The direct product model for the mtmm matrix parameterized as a second order factor analysis model

The composite direct product model for the multitrait-multimethod matrix is reparameterized as a second-order factor analysis model. This facilitates the use of widely available computer programs such as LISREL and LISCOMP for fitting the model.Bruce Bloxom. Paul Horst and Karl Jöreskog contributed helpful comments to an earlier version of this paper. Their suggestions are gratefully acknowledged.     

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.     

Multiplicative Covariance Structure Models in the Analysis of Scores on a Chinese Version of an Academic Self-Concept Scale

The purpose of this study was to examine the construct validity of scores on a Chinese version of an academic self-concept measure entitled Dimensions of Self-Concept (DOSC) using composite direct product (CDP) models. Measures of five traits-Level of Aspiration, Anxiety, Academic Interest and Satisfaction, Leadership and Initiative, and Identification vs. Alienation-were obtained from a convenience sample of 769 junior high school students by using self ratings, peer ratings, and parent ratings. The degree of convergent and discriminant validity was moderate to low based on the evaluation in terms of both Campbell and Fiske (1959) guidelines and the comparison of nested multitrait-multimethod CDP models. In particular, concern about the discriminant validity of scores on traits of Level of Aspiration, Academic Interest and Satisfaction, and Identification vs. Alienation was raised. Implications for the use of CDP models in the assessment of construct validity of scores on an academic self-concept measure were discussed.     

Positioning models in marketing: Toward a normative-integrated model

In this paper we argue that the optimal use of positioning models employed in marketing communication (e.g., multiattribute attitude models, self-image congruence models) is a function of situational factors such as product utilitarianism and product value-expressiveness. A normative model is introduced to show how positioning models can be used effectively.     

新世纪20年国内心理统计方法研究回顾

新世纪头20年, 国内心理学11本专业期刊一共发表了213篇统计方法研究论文。研究范围主要包括以下10类(按论文篇数排序)：结构方程模型、测验信度、中介效应、效应量与检验力、纵向研究、调节效应、探索性因子分析、潜在类别模型、共同方法偏差和多层线性模型。对各类做了简单的回顾与梳理。结果发现, 国内心理统计方法研究的广度和深度都不断增加, 研究热点在相互融合中共同发展; 但综述类论文比例较大, 原创性研究论文比例有待提高, 研究力量也有待加强。     

Reliability coefficients as a function of individual differences induced by a learning process assuming identical organisms

In this article we show that a particular mathematical learning model, the Bower-Trabasso (1964) concept identification model taken together with an assumption of independence of replicate measurements, implies the existence of substantial and statistically significant performance differences across individuals. The individual differences in turn imply a sizeable reliability coefficient. These results contradict naive intuition, for this model (like many other mathematical models of learning) assumes that all individuals begin the experiment with identical parameter values for the process under study. Thus at least one such model has the characteristic of implying the generation of individual performance differences among originally identical organisms.Examination of data from an experiment by Cotton shows that the Hoyt reliability coefficient under classical test theory, a lower bound for the (composite) reliability of total scores for a series of trials, increases with the number of trials analyzed and exceeds the corresponding theoretical values implied by the Bower-Trabasso model. An experiment by Levine was also analyzed because its use of blank trials between feedback trials permitted direct calculation of composite reliability (or more properly stated composite consistency). For this experiment, the theoretical development just discussed (Case I) was used together with Restle's hypothesis selection model specialized to include a local consistency assumption, the so-called P₂ model of Gregg and Simon (Case II). Moderate conformity of empirical and theoretical reliabilities was found, with discrepancies between observed and predicted values usually being smaller with Case II. However, the Hoyt reliability coefficient is not a lower bound for composite reliability in Case II, because composite reliability is underestimated when identical stimuli are not used for comparable trials.Despite the Bower-Trabasso assumption of no initial differences, it seems reasonable to attribute the difference between predicted and obtained reliabilities to preexisting individual differences. Implications of the tentative conclusion that individual differences in concept identification performance are attributable to a combination of preexisting differences and differences induced in a current task are discussed briefly.     

When thinking is beneficial and when it is not: The effects of thin and round advertising models

This study addresses the advertising effectiveness of round and thin models. Integrating previous findings and theories, the authors predict and find that impulsive and reflective product evaluations as responses to thin and round advertisement models diverge. Specifically, four experiments indicate that impulsive product evaluations follow a priming logic, such that the beauty of the model spills over directly onto product evaluations; thin models thus produce more favorable implicit responses than do round models. For reflective product evaluations however, this pattern appears reversed. Moreover, these explicit product evaluations are mediated by campaign liking.     

A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses

The paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model. The model considers time-dependent latent variables and item-specific random effects to be accountable for the interdependencies of the multivariate ordinal items. Time-dependent latent variables are linked with an autoregressive model. Simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood. Model selection criteria developed for composite likelihood estimation are used in the applications. Furthermore, lower-order residuals are used as measures-of-fit for the selected models.     

Explaining the extraversion/positive affect relation: sociability cannot account for extraverts' greater happiness

The association between Extraversion and positive affect is one of the most robust findings in the study of personality and emotion. Temperament models posit that the association is direct; instrumental models posit that the association is mediated by additional processes. Two experience sampling studies were conducted to test instrumental mechanisms that might underlie the effect. According to a mediation model, extraverts' greater social activity can account for their increased positive affect when compared to introverts. According to a person-by-situation interaction model, extraverts react more positively to social situations than do introverts, and this interaction can account for the association. Only weak support for the instrumental models was found; consistent with temperament models, a moderate direct association remained even after controlling for these effects.     

