A bayesian approach to confirmatory factor analysis

Confirmatory factor analysis is considered from a Bayesian viewpoint, in which prior information on parameter is incorporated in the analysis. An iterative algorithm is developed to obtain the Bayes estimates. A numerical example based on longitudinal data is presented. A simulation study is designed to compare the Bayesian approach with the maximum likelihood method.Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong.     

A note on sufficient conditions that a common factor will be determinate in an infinite domain of variables

It is proved for the common factor model withr common factors that under certain condition s which maintain the distinctiveness of each common factor a given common factor will be determinate if there exists an unlimited number of variables in the model each having an absolute correlation with the factor greater than some arbitrarily small positive quantity.The author is indebted to R. P. McDonald for suggesting the proof of Guttman's determinantal equation for the squared multiple correlation in predicting a factor from the observed variables used in the parenthetical note.     

The microanalysis of fixed-interval responding

The fixed-interval schedule of reinforcement is one of the more widely studied schedules in the experimental analysis of behavior and is also a common baseline for behavior pharmacology. Despite many intensive studies, the controlling variables and the pattern of behavior engendered are not well understood. The present study examined the microstructure and superstructure of the behavior engendered by a fixed-interval 5- and a fixed-interval 15-minute schedule of food reinforcement in the pigeon. Analysis of performance typical of fixed-interval responding indicated that the scalloped pattern does not result from smooth acceleration in responding, but, rather, from renewed pausing early in the interval. Individual interresponse-time (IRT) analyses provided no evidence of acceleration. There was a strong indication of alternation in shorter-longer IRTs, but these shorter-longer IRTs did not occur at random, reflecting instead a sequential dependency in successive IRTs. Furthermore, early in the interval there was a high relative frequency of short IRTs. Such a pattern of early pauses and short IRTs does not suggest behavior typical of reinforced responding as exemplified by the pattern found near the end of the interval. Thus, behavior from clearly scalloped performance can be classified into three states: postreinforcement pause, interim behavior, and terminal behavior.     

Testing for independence between pairs of autocorrelated binomial data sequences

A problem arises in analyzing the existence of interdependence between the behavioral sequences of two individuals: tests involving a statistic such as chi-square assume independent observations within each behavioral sequence, a condition which may not exist in actual practice. Using Monte Carlo simulations of binomial data sequences, we found that the use of a chi-square test frequently results in unacceptable Type I error rates when the data sequences are autocorrelated. We compared these results to those from two other methods designed specifically for testing for intersequence independence in the presence of intrasequence autocorrelation. The first method directly tests the intersequence correlation using an approximation of the variance of the intersequence correlation estimated from the sample autocorrelations. The second method uses tables of critical values of the intersequence correlation computed by Nakamuraet al. (J. Am. Stat. Assoc., 1976,71, 214–222). Although these methods were originally designed for normally distributed data, we found that both methods produced much better results than the uncorrected chi-square test when applied to binomial autocorrelated sequences. The superior method appears to be the variance approximation method, which resulted in Type I error rates that were generally less than or equal to 5% when the level of significance was set at .05.     

Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating

Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X ₁, ...,X _s ,Y ₁, ...,Y _p ,Z ₁, ...,Z _q ) and describe an application of these estimation techniques to linear, observed-score, test equating.The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.     

A more powerful method for testing for agreement between a judge and a known standard

We assume that a judge's task is to categorize each ofN subjects into one ofr known classes. The design of primary interest is employed if the judge is presented withs groups, each containingr subjects, such that each group of sizer consists of exactly one subject of each of ther types. The probability distribution for the total number of correct choices is developed and used to test the null hypothesis that the judge is guessing in favor of the alternative that he or she is operating at a better than chance level. The power of the procedure is shown to be superior to two other procedures which appear in the literature.The authors are grateful for the suggestions of the referees and for computer funding provided by the Northeast Regional Data Center at the University of Florida.     

A simple BASIC program to generate values for variable-interval schedules of reinforcement

A BASIC program to generate values for variable-interval (VI) schedules of reinforcement is presented. A VI schedule should provide access to reinforcement with a constant probability over a time horizon. If the values in a VI schedule are calculated from an arithmetic progression, the probability of reinforcement is positively correlated with the time since the last reinforcer was delivered. Fleshler and Hoffman (1962) developed an iterative equation to calculate VI schedule values so that the probability of reinforcement remains constant. This easy-to-use program generates VI schedule values according to the Fleshler and Hoffman equation, randomizes the values, and saves the values in ASCII to a disk file.     

Some values guiding community research and action

The dual purposes of applied research-contributing to understanding and improvement-are only partially served by method systems that encourage studying (with increasing precision) a narrow range of questions of modest societal importance. To optimize contributions to challenging societal problems, a field's cherished standards should be adapted to support more adventuresome forms of community research and action. This paper outlines 10 values for community research and action, based on insights from the fields of behavioral and community psychology. These values-reflect the goals and challenges of establishing collaborative relationships with research participants, determining research goals and methods, designing and disseminating interventions, communicating research findings, and advocating for community change. Critical challenges are outlined, and implications for the field and its clients are discussed.     

EFFECTS OF CONTEXTUAL COMPETENCE ON SOCIAL INITIATIONS

The frequency of social initiations and satisfaction with interactions in three dyads, each consisting of 1 student with disabilities and 1 nondisabled peer, were assessed under two alternating conditions: Condition 1 assessed the interactions around a set of four trained computer games, and Condition 2 assessed interactions when students were playing a set of four untrained computer games. Training was conducted with a multiple baseline design across participants and was followed by social interaction probes using an alternating treatments design. The results indicated greater frequencies of social initiations by 5 of 6 participants, higher degrees of game satisfaction by all participants, and equal or higher degrees of peer satisfaction by 5 of 6 participants when playing trained games in comparison to untrained games.