Effect analysis and causation in linear structural equation models

This paper considers total and direct effects in linear structural equation models. Adopting a causal perspective that is implicit in much of the literature on the subject, the paper concludes that in many instances the effects do not admit the interpretations imparted in the literature. Drawing a distinction between concomitants and factors, the paper concludes that a concomitant has neither total nor direct effects on other variables. When a variable is a factor and one or more intervening variables are concomitants, the notion of a direct effect is not causally meaningful. Even when the notion of a direct effect is meaningful, the usual estimate of this quantity may be inappropriate. The total effect is usually interpreted as an equilibrium multiplier. In the case where there are simultaneity relations among the dependent variables in tghe model, the results in the literature for the total effects of dependent variables on other dependent variables are not equilibrium multipliers, and thus, the usual interpretation is incorrect. To remedy some of these deficiencies, a new effect, the total effect of a factorX on an outcomeY, holding a set of variablesF constant, is defined. When defined, the total and direct effects are a special case of this new effect, and the total effect of a dependent variable on a dependent variable is an equilibrium multiplier.For helpful comments, I am grateful to G. Arminger, K. Bollen, W. Faris, R. m. Hauser, T. Petersen, three anonymous Psychometrikas reviewers, and the Editor. For computational assistance, I am grateful to B. D. Kim.     

The Problem of local optimality with OSMOD

The possibility of obtaining locally optimal solutions with categorical data is pointed out for the original version of OSMOD development by Saito and Otsu. A revision of the initialization strategy in OSMOD is suggested, and its effectiveness in diminishing this possibility is demonstrated.     

Noniterative estimation and the choice of the number of factors in exploratory factor analysis

Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors, and discusses the properties of the noniterative estimation method of Ihara and Kano in exploratory factor analysis. The consistency of the Ihara and Kano estimator is shown to hold even for an overestimated number of factors, which provides a theoretical basis for the rare occurrence of improper solutions and for a new method of choosing the number of factors. The comparative study of their estimator and that based on maximum likelihood is carried out by a Monte Carlo experiment.The author would like to express his thanks to Masashi Okamoto and Masamori Ihara for helpful comments and to the editor and referees for critically reading the earlier versions and making many valuable suggestions. He also thanks Shigeo Aki for his comments on physical random numbers.     

On the distinction between perception and cognition

To uphold the distinction between perception and cognition for certain classes of tasks or phenomena, it is proposed that three criteria must be met: (1) when perceptual and cognitive functions serve different biological purposes, (2) when stimulus information in dynamic events is necessary, but not sufficient for veridical perception, and (3) when the task emphasizes explicit retrieval, as opposed to implicit use of information. Conversely, when the three criteria have not been met, conditions for theoretical unification exist.     

Dimensionality of the Multiple Affect Adjective Check List-Revised: A comparison of factor analytic procedures

The purpose of the study was to determine the factor structure of the revised Multiple Affect Adjective Check List (MAACL-R). The data from 307 undergraduate students who completed the MAACL-R were factor analyzed using both principal-components and principal-axis techniques. Based upon research with the original MAACL, two- and five-factor solutions to the MAACL-R factor structure were examined. The principal-components and principal-axis techniques yielded similar item loadings for each solution and the results of both techniques indicated the superiority of the two-factor solution. The two identified factors could be best characterized as representing independent dimensions of negative and positive affect. These findings are interpreted as providing support for the use of the MAACL-R summary scores of Dysphoria and PASS (Positive Affect and Sensation Seeking) rather than for the use of the five MAACL-R subscales.     

More on EM for ML factor analysis

We address several issues that are raised by Bentler and Tanaka's [1983] discussion of Rubin and Thayer [1982]. Our conclusions are: standard methods do not completely monitor the possible existence of multiple local maxima; summarizing inferential precision by the standard output based on second derivatives of the log likelihood at a maximum can be inappropriate, even if there exists a unique local maximum; EM and LISREL can be viewed as complementary, albeit not entirely adequate, tools for factor analysis.This work was partially supported by the Program Statistics Research Project at Educational Testing Service.     

Some contributions to efficient statistics in structural models: Specification and estimation of moment structures

Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution theory based on multivariate normality. In psychometrics the multinormality assumption is often incorrect, so that statistical tests on parameters, or model goodness of fit, will frequently be incorrect as well. It is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary. Structural representations are developed for generalizations of the Bentler-Weeks, Jöreskog-Keesling-Wiley, and factor analytic models. Some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed. Limited information estimators are obtained as well. The special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail. The argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory, which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds. Many open research areas are described.     

A comparison of factor analysis programs in SPSS,BMDP, and SAS

Factor analysis programs in SAS, BMDP, and SPSS are discussed and compared in terms of documentation, methods and options available, internal logic, computational accuracy, and results provided. Some problems with respect to logic and output are described. Based on these comparisons, recommendations are offered which include a clear overall preference for SAS, and advice against general use of SPSS for factor analysis.     

Procrustes matching by congruence coefficients

Matching by Procrustes methods involves the transformation of one matrix to match with another. A special least squares criterion, the congruence coefficient, has advantages as a criterion for some factor analytic interpretations. A Procrustes method maximizing the congruence coefficient is given. This solution is identical to Mosier's [1939] approximate solution, but is an exact solution for maximum congruence.