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.     

Additive structure in qualitative data: An alternating least squares method with optimal scaling features

A method is developed to investigate the additive structure of data that (a) may be measured at the nominal, ordinal or cardinal levels, (b) may be obtained from either a discrete or continuous source, (c) may have known degrees of imprecision, or (d) may be obtained in unbalanced designs. The method also permits experimental variables to be measured at the ordinal level. It is shown that the method is convergent, and includes several previously proposed methods as special cases. Both Monte Carlo and empirical evaluations indicate that the method is robust.This research was supported in part by grant MH-10006 from the National Institute of Mental Health to the Psychometric Laboratory of the University of North Carolina. We wish to thank Thomas S. Wallsten for comments on an earlier draft of this paper. Copies of the paper and of ADDALS, a program to perform the analyses discussed herein, may be obtained from the second author.     

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.     

Is philosophy progressive?

Any adequate attempt to discuss progressivity in philosophy should provide some explanation of why philosophy persistently honours the old and the false and deals with original texts in a way in which science does not. An attempt is made to answer this question by appealing to: (1) the aporetic character of philosophy; (2) the semantical solipsism of philosophy; (3) the subjectivity of philosophy, and; (4) poetical continuities in philosophy.     

The disputation — a special type of cooperative argumentative dialogue

This article consists of three parts, two introductory, in which the limits and the methods of analysis of dialogues are expounded, and the major part, in which the main features of a philosophical theory of disputation are outlined.

Control of responding by sounds of different quality: an evolutionary analysis.

Two experiments investigated the acquisition of discriminations between two acoustic stimuli of different quality (noise bursts vs. a 2-kHz pulsed signal) when features of the everyday environment were incorporated into the experiments. In Experiment 1, rats were trained, using food, to press a lever. Throughout all sessions, 5-s trials of noise bursts (the random stimulus) were presented, after variable intertrial intervals, through a remote speaker mounted outside the experimental enclosure. The noise burst occurred randomly with respect to reinforcement of lever pressing and had no programmed relationship to the animal's behavior. When lever pressing was established, the 2-kHz signal was presented through a speaker adjacent to the response lever according to a different set of variable intertrial intervals. A response in the presence of the 2-kHz signal terminated the trial and was reinforced. The 2-kHz signal acquired control of responding within the first few trials, whereas the random stimulus exerted no control of responding. In Experiment 2, rats were trained to press the lever in the presence of the 2-kHz signal presented through the adjacent speaker on a variable intertrial interval. After 14 sessions, 5-s trials of noise bursts (random stimulus) were presented through the remote speaker on the second variable intertrial interval. The random stimulus initially elicited exploratory behavior, which then rapidly declined. Subsequently, the random stimulus exerted no or weak control of responding. The introduction of the random stimulus had no effect on responding in the presence of the adjacent stimulus. In Experiments 3 and 4 the random stimulus was presented through the adjacent speaker, and the stimulus correlated with reinforcement was presented through the remote speaker. In both experiments, there was persistent control of responding by the random stimulus and slow development of control by the stimulus correlated with reinforcement. In Experiment 5, both stimuli were presented through the adjacent speaker. There was persistent control of responding by the random stimulus.     

FACAIC: Model selection algorithm for the orthogonal factor model using AIC and CAIC

This paper describes the authors' FORTRAN algorithm FACAIC for choosing the number of factors for an orthogonal factor model using Akaike's Information Criterion. FACAIC utilizes the IMSL subroutine OFCOMM.The authors dedicate this algorithm to Professor Hirotugu Akaike in appreciation of his pioneering work on AIC which was originally intended for the factor analysis and other statistical model identification problems.     

Correspondence analysis of incomplete contingency tables

Correspondence analysis can be described as a technique which decomposes the departure from independence in a two-way contingency table. In this paper a form of correspondence analysis is proposed which decomposes the departure from the quasi-independence model. This form seems to be a good alternative to ordinary correspondence analysis in cases where the use of the latter is either impossible or not recommended, for example, in case of missing data or structural zeros. It is shown that Nora's reconstitution of order zero, a procedure well-known in the French literature, is formally identical to our correspondence analysis of incomplete tables. Therefore, reconstitution of order zero can also be interpreted as providing a decomposition of the residuals from the quasi-independence model. Furthermore, correspondence analysis of incomplete tables can be performed using existing programs for ordinary correspondence analysis.     

Consistent estimation in the rasch model based on nonparametric margins

Consider the class of two parameter marginal logistic (Rasch) models, for a test ofm True-False items, where the latent ability is assumed to be bounded. Using results of Karlin and Studen, we show that this class of nonparametric marginal logistic (NML) models is equivalent to the class of marginal logistic models where the latent ability assumes at most (m + 2)/2 values. This equivalence has two implications. First, estimation for the NML model is accomplished by estimating the parameters of a discrete marginal logistic model. Second, consistency for the maximum likelihood estimates of the NML model can be shown (whenm is odd) using the results of Kiefer and Wolfowitz. An example is presented which demonstrates the estimation strategy and contrasts the NML model with a normal marginal logistic model.This research was supported by NIMH traning grant, 2 T32 MH 15758-06 and by ONR contract N00014-84-K-0588. The author would like to thank Diane Lambert, John Rolph, and Stephen Fienberg for their assistance. Also, the comments of the referees helped to substantially improve the final version of this paper.