Data, model, conclusion, doing it again

This paper explores the robustness of conclusions from a statistical model against variations in model choice (rather than variations in random sampling and random assignment to treatments, which are the usual variations covered by inferential statistics). After the problem formulation in section 1, section 2 presents an example from Box and Tiao in which variation in parent distribution is modeled for a one sample location problem. An adaptive Bayesian procedure permits to use a weighted mixture of parent distributions rather than choosing just one, such as a normal or a uniform distribution.In section 3 similar considerations are applied to an event history model for the influence of education and gender on age at first marriage, but here the conclusions are hardly influenced by the choice of the duration distribution. In section 4 a brief discussion of model choice in factor analysis and structural equation models is followed by a more elaborate treatment of the choice of integer valued slopes for item response functions in the OPLM model which is an extension of the Rasch model. A modest simulation study suggests that Adaptive Bayesian Modeling with a mixture of sets of slopes works better than fixing one set of postulated slopes.The paper concludes with some remarks on the roles and sources of prior distributions followed by a short epilogue which argues that simultaneous consideration of a class of models for the same data is sometimes superior to exclusively analyzing the data under one specific model chosen from such a class.This article is based on the Presidential Address Ivo W. Molenaar gave on June 20, 1998 at the 1998 Annual Meeting of the Psychometric Society held at the University of Illinois in Champaign, Illinois. Thanks is given to John Wiley & Sons and George C. Tiao for granting permission to reprint three figures from the book George C. Tiao wrote with George E. P. Box titled Bayesian Inference in Statistical Analysis.—EditorThanks are due to Anne Boomsma, Jeffrey Hoogland, Mark Huisman, Tom Snijders, Marijtje Van Duijn, and Norman Verhelst for suggesting improvements and/or assisting with data analyses.     

Neuroticism,coping and change in MCMI-II clinical syndromes: test of a mediator model

The aim of the study was to examine prospectively whether coping mediated the relation between Neuroticism and change in different clinical mental syndromes. Assessments were conducted with 154 former psychiatric outpatients six and seven years after their initial contact with an outpatient clinic. Dispositional coping mediated the relation between Neuroticism and change in four of the nine clinical scales of the Millon Clinical Multiaxial Inventory (MCMI-II) (Millon, 1987). High Neuroticism led to coping strategies of disengagement and the venting of emotions and to a lack of problem-focused coping, which in turn translated into a relative increase on the MCMI-II scales. The mediator model of coping was found to apply to the MCMI-II scales "somatoform disorder’, ‘dysthymia’, ‘alcohol dependence’ and ‘thought disorder’. Results are discussed under the perspective of an integration of the positions of the transactional theory of stress and personality psychology. .     

Optimal sequential designs for on-line item estimation

Replenishing item pools for on-line ability testing requires innovative and efficient data collection designs. By generating localD-optimal designs for selecting individual examinees, and consistently estimating item parameters in the presence of error in the design points, sequential procedures are efficient for on-line item calibration. The estimating error in the on-line ability values is accounted for with an item parameter estimate studied by Stefanski and Carroll. LocallyD-optimaln-point designs are derived using the branch-and-bound algorithm of Welch. In simulations, the overall sequential designs appear to be considerably more efficient than random seeding of items.This report was prepared under the Navy Manpower, Personnel, and Training R&D Program of the Office of the Chief of Naval Research under Contract N00014-87-0696. The authors wish to acknowledge the valuable advice and consultation given by Ronald Armstrong, Charles Davis, Bradford Sympson, Zhaobo Wang, Ing-Long Wu and three anonymous reviewers.     

The relation of family cohesion to marital adjustment

The purpose of this study was to investigate the relationship between family cohesion and marital adjustment. The sample consisted of 70 married graduate students from the State University of New York at Buffalo. The Family Adaptability and Cohesion Evaluation Scale was used to measure family cohesion. The Dyadic Adjustment Scale was used to measure marital adjustment. The Demographic Data Sheet was used for demographic characteristics. Overall, the result of ANOVA with planned comparison revealed that high marital adjustment was not only associated with a moderate level of family cohesion but also associated with a high level of family cohesion.This article is based on the first author's doctoral dissertation at State University of New York at Buffalo.     

