Finite mixtures in confirmatory factor-analysis models

In this paper, various types of finite mixtures of confirmatory factor-analysis models are proposed for handling data heterogeneity. Under the proposed mixture approach, observations are assumed to be drawn from mixtures of distinct confirmatory factor-analysis models. But each observation does not need to be identified to a particular model prior to model fitting. Several classes of mixture models are proposed. These models differ by their unique representations of data heterogeneity. Three different sampling schemes for these mixture models are distinguished. A mixed type of the these three sampling schemes is considered throughout this article. The proposed mixture approach reduces to regular multiple-group confirmatory factor-analysis under a restrictive sampling scheme, in which the structural equation model for each observation is assumed to be known. By assuming a mixture of multivariate normals for the data, maximum likelihood estimation using the EM (Expectation-Maximization) algorithm and the AS (Approximate-Scoring) method are developed, respectively. Some mixture models were fitted to a real data set for illustrating the application of the theory. Although the EM algorithm and the AS method gave similar sets of parameter estimates, the AS method was found computationally more efficient than the EM algorithm. Some comments on applying the mixture approach to structural equation modeling are made.Note: This paper is one of the Psychometric Society's 1995 Dissertation Award papers.—EditorThis article is based on the dissertation of the author. The author would like to thank Peter Bentler, who was the dissertation chair, for guidance and encouragement of this work. Eric Holman, Robert Jennrich, Bengt Muthén, and Thomas Wickens, who served as the committee members for the dissertation, had been very supportive and helpful. Michael Browne is appreciated for discussing some important points about the use of the approximate information in the dissertation. Thanks also go to an anonymous associate editor, whose comments were very useful for the revision of an earlier version of this article.     

Contributions of the striatum to learning, motivation, and performance: an associative account

It has long been recognized that the striatum is composed of distinct functional sub-units that are part of multiple cortico-striatal-thalamic circuits. Contemporary research has focused on the contribution of striatal sub-regions to three main phenomena: learning of associations between stimuli, actions and rewards; selection between competing response alternatives; and motivational modulation of motor behavior. Recent proposals have argued for a functional division of the striatum along these lines, attributing, for example, learning to one region and performance to another. Here, we consider empirical data from human and animal studies, as well as theoretical notions from both the psychological and computational literatures, and conclude that striatal sub-regions instead differ most clearly in terms of the associations being encoded in each region.     

On the limitations of fixed‐step‐size adaptive methods with response confidence

The family of (non‐parametric, fixed‐step‐size) adaptive methods, also known as ‘up–down’ or ‘staircase’ methods, has been used extensively in psychophysical studies for threshold estimation. Extensions of adaptive methods to non‐binary responses have also been proposed. An example is the three‐category weighted up–down (WUD) method (Kaernbach, 2001) and its four‐category extension (Klein, 2001). Such an extension, however, is somewhat restricted, and in this paper we discuss its limitations. To facilitate the discussion, we characterize the extension of WUD by an algorithm that incorporates response confidence into a family of adaptive methods. This algorithm can also be applied to two other adaptive methods, namely Derman's up–down method and the biased‐coin design, which are suitable for estimating any threshold quantiles. We then discuss via simulations of the above three methods the limitations of the algorithm. To illustrate, we conduct a small scale of experiment using the extended WUD under different response confidence formats to evaluate the consistency of threshold estimation.     

Spiritual Versus Religious Identity: A Necessary Distinction in Understanding Clinicians’ Behavior and Attitudes Toward Clinical Practice and Medical Student Teaching in This Realm

Social sciences view spirituality and religion separately; medicine views them together. We identified distinctions regarding clinical practice and teaching among clinician educators based on their self-identified spirituality versus religiosity. We emailed a 24-item survey on spiritual/religious (S/R) issues to clinician educators (n = 1,067) at our institution. Three summary scales were created. Responses to statements, ‘I consider myself to be spiritual’ and ‘I consider myself to be religious’ generated four comparison groups: ‘spiritual only,’ ‘religious only,’ ‘both spiritual and religious’ and ‘neither.’ Analyses employed ANOVA and T tests. A total of 633 (59 %) surveys were completed. Four percentage self-identified as ‘religious only’; remaining respondents divided evenly, about 30 % into each of the other categories. Groups differed from one another on all summary scales (p < .0001). Using T tests, the ‘spiritual only’ group differed from the ‘religious only’ group regarding teaching. The ‘spiritual and religious’ group had the highest mean ratings for all summary scales. The ‘neither’ and ‘religious only’ group had the lowest mean ratings. Clinicians’ spiritual versus religious identity is associated with differences in behavior/attitudes regarding S/R toward clinical practice and medical student teaching. These findings elucidate opportunities for faculty development to explore effects of beliefs on behavior and attitudes within this realm.     

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 Computationally Efficient State Space Approach to Estimating Multilevel Regression Models and Multilevel Confirmatory Factor Models

Although the state space approach for estimating multilevel regression models has been well established for decades in the time series literature, it does not receive much attention from educational and psychological researchers. In this article, we (a) introduce the state space approach for estimating multilevel regression models and (b) extend the state space approach for estimating multilevel factor models. A brief outline of the state space formulation is provided and then state space forms for univariate and multivariate multilevel regression models, and a multilevel confirmatory factor model, are illustrated. The utility of the state space approach is demonstrated with either a simulated or real example for each multilevel model. It is concluded that the results from the state space approach are essentially identical to those from specialized multilevel regression modeling and structural equation modeling software. More importantly, the state space approach offers researchers a computationally more efficient alternative to fit multilevel regression models with a large number of Level 1 units within each Level 2 unit or a large number of observations on each subject in a longitudinal study.     

Four Covariance Structure Models for Canonical Correlation Analysis: A COSAN Modeling Approach

The mathematical connection between canonical correlation analysis (CCA) and covariance structure analysis was first discussed through the Multiple Indicators and Multiple Causes (MIMIC) approach. However, the MIMIC approach has several technical and practical challenges. To address these challenges, a comprehensive COSAN modeling approach is proposed. Specifically, we define four COSAN-CCA models to correspond with four possible combinations of the data to be analyzed and the unique parameters to be estimated. In terms of the data, one can analyze either the unstandardized or standardized variables. In terms of the unique parameters, one can estimate either the weights or loadings. Besides the unique parameters of each COSAN-CCA model, all four COSAN-CCA models also estimate the canonical correlations as their common parameters. Taken together, the four COSAN-CCA models provide the correct point estimates and standard error estimates for all commonly used CCA parameters. Two numeric examples are used to compare the standard error estimates obtained from the MIMIC approach and the COSAN modeling approach. Moreover, the standard error estimates from the COSAN modeling approach are validated by a simulation study and the asymptotic theory. Finally, software implementation and future extensions are discussed.     

The effects of physical contact and decision type on moral decision making: A study of harm to save moral behavior

This study examined the relationship between physical contact and decision type in predicting “harm to save” behavior. Participants were assigned to making either a judgment or a choice involving moral dilemmas. All participants were presented with dilemmas that either required or did not require having physical contact with potential victims. Participants were asked to decide whether to sacrifice fewer people to save more (utilitarian responses) or not to do so and thus more people would die (deontological responses). The study sample included 345 participants who completed a set of self‐report measures. Results indicated an interaction between physical contact and decision type. In the choice condition only, participants reported significantly less utilitarian responses to the dilemmas that required having physical contact with the person to be harmed than to dilemmas that did not require physical contact. This difference was not found in the judgment condition. These results contribute to a greater understanding of the nature and potential malleability of human morality.