An incomplete data approach to the analysis of covariance structures

In this paper, linear structural equation models with latent variables are considered. It is shown how many common models arise from incomplete observation of a relatively simple system. Subclasses of models with conditional independence interpretations are also discussed. Using an incomplete data point of view, the relationships between the incomplete and complete data likelihoods, assuming normality, are highlighted. For computing maximum likelihood estimates, the EM algorithm and alternatives are surveyed. For the alternative algorithms, simplified expressions for computing function values and derivatives are given. Likelihood ratio tests based on complete and incomplete data are related, and an example on using their relationship to improve the fit of a model is given.This research forms part of the author's doctoral thesis and was supported by a Commonwealth Postgraduate Research Award. The author also wishes to acknowledge the support of CSIRO during the preparation of this paper and the referees' comments which led to substantial improvements.     

FUNCTIONAL ANALYSIS AND TREATMENT OF EYE POKING

In four studies we analyzed the eye poking of a youth with profound disabilities. In Study 1, a functional analysis showed that eye poking occurred during the no-attention condition, but not during demand, attention, or recreation conditions. The analysis did not identify socially mediated variables involved in the maintenance of eye poking; rather, eye poking may have been maintained by consequences produced directly by the response. In Study 2 we had the student wear goggles to prevent potential reinforcement from finger—eye contact. The results of Study 2 indicated that eye-poking attempts were reduced when the student wore goggles. We then tested in Study 3 the effects of two alternative topographies of stimulation. Study 3 demonstrated that eye poking was reduced when a video game was provided as a competing source of visual stimulation, and that music was less effective in reducing eye poking. In Study 4, a contingency analysis using the video game was conducted in an attempt to (a) reduce the frequency of eye poking and (b) study whether the video game functioned as a reinforcer. The results of Study 4 demonstrated substantive reductions in the frequency of eye poking, and suggested that the video game served as a reinforcer.     

Gender and Grade Differences in Latent Ability Variables

Scores in ability tests administered to students in grades 4–9 were simultaneously factor-analyzed within twelve gender by grade groups. Gender and grade differences in means and variances were studied for five latent ability factors according to a hierarchical model and compared with means and variances in the observed scores.
Girls had higher means than boys in a general ability factor (G), in a residual general speed factor (Gs') and in a residual factor of numerical facility (N'). Boys were higher in a residual vocabulary factor (V') and most of all in a residual spatial visualization factor (Vz'). Boys had larger variances than girls in N' and Gs'. In general the differences in means and variances were in the same direction for the closest corresponding observed scores, but some striking discrepancies between latent and observed scores were found. As a rule, the discrepancies were due to the complexity of the tests where one factor could compensate for another.
In the discussion it was pointed out that some of the differences found were likely to have changed between the testing in the late 1950s and the present. Nevertheless the demonstration of the divergence between analyses of latent vs. observed scores remains valid.     

Rasch's model for reading speed with manifest explanatory variables

In educational and psychological measurement we find the distinction between speed and power tests. Although most tests are partially speeded, the speed element is usually neglected. Here we consider a latent trait model developed by Rasch for the response time on a (set of) pure speed test(s), which is based on the assumption that the test response times are approximately gamma distributed, with known shape parameters and scale parameters depending on subject ability and test difficulty parameters. In our approach the subject parameters are treated as random variables having a common gamma distribution. From this, maximum marginal likelihood estimators are derived for the test difficulties and the parameters of the latent subject distribution. This basic model can be extended in a number of ways. Explanatory variables for the latent subject parameters and for the test parameters can be incorporated in the model. Our methods are illustrated by the analysis of a simulated and an empirical data set.     

TREATMENT INTEGRITY IN APPLIED BEHAVIOR ANALYSIS WITH CHILDREN

Functional analysis of behavior depends upon accurate measurement of both independent and dependent variables. Quantifiable and controllable operations that demonstrate these functional relationships are necessary for a science of human behavior. Failure to implement independent variables with integrity threatens the internal and external validity of experiments. A review of all applied behavior analysis studies with children as subjects that have been published in the Journal of Applied Behavior Analysis between 1980 and 1990 found that approximately 16% of these studies measured the accuracy of independent variable implementation. Two thirds of these studies did not operationally define the components of the independent variable. Specific recommendations for improving the accuracy of independent variable implementation and for defining independent variables are discussed.     

