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).     

Analyzing preventive trials with generalized additive models

Described a new class of nonparametric regression procedures called generalized additive models (Hastie and Tibshirani, 1991) for assessing intervention effects in mental health preventive field trials. Such models are often better than analysis of covariance models for examining intervention effects adjusted for one or more baseline characteristics and for assessing potential interactions between the intervention and baseline characteristics. Because of these advantages, generalized additive models are important tools analysts should consider in evaluating preventive field trials. We apply generalized additive models as well as more standard linear models to data from a preventive trial aimed at improving mental health and school performance outcomes through a universal intervention in first and second grades. Practical guidance is given to researchers regarding when generalized additive models would be beneficial.     

A multidimensional latent trait model for measuring learning and change

A latent trait model is presented for the repeated measurement of ability based on a multidimensional conceptualization of the change process. A simplex structure is postulated to link item performance under a given measurement condition or occasion to initial ability and to one or more modifiabilities that represent individual differences in change. Since item discriminations are constrained to be equal within a measurement condition, the model belongs to the family of multidimensional Rasch models. Maximum likelihood estimators of the item parameters and abilities are derived, and an example provided that shows good recovery of both item and ability parameters. Properties of the model are explored, particularly for several classical issues in measuring change.     

Measuring clinical pain

There are two goals in attempts to measure, the intention to describe and the intention to compare. These two functions work hand in hand and are brought to fruition in psychological and educational testing only by psychometrics that can produce person-free item calibrations and item-free person measures. The only such psychometrics that currently exist is that based on George Rasch's work. One of the consequences of using the tools Rasch left us is the Pain Scale, a rating scale that asks the person in pain to compare the intensityof his/her own pain with that he/she imagines is described by some 25 adjectives. Analyses of the responses of 53 people with chronic lower back pain to the Pain Scale using the Rasch partial-credit latent-trait model show that they were very much in agreement about the amount of hurt implied by each of the adjectives. An examination of person fit to the partial-credit model gave no hint of a response set in the data but two people did differ very much from their peers in their operational definitions of back pain and were studied separately. The evidence from these two people suggested that they either could not understand the task before them or could not get enough perspective on their pain to describe its intensity.I would like to thank Benjamin Wright and Geoff Masters for their help with this research. Drs. David J. Smith and James B. Boscardin were the first to bring my attention to the problem of measuring pain and were generous in their financial support of this work.     

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     

Economics, ecologics, and mechanics: The dynamics of responding under conditions of varying motivation

The mechanics of behavior developed by Killeen (1994) is extended to deal with deprivation and satiation and with recovery of arousal at the beginning of sessions. The extended theory is validated against satiation curves and within-session changes in response rates. Anomalies, such as (a) the positive correlation between magnitude of an incentive and response rates in some contexts and a negative correlation in other contexts and (b) the greater prominence of incentive effects when magnitude is varied within the session rather than between sessions, are explained in terms of the basic interplay of drive and incentive motivation. The models are applied to data from closed economies in which changes of satiation levels play a key role in determining the changes in behavior. Relaxation of various assumptions leads to closed-form models for response rates and demand functions in these contexts, ones that show reasonable accord with the data and reinforce arguments for unit price as a controlling variable. The central role of deprivation level in this treatment distinguishes it from economic models. It is argued that traditional experiments should be redesigned to reveal basic principles, that ecologic experiments should be redesigned to test the applicability of those principles in more natural contexts, and that behavioral economics should consist of the applications of these principles to economic contexts, not the adoption of economic models as alternatives to behavioral analysis.     

Psychometric latent response models

In this paper, some psychometric models will be presented that belong to the larger class oflatent response models (LRMs). First, LRMs are introduced by means of an application in the field ofcomponential item response theory (Embretson, 1980, 1984). Second, a general definition of LRMs (not specific for the psychometric subclass) is given. Third, some more psychometric LRMs, and examples of how they can be applied, are presented. Fourth, a method for obtaining maximum likelihood (ML) and some maximum a posteriori (MAP) estimates of the parameters of LRMs is presented. This method is then applied to theconjunctive Rasch model. Fifth and last, an application of the conjunctive Rasch model is presented. This model was applied to responses to typical verbal ability items (open synonym items).This paper presents theoretical and empirical results of a research project supported by the Research Council [Onderzoeksraad] of the University of Leuven (grant number 89-9) to Paul De Boeck and Luc Delbeke.     

Cuban Mothers' Schemas of ADHD: Development, Characteristics, and Help Seeking Behavior

Parents play a crucial role in the diagnosis and treatment of Attention-Deficit Hyperactivity Disorder (ADHD), one of the most prevalent developmental disorders of young children We report the findings of a qualitative study of Cuban-American mothers of 7 to 10 year old children with ADHD. Results suggest that mothers lacked a cultural model for ADHD and held a cultural model of normal child development which hampered their development of a schema of ADHD. Development of ADHD schemas were motivated by perplexity at their children's behavior and by the high value mothers ascribed to academic achievement. Although the schemas developed by the mothers were labeled as ADHD, their behavioral characterizations of their children, their attributions for the condition and for its causes, and their management strategies were not always in agreement with those of the biomedical model for the condition. However, once mothers classified their children's behavior as atypical, they actively sought assistance from the professional sector.     

‘Attentional Bias’ in correlation judgments? Smedslund (1963) revisited

Smedslund (1963) reports one of the first studies that investigated human judgments of correlation. Smedslund's conclusion, that people reason about correlation mostly from a consideration of the number of times two variables co-occur, has become textbook wisdom (e.g. Baron's "attentional bias", 1994). Yet the data reported in Smedslund's paper fall short of endorsing such a conclusion. After reviewing the original paper, we present the method with which we replicated Smedslund's main experiment. In Experiment 1 subjects were presented with symptom-disease correlation data through a simulated medical diagnosis task. Subjects clearly discriminated between data sets which shared an equal number of symptom-disease co-occurrences but which otherwise showed different levels of correlation. Subjects' diagnoses showed a propensity to predict the disease in the presence of the symptom, and symptom-disease co-occurrences were overestimated in two of the five data sets presented to the subjects. Experiment 2 used a novel abstract scenario with a symmetric predictor variable. Judgments again indicated good discrimination, and biases in prediction responses and case recall were eliminated. In both experiments, judgments of zero correlation were a function of the outcome base rate. We evaluate and contrast the extent to which Cheng's (1997) model of causal induction and two associative models, Rescorla and Wagner (1972) and Pearce (1987) can anticipate the observed pattern in the mean judgments.