Logistic latent trait models with linear constraints

Two linearly constrained logistic models which are based on the well-known dichotomous Rasch model, the ‘linear logistic test model’ (LLTM) and the ‘linear logistic model with relaxed assumptions’ (LLRA), are discussed. Necessary and sufficient conditions for the existence of unique conditional maximum likelihood estimates of the structural model parameters are derived. Methods for testing composite hypotheses within the framework of these models and a number of typical applications to real data are mentioned.     

Comparisons of models of associative recall

We tested three mathematical models of associative recall that differ in the assumed structure of the memory trace (direct or indirect connections between parts) and the interdependence of the connections (independent or correlated). The three models compared are the “horizontal” model with direct, independent connections, the “schema” model with indirect, independent connections, and the “fragment” model with indirect, correlated connections. In Experiment 1, subjects studied quartets of minimally related words and then recalled, using one or two words of each quartet as cues. The horizontal and schema models predicted the data very well, but the fragment model did poorly. In Experiment 2, related word quintets were learned, and recall cues contained one, two, or three words of a quintet. Only the schema model adequately fit these data. Experiment 3 directly tested the fragment model, using sequential tests of unrelated word quartets. Even an augmented fragment model with extra recall failure parameters was decisively rejected by these data. Both the horizontal and schema models gave satisfactory qualitative accounts, although poor quantitative fits. A means of deriving the models through a spreading activation semantic network of preexperimental knowledge is suggested, and related models are discussed.     

Engagement within occupational trainees: Individual difference predictors and commitment outcome

The present study examines occupational entrants' experiences of their vocational training, its relation with relevant internal characteristics, and its proposed impact on commitment to the profession. Particular focus is paid to trainees' engagement, hypothesizing motivation and self-efficacy as predictors, and occupational commitment as a distal outcome. Data were from 247 recent entrants into professional degree programs (architecture, engineering). All hypothesized predictive relations were supported, such that motivation (as both a composite and as solely intrinsic) and self-efficacy are predictive of engagement, and engagement is predictive of occupational commitment among early-stage trainees. Further, engagement partially mediated the relation between self-efficacy and commitment, and fully mediated the relation between motivation and commitment. Squared multiple correlations for endogenous variables indicated substantial variance in engagement and commitment accounted for by their respective predictors. Moreover, two structural equation models were examined and compared, proposing more holistic nomological nets for how these constructs fit together. A respecified model accounting for a sole focus on intrinsic motivation and a direct path between motivation and commitment was an excellent fit, superseding a competing model conceptualizing motivation as a composite and only an indirect motivation–commitment path. Finally, need for achievement moderated the relation between motivation and engagement such that the relation is stronger for individuals high in need for achievement than it is for those low in the desire to grow in their profession. The study contributes to our understanding of how early occupational trainees' experiences of work and individual characteristics impact their commitment to their intended profession.     

Capturing equilibrium models in modal logic

Here-and-there models and equilibrium models were investigated as a semantical framework for answer-set programming by Pearce, Valverde, Cabalar, Lifschitz, Ferraris and others. The semantics of equilibrium logic is given in an indirect way: the notion of an equilibrium model is defined in terms of quantification over here-and-there models. We here give a direct semantics of equilibrium logic, stated for a modal language embedding the language of equilibrium logic.     

Structural Equation Models in a Redundancy Analysis Framework With Covariates

A recent method to specify and fit structural equation modeling in the Redundancy Analysis framework based on so-called Extended Redundancy Analysis (ERA) has been proposed in the literature. In this approach, the relationships between the observed exogenous variables and the observed endogenous variables are moderated by the presence of unobservable composites, estimated as linear combinations of exogenous variables. However, in the presence of direct effects linking exogenous and endogenous variables, or concomitant indicators, the composite scores are estimated by ignoring the presence of the specified direct effects.

To fit structural equation models, we propose a new specification and estimation method, called Generalized Redundancy Analysis (GRA), allowing us to specify and fit a variety of relationships among composites, endogenous variables, and external covariates. The proposed methodology extends the ERA method, using a more suitable specification and estimation algorithm, by allowing for covariates that affect endogenous indicators indirectly through the composites and/or directly. To illustrate the advantages of GRA over ERA we propose a simulation study of small samples. Moreover, we propose an application aimed at estimating the impact of formal human capital on the initial earnings of graduates of an Italian university, utilizing a structural model consistent with well-established economic theory.     

A tutorial on Bayes factor estimation with the product space method

The Bayes factor is an intuitive and principled model selection tool from Bayesian statistics. The Bayes factor quantifies the relative likelihood of the observed data under two competing models, and as such, it measures the evidence that the data provides for one model versus the other. Unfortunately, computation of the Bayes factor often requires sampling-based procedures that are not trivial to implement. In this tutorial, we explain and illustrate the use of one such procedure, known as the product space method (Carlin & Chib, 1995). This is a transdimensional Markov chain Monte Carlo method requiring the construction of a “supermodel” encompassing the models under consideration. A model index measures the proportion of times that either model is visited to account for the observed data. This proportion can then be transformed to yield a Bayes factor. We discuss the theory behind the product space method and illustrate, by means of applied examples from psychological research, how the method can be implemented in practice.