Change mechanisms in cognitive therapy of a simple phobia: Logical analysis and empirical hypothesis testing

The effectiveness of two hypothesized change mechanisms in cognitive therapy was investigated: logical analysis and empirical hypothesis testing. Thirty-eight spider phobics, as determined by performance on a behavioral avoidance test, were randomly assigned to either one of these two conditions or to a no-treatment control condition. Subjects participated in three group sessions. Outcome phobia questionnaire data suggested that both mechanisms produced desirable changes in a short period of time, with stronger evidence that logical analysis was superior to the control. Outcome from the behavior avoidance test and self-efficacy ratings failed to reach statistical significance but the trends were in the direction of positive change. Results are discussed in terms of the tripartite response dessynchrony hypothesis. Suggestions for future process research in cognitive therapy are provided.William O'Donohue, Ph.D., is an assistant professor of psychology at Northern Illinois University.Jeff Szymanski is a graduate student in clinical psychology at Northern Illinois University.The authors would like to thank Christine Casselles, Melissa McKelvie, Thomas M. Brown, Jill C. Rudman, Bonnie Schrieber, Amy Ray, Anne Valle, Lisa Herold, Jacqueline Ryan, Heather Barta, and Angela Leek for their assistance in this project. Moreover, the authors are grateful to Sol Feldman and Jane Fisher for their comments on an earlier version of this paper.     

A simple Gauss-Newton procedure for covariance structure analysis with high-level computer languages

An implementation of the Gauss-Newton algorithm for the analysis of covariance structures that is specifically adapted for high-level computer languages is reviewed. With this procedure one need only describe the structural form of the population covariance matrix, and provide a sample covariance matrix and initial values for the parameters. The gradient and approximate Hessian, which vary from model to model, are computed numerically. Using this approach, the entire method can be operationalized in a comparatively small program. A large class of models can be estimated, including many that utilize functional relationships among the parameters that are not possible in most available computer programs. Some examples are provided to illustrate how the algorithm can be used.We are grateful to M. W. Browne and S. H. C. du Toit for many invaluable discussions about these computing ideas. Thanks also to Scott Chaiken for providing the data in the first example. They were collected as part of the U.S. Air Force's Learning Ability Measurement Project (LAMP), sponsored by the Air Force Office of Scientific Research (AFOSR) and the Human Resource Directorate of the Armstrong Laboratory (AL/HRM).     

Fifth grade school adjustment and later arrest rate: A longitudinal study of middle school antisocial boys

This study investigated the efficacy of three different regression models in predicting arrest rate over the fifth to seventh grade range for a sample of antisocial and at risk control middle school boys (N=76). These boys were selected from a larger sample of approximately 200 boys and their families for inclusion in a long term longitudinal study beginning in the fourth grade. Subjects in the present study were identified when they were in the fifth grade and school measures of adjustment were recorded annually for them on two occasions (fall, spring) through the ninth grade. Predictors were derived from the following variables: (a) teacher ratings of social skills; (b) direct observations of academic engagement in classroom settings; (c) direct observations of the playground social behavior of target subjects and peers; and (d) discipline contacts with the principal's office as extracted from archival school records. These predictor variables appeared to assess respectively teacher related and peer related forms of school adjustment. The regression models investigated yielded R-Squares of approximately 30 between arrest rate and two to three predictor variables in each analysis. However, following the deletion of two subject cases that represented extreme instances of underprediction (i.e., subjects who were arrested [i.e., seven arrests each] but whose fifth grade behavioral profiles suggested they would not be), the obtained R-Squares increased to approximately .55. Implications of the findings for the early screening and identification of at risk students are discussed.     

VIDEO-BASED TRAINING OF RESPITE CARE PROVIDERS: AN INTERACTIONAL ANALYSIS OF PRESENTATION FORMAT

We conducted two studies to evaluate a video-based instructional package for training respite care providers and the role of presentation format (viewing the videotapes alone, with a partner, and with structured group training) as a contextual variable. In Study 1, the results of a within-subjects Latin square design nested within a multiple baseline showed that performance during simulated (role-played) respite care situations improved in five of the six skill areas for the 12 trainees following presentation of the videotape, with no differences between presentation formats. Correct responding generalized to respite care situations involving a developmentally disabled child, and in most cases, acquired skills were maintained for up to 6 months. In Study 2, we conducted a clinical replication of Study 1 under conditions more closely approximating those in which the training program would be implemented by respite care agencies. Results of the between-groups analysis were consistent with the findings of Study 1.     

Testing the conditional independence and monotonicity assumptions of item response theory

When item characteristic curves are nondecreasing functions of a latent variable, the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses. This general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves. The proposed tests are simple, have known asymptotic null distributions, and possess certain optimal properties. In an example, the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves.The author acknowledges Paul W. Holland for valuable conversations on the subject of this paper; Henry Braun and Fred Lord for comments at a presentation on this subject which led to improvements in the paper; Carl H. Haag for permission to use the data in §4; Bruce Kaplan for assistance with computing; and two referees for helpful suggestions. Requests for reprints should be sent to Paul R. Rosenbaum