‘So you did what you wanted then’: Discourse analysis,personal agency,and psychotherapy

This paper explores issues concerning personal agency in discursive psychology and discourse analysis, with a particular emphasis on agency in terms of motivational accounts of the person. Issues are discussed in relation to the efficacy, acceptability, and accessibility of discourse analytic research for the practising psychotherapist. We suggest that such an approach may raise problems in four areas. First, we argue that without explicit theorization of the subject as language user, discourse analysis may be vulnerable to the charge of determinism. Second, theorization of the subject as language user may be required to account successfully for individual consistency and continuity of identity. Third, although claiming to critique commonsense notions of subjectivity, implicit dualist assumptions facilitate a reading of discursive psychology that is compatible with a motivational model of the person. Finally, we argue that discursive psychology itself implies a particular model of the strategically motivated language user. We conclude that, although these issues require clarification, discursive psychology and discourse analysis have much to offer psychotherapy research.     

The relation between the generalized matching law and signal-detection theory

The generalized matching law can be applied to a signal-detection matrix to give two equations. The first relates responding in the presence of the stimulus to the reinforcements for the responses, and the second relates responding in the absence of the stimulus to the reinforcements for the responses. Evidence for stimulus discrimination is given by biases that are opposite in sign in the two equations. As the logarithmic ratio and z proportion transformations are similar, the combination of the absolute values of the two logarithmic biases gives a measure equivalent to the signal-detection measures d′ and η. The two equations can also be combined to eliminate the biases caused by the signalling stimuli and to produce a generalized matching-law statement relating overall performance to the obtained reinforcements.     

Optimal scaling of paired comparison and rank order data: An alternative to guttman's formulation

A formulation, which is different from Guttman's is presented. The two formulations are both called the optimal scaling approach, and are proven to provide identical scale values. The proposed formulation has at least two advantages over Guttman's. Namely, (i) the former serves to clarify close relations of the optimal scaling approach to those of Slater and the vector model of preferential choice, and (ii) in addition to the stimulus scale values, it provides scores for the subjects, which indicate the degrees of response consistency (transitivity), relative to the optimum solution. The method is assumption-free and capable of multidimensional analysis.This study was partly supported by the National Research Council Grant (No. A4581) to S. Nishisato. The author is indebted to Dr. Bert F. Green, Jr., Mr. Tomoichi Ishizuka, and anonymous reviewers for their valuable comments on an earlier draft.     

Approximate interval estimation for a certain intraclass correlation coefficient

When the raters participating in a reliability study are a random sample from a larger population of raters, inferences about the intraclass correlation coefficient must be based on the three mean squares from the analysis of variance table summarizing the results: between subjects, between raters, and error. An approximate confidence interval for the parameter is presented as a function of these three mean squares.Dr. Fleiss is also with the Biometrics Research Unit of the New York State Psychiatric Institute. This work was supported in part by grant DE 04068 from the National Institute of Dental Research.     

Contributions to factor analysis of dichotomous variables

A new method is proposed for the factor analysis of dichotomous variables. Similar to the method of Christoffersson this uses information from the first and second order proportions to fit a multiple factor model. Through a transformation into a new set of sample characteristics, the estimation is considerably simplified. A generalized least-squares estimator is proposed, which asymptotically is as efficient as the corresponding estimator of Christoffersson, but which demands less computing time.This research was supported by the Bank of Sweden Tercentenary Foundation under project Structural Equation Models in the Social Sciences, project director Karl G. Jöreskog.     

Statistical inference based on ranks

This paper develops a unified approach, based on ranks, to the statistical analysis of data arising from complex experimental designs. In this way we answer a major objection to the use of rank procedures as a major methodology in data analysis. We show that the rank procedures, including testing, estimation and multiple comparisons, are generated in a natural way from a robust measure of scale. The rank methods closely parallel the familiar methods of least squares, so that estimates and tests have natural interpretations.This research was supported in part by grant MCS76-07292 from the National Science Foundation.