The Use of Multitrait–Multimethod Data for Detecting Nonlinear Relationships: The Case of Psychological Climate and Job Satisfaction

Previous monomethod research has found mixed support for nonlinear effects between certain job characteristics (e.g., job autonomy, job complexity) and outcome variables (e.g., job performance). We hypothesized that these weak nonlinear findings may be due to the prevalence of monomethod research that can lead to a lack of complete measurement and/or introduce common methods variance, either of which may mask the true shape of relationships. Using hierarchical regression analyses and a multitrait–multimethod (MTMM) research design, we found strikingly different results between monomethod and MTMM data when considering the relationships between three psychological climate variables and job satisfaction. While the monomethod results mirrored earlier inconclusive findings, the MTMM data indicated that nonlinear equations explained significantly more of the relationship between all three climate dimensions and job satisfaction. These results suggest that the use of MTMM data allows one to more effectively test for nonlinear effects. Furthermore, these nonlinear results suggest that the format of employee questionnaires should probably change from asking how much an employee has of certain constructs to asking does the employee want more or less of these constructs.     

The "Natural" and the "Formal"

The paper presents an argument against a metaphysical conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: the realm of the natural, constituted by the things of our empirical world, and the realm of the formal, constituted by the structures that we use as prisms to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic.     

Likelihood inference on the underlying structure of IRT models

The assumptions underlying item response theory (IRT) models may be expressed as a set of equality and inequality constraints on the parameters of a latent class model. It is well known that the same assumptions imply that the parameters of the manifest distribution have to satisfy a more complicated set of inequality constraints which, however, are necessary but not sufficient. In this paper, we describe how the theory for likelihood-based inference under equality and inequality constraints may be used to test the underlying assumptions of IRT models. It turns out that the analysis based directly on the latent structure is simpler and more flexible. In particular, we indicate how several interesting extensions of the Rasch model may be obtained by partial relaxation of the basic constraints. An application to a data set provided by Educational Testing Service is used to illustrate the approach.We thank Dr. Gorman and Dr. Rogers of the Educational Testing Service for providing the data analyzed in Section 4. We also thank three reviewers for comments and suggestions.This revised article was published online in August 2005 with the PDF paginated correctly.     

Translating Toulmin Diagrams: Theory Neutrality in Argument Representation

The Toulmin diagram layout is very familiar and widely used, particularly in the teaching of critical thinking skills. The conventional box-and-arrow diagram is equally familiar and widespread. Translation between the two throws up a number of interesting challenges. Some of these challenges (such as the relationship between Toulmin warrants and their counterparts in traditional diagrams) represent slightly different ways of looking at old and deep theoretical questions. Others (such as how to allow Toulmin diagrams to be recursive) are diagrammatic versions of questions that have already been addressed in artificial intelligence models of argument. But there are further questions (such as the relationships between refutations, rebuttals and undercutters, and the roles of multiple warrants) that are posed as a specific result of examining the diagram inter-translation problem. These three classes of problems are discussed. To the first class are addressed solutions based on engineering pragmatism; to the second class, are addressed solutions drawn from the appropriate literature; and to the third class, fuller exploration is offered justifying the approaches taken in developing solutions that offer both pragmatic utility and theoretical interest. Finally, these solutions are explored briefly in the context of the Araucaria system, showing the ways in which analysts can tackle arguments either using one diagrammatic style or another, or even a combination of the two.     

“Seeing Conversion Whole”: Testing a Model of Religious Conversion

Rambo (1993) theorized that religious conversion consists of a process involving seven dimensions, labeled context, crisis, quest, encounter, interaction, commitment, and consequences. To test the Rambo model, a new measure, the 97-item Adult Religious Conversion Experiences Questionnaire (ARCEQ), was developed, revised on the basis of feedback from a focus group, and administered by mail to 110 adult volunteers who self-identified as having experienced conversion. Reliability analysis of the subscales of the ARCEQ resulted in five (crisis, quest, encounter, commitment, and consequences) meeting the criterion ( > .80). A sixth (interaction) achieved a reliability of .76 and was retained, but the seventh (context) was dropped. Principal components factor analysis with Varimax rotation produced factors labeled Redemptive Love, Zealous Dedication, Dysphoric Need, Openness to Uncertainty, Extrinsic Crisis, and Experiential Learning, which could readily be interpreted in relation to Rambo's model. Subsidiary analyses showed a number of significant correlations between demographic characteristics of the sample and differences in religious conversion experience.     

Assessing the distinguishability of models and the informativeness of data

A difficulty in the development and testing of psychological models is that they are typically evaluated solely on their ability to fit experimental data, with little consideration given to their ability to fit other possible data patterns. By examining how well model A fits data generated by model B, and vice versa (a technique that we call landscaping), much safer inferences can be made about the meaning of a model's fit to data. We demonstrate the landscaping technique using four models of retention and 77 historical data sets, and show how the method can be used to: (1) evaluate the distinguishability of models, (2) evaluate the informativeness of data in distinguishing between models, and (3) suggest new ways to distinguish between models. The generality of the method is demonstrated in two other research areas (information integration and categorization), and its relationship to the important notion of model complexity is discussed.     

Influence of consonantal context on the pronunciation of vowels: a comparison of human readers and computational models

In two experiments, we found that college students' pronunciations of vowels in nonwords are influenced both by preceding and following consonants. The predominance of rimes in previous studies of reading does not appear to arise because readers are unable to pick up associations that cross the onset-rime boundary, but rather because English has relatively few such associations. Comparisons between people's vowel pronunciations and those produced by various computational models of reading showed that no model provided a good account of human performance on nonwords for which the vowel shows contextual conditioning. Possible directions for improved models are suggested.     

Remarks on the identifiability of thurstonian paired comparison models under multiple judgment

It is well-known that the representations of the Thurstonian models for difference judgment data are not unique. It has been shown that equivalence classes can be formed to provide a more meaningful partition of the covariance structures of the Thurstonian ranking models. In this paper, we examine the equivalence relations between Thurstonian covariance structure models for paired comparison data obtained under multiple judgment and discuss their implications on the general identification constraints and methods to check for parameter identifiability in restricted models.The author is indebted to Ulf Böckenholt and Albert Maydeu-Olivares for their significant comments and suggestions which led to considerable improvement in this article.     

Model comparison of nonlinear structural equation models with fixed covariates

Recently, it has been recognized that the commonly used linear structural equation model is inadequate to deal with some complicated substantive theory. A new nonlinear structural equation model with fixed covariates is proposed in this article. A procedure, which utilizes the powerful path sampling for computing the Bayes factor, is developed for model comparison. In the implementation, the required random observations are simulated via a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm. It is shown that the proposed procedure is efficient and flexible; and it produces Bayesian estimates of the parameters, latent variables, and their highest posterior density intervals as by-products. Empirical performances of the proposed procedure such as sensitivity to prior inputs are illustrated by a simulation study and a real example.This research is fully supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project No. CUHK 4346/01H). The authors are thankful to the Editor, the Associate Editor, and anonymous reviewers for valuable comments which improve the paper significantly, and grateful to ICPSR and the relevant funding agency for allowing use of the data in the example. The assistance of Michael K.H. Leung and Esther L.S. Tam is gratefully acknowledged.