Fitting direct covariance structures by the MSTRUCT modeling language of the CALIS procedure

This paper demonstrates the usefulness and flexibility of the general structural equation modelling (SEM) approach to fitting direct covariance patterns or structures (as opposed to fitting implied covariance structures from functional relationships among variables). In particular, the MSTRUCT modelling language (or syntax) of the CALIS procedure (SAS/STAT version 9.22 or later: SAS Institute, 2010) is used to illustrate the SEM approach. The MSTRUCT modelling language supports a direct covariance pattern specification of each covariance element. It also supports the input of additional independent and dependent parameters. Model tests, fit statistics, estimates, and their standard errors are then produced under the general SEM framework. By using numerical and computational examples, the following tests of basic covariance patterns are illustrated: sphericity, compound symmetry, and multiple‐group covariance patterns. Specification and testing of two complex correlation structures, the circumplex pattern and the composite direct product models with or without composite errors and scales, are also illustrated by the MSTRUCT syntax. It is concluded that the SEM approach offers a general and flexible modelling of direct covariance and correlation patterns. In conjunction with the use of SAS macros, the MSTRUCT syntax provides an easy‐to‐use interface for specifying and fitting complex covariance and correlation structures, even when the number of variables or parameters becomes large.     

A general proof of consistency of heuristic classification for cognitive diagnosis models

The Asymptotic Classification Theory of Cognitive Diagnosis (Chiu et al., 2009, Psychometrika, 74, 633–665) determined the conditions that cognitive diagnosis models must satisfy so that the correct assignment of examinees to proficiency classes is guaranteed when non‐parametric classification methods are used. These conditions have only been proven for the Deterministic Input Noisy Output AND gate model. For other cognitive diagnosis models, no theoretical legitimization exists for using non‐parametric classification techniques for assigning examinees to proficiency classes. The specific statistical properties of different cognitive diagnosis models require tailored proofs of the conditions of the Asymptotic Classification Theory of Cognitive Diagnosis for each individual model – a tedious undertaking in light of the numerous models presented in the literature. In this paper a different way is presented to address this task. The unified mathematical framework of general cognitive diagnosis models is used as a theoretical basis for a general proof that under mild regularity conditions any cognitive diagnosis model is covered by the Asymptotic Classification Theory of Cognitive Diagnosis.     

The possible benefits of difficulty: how stress can increase and decrease subjective well-being

This study explores the effects of stress, trauma, coping and growth orientation on subjective well-being. Based on cognitive stress theory, it was hypothesized that adversity may contribute to increased or decreased well-being, depending on the subsequent meaning these experiences are given. Survey data from Norwegian UN/NATO veterans (N= 142) showed that stress and well-being were negatively associated (r=-0.20, p < 0.05) at the level of zero-order correlations. However, a full structural equation model revealed that the effect of stress on well-being was mediated positively through a problem-focused coping process combined with a growth component. Stress was negatively mediated through an avoidant-focused coping process and a distress component. The effect from stress was fully mediated in the model. The hypothesis that stress can produce both increased and decreased subjective well-being was confirmed.     

School profiles of at-risk student concentration: Differential growth in oral reading fluency

The present study provides a data-driven approach to identifying groups of schools based on the concentration of at-risk students the school serves. The percentage of English language learners, minority students, and students eligible for free or reduced priced lunch were used as indicators in a latent profile analysis of 569 schools. The goal of the present study was to determine whether school-level average student reading performance varied as a function of the groups identified in the latent profile analysis. To do so, groups extracted by the latent profile analysis were used as school-level predictors of growth in oral reading fluency, which was modeled at the within-student level of a three-level hierarchical growth curve model. Oral reading fluency was measured at four points during the year in a large cross-sectional sample of first-, second-, and third-grade students. Results indicated that schools were able to be classified into four distinct groups based on their concentrations and types of at-risk students. Further, in all three grades, there were significant differences between the four identified groups observed in average reading fluency scores at the beginning of the year, the end of the year, and growth during the year indicating that groups based on school-concentration of at-risk students were significantly related to average student achievement in reading ability.     

Beta-MPT: Multinomial processing tree models for addressing individual differences

Traditionally, multinomial processing tree (MPT) models are applied to groups of homogeneous participants, where all participants within a group are assumed to have identical MPT model parameter values. This assumption is unreasonable when MPT models are used for clinical assessment, and it often may be suspect for applications to ordinary psychological experiments. One method for dealing with parameter variability is to incorporate random effects assumptions into a model. This is achieved by assuming that participants’ parameters are drawn independently from some specified multivariate hyperdistribution. In this paper we explore the assumption that the hyperdistribution consists of independent beta distributions, one for each MPT model parameter. These beta-MPT models are ‘hierarchical models’, and their statistical inference is different from the usual approaches based on data aggregated over participants. The paper provides both classical (frequentist) and hierarchical Bayesian approaches to statistical inference for beta-MPT models. In simple cases the likelihood function can be obtained analytically; however, for more complex cases, Markov Chain Monte Carlo algorithms are constructed to assist both approaches to inference. Examples based on clinical assessment studies are provided to demonstrate the advantages of hierarchical MPT models over aggregate analysis in the presence of individual differences.     

A Signal Detection Model for Multiple-Choice Exams

A model for multiple-choice exams is developed from a signal-detection perspective. A correct alternative in a multiple-choice exam can be viewed as being a signal embedded in noise (incorrect alternatives). Examinees are assumed to have perceptions of the plausibility of each alternative, and the decision process is to choose the most plausible alternative. It is also assumed that each examinee either knows or does not know each item. These assumptions together lead to a signal detection choice model for multiple-choice exams. The model can be viewed, statistically, as a mixture extension, with random mixing, of the traditional choice model, or similarly, as a grade-of-membership extension. A version of the model with extreme value distributions is developed, in which case the model simplifies to a mixture multinomial logit model with random mixing. The approach is shown to offer measures of item discrimination and difficulty, along with information about the relative plausibility of each of the alternatives. The model, parameters, and measures derived from the parameters are compared to those obtained with several commonly used item response theory models. An application of the model to an educational data set is presented.     

Strategic grouping in the spatial span memory task

Spatial short-term memory performance was examined in relation to participants’ strategies. A total of 20 adult participants viewed and reproduced sequences of locations that varied in length (five, six, seven, or eight locations) and spatial separability (a manipulation of the configurations). In trial-by-trial self-reports, participants described five types of strategies. Chunking the spatial sequences into groups of three or four locations was the sole strategy associated with increased accuracy. Participants demonstrated considerable variability in the strategies that they selected, suggesting that cognitive resources are allocated to strategy selection, execution, and monitoring in the spatial span task. Spatially separable sequences were more accurately recalled than nonseparable sequences, independent of strategic grouping, suggesting two levels of grouping in the spatial span task.     

A Minister's Information-Handling

ABSTRACT

One of the roles which ministers perform is that of “caregiver.” Caregiving functions include such activities as visiting parishioners, hearing confessions, and counselling people. These functions are carried out within a legal context. In this paper, two aspects of the parish minister's information handling in respect to his/her role as caregiver are examined. Specific attention is given to the pastor's vulnerability, while carrying out pastoral duties, to civil lawsuits for malpractice and to her/his expectation of privilege against testifying in criminal proceedings. It is observed that in North America, considerable confusion exists over who actually owns and who can control the information a minister acquires and disseminates.