and commonly invoked fit thresholds to help determine the dimensionality of an assessment. However, these indices and thresholds may mislead as they were developed in a confirmatory framework for models with continuous, not categorical, indicators. The present study used Monte Carlo simulation methods to investigate the ability of popular model fit statistics (chi-square, root mean square error of approximation, the comparative fit index, and the Tucker–Lewis index) and their standard cutoff values to detect the optimal number of latent dimensions underlying sets of dichotomous items. Models were fit to data generated from three-factor population structures that varied in factor loading magnitude, factor intercorrelation magnitude, number of indicators, and whether cross loadings or minor factors were included. The effectiveness of the thresholds varied across fit statistics, and was conditional on many features of the underlying model. Together, results suggest that conventional fit thresholds offer questionable utility in the context of IFA.     

Testing an Adaptationist Theory of Trait Covariation: Relative Bargaining Power as a Common Calibrator of an Interpersonal Syndrome

This article provides the first test of an adaptationist ‘common calibration’ theory to explain the origins of trait covariation, which holds that (i) personality traits are often facultatively calibrated in response to cues that ancestrally predicted the reproductive payoffs of different trait levels and (ii) distinct traits that are calibrated on the basis of common input cues will exhibit consistent patterns of covariation. This theory is applied to explain the covariation within a ‘personality syndrome’ encompassing various interpersonal trait dimensions (e.g. extraversion, emotionality and attachment styles). Specifically, it is hypothesized that these traits are inter‐correlated because each is calibrated in response to relative bargaining power (RBP)—a joint function of one's ability to benefit others and harm others. Path analyses from a correlational study compellingly supported this theoretical model: Objective and self‐perceived measures of RBP‐enhancing phenotypic features (physical attractiveness and physical strength) influenced an internal regulatory variable indexing RBP (i.e. self‐perceived RBP), which in turn had robust effects on each of the focal personality traits. Moreover, in support of the theory's core postulate, controlling for self‐perceived RBP greatly reduced the covariation within the interpersonal syndrome. These novel findings illustrate the promise of an evolutionary psychological approach to elucidating trait covariation. Copyright © 2013 John Wiley & Sons, Ltd.     

The contribution of executive function and social understanding to preschoolers’ letter and math skills

The influence of executive function and social understanding on letter and math skills was examined in 129 3–5-year-olds. Tasks were administered to measure working memory, inhibition, social understanding, letter and math skills, and vocabulary. Using latent variable analyses, multiple models were compared in order to examine the influence of executive function and social understanding on participants’ emerging academic skills. In the best-fitting model, working memory contributed to letter and math skills, over and above inhibition, social understanding, age, and vocabulary. Inhibition and social understanding did not uniquely contribute to letter and math skills, but significant relations were found among working memory, inhibition, and social understanding. Findings are discussed with respect to improving ways to examine the complex relations among preschoolers’ executive function, social understanding, and school readiness skills.