A general model for the analysis of multilevel data

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of the model include repeated measures designs, multiple matrix samples, multilevel latent variable models, multiple time series, and variance and covariance component models.We would like to acknowledge the helpful comments of Ruth Silver. We also wish to thank the referees for helping to clarify the paper. This work was partly carried out with research funds provided by the Economic and Social Research Council (U.K.).     

Confidence in judgments based on incomplete information: An investigation using both hypothetical and real gambles

This study assessed how confidence in judgments is affected by the need to make inferences about missing information. Subjects indicated their likelihood of taking each of a series of gambles based on both probability and payoff information or only one of these sources of information. They also rated their confidence in each likelihood judgment. Subjects in the Explicit Inference condition were asked to explicitly estimate the values of missing information before making their responses while subjects in the Implicit Inference condition were not. The manner in which probability information was framed was also manipulated. Experiment 1 employed hypothetical gambles and Experiment 2 employed gambles with real money. Expressed likelihood of taking gambles was higher when probability was phrased in terms of '% chance of winning' rather than '% chance of losing', but this difference was somewhat less with real gambles than with hypothetical gambles. Confidence ratings in each experiment were actually higher on incomplete information trials than on complete information trials in the Explicit Inference condition. Results were related to the general issue of confidence in judgments.     

Effectiveness of the GOFER course in decision making for high school students

The paper describes and evaluates the GOFER course in decision making for high school students (Mann, Harmoni and Power, 1988). The course was based on principles from the conflict theory of decision making (Janis and Mann, 1977) and was designed to provide adolescents with an understanding of factors that produce good and poor decision making as well as knowledge and practice of sound decision skills. Two evaluation studies were conducted to examine effectiveness of the course. Study 1 was conducted with young adolescents (12 year olds). It found a significant difference between students trained in the course and a control group on measures of self-esteem as a decision maker, self reported decision habits and knowledge of decision strategy. Study 2 was conducted with mid-adolescents (15 year olds). It, too, found a significant difference between students who took the course and a control group on measures of self esteem as a decision maker and self-reported decision habits. It is concluded that while the evaluation study fell short of an ideal test, the GOFER course met the criteria of improving student knowledge, raising confidence in decision making and changing self reported decision habits.     

Multilevel models in developmental psychological research: Rationales and applications

The armoury of statistical techniques has recently been enhanced with the multilevel model for longitudinal data. The present article explains the multilevel model for longitudinal data to the statistically non-sophisticated reader. It shows how the model relates to the five rationales of longitudinal research, as they were put forward by Baltes and Nesselroade (1979). In addition, it shows how the model matches Wohlwill's methodology of developmental functions. To elucidate the model further, three applications are given. The applications pertain to the development of children's sleeping duration during the first 18 months of life, the effects of early hospitalization on the daily frequency of crying, and the developmental relationship between social and solitary play.     

Minimizing the number of observations: A generalization of the spearman-brown formula

A new method for determining the minimum number of observations per subject needed to achieve a specific generalizability coefficient is presented. This method, which consists of a branch-and-bound algorithm, allows for the employment of constraints specified by the investigator.     

Criterion-related construct validity

Established results on latent variable models are applied to the study of the validity of a psychological test. When the test predicts a criterion by measuring a unidimensional latent construct, not only must the total score predict the criterion, but the joint distribution of criterion scores and item responses must exhibit a certain pattern. The presence of this population pattern may be tested with sample data using the stratified Wilcoxon rank sum test. Often, criterion information is available only for selected examinees, for instance, those who are admitted or hired. Three cases are discussed: (i) selection at random, (ii) selection based on the current test, and (iii) selection based on other measures of the latent construct. Discriminant validity is also discussed.This work was supported in part by Grant SES-87-01890 from the Measurement Methods and Data Improvement Program of the U.S. National Science Foundation.     

Connectionist models of conditioning: A tutorial

Models containing networks of neuron-like units have become increasingly prominent in the study of both cognitive psychology and artificial intelligence. This article describes the basic features of connectionist models and provides an illustrative application to compound-stimulus effects in respondent conditioning. Connectionist models designed specifically for operant conditioning are not yet widely available, but some current learning algorithms for machine learning indicate that such models are feasible. Conversely, designers for machine learning appear to have recognized the value of behavioral principles in producing adaptive behavior in their creations.     

A structural model for postpartum responses to the somatic and cognitive items on the Beck Depression Inventory

A distinction can be drawn between those items on the Beck Depression Inventory (BDI) that reflect mainly cognitive and emotional symptoms and those that reflect somatic symptoms. Responses to the BDI were obtained from women at 3, 6, 9, and 24 weeks postpartum. The covariances of cognitive and somatic symptom scores across the four time points were closely fit by a structural equations model referred to as the simplex. The modeling indicates that earlier cognitive scores directly predict later somatic scores but that early somatic scores do not directly predict later cognitive scores. Other data confirm the results.Much of this research was supported while the first author was an NIMH Fellow at the University of Iowa (MH15168).     

A taxonomy of item response models

A number of models for categorical item response data have been proposed in recent years. The models appear to be quite different. However, they may usefully be organized as members of only three distinct classes, within which the models are distinguished only by assumptions and constraints on their parameters. “Difference models” are appropriate for ordered responses, “divide-by-total” models may be used for either ordered or nominal responses, and “left-side added” models are used for multiple-choice responses with guessing. The details of the taxonomy and the models are described in this paper. The present study was supported in part by two postdoctoral fellowships awarded to Lynne Steinberg: an Educational Testing Service Postdoctoral Fellowship at ETS, Princeton, NJ and an NIMH Individual National Research Service Award at Stanford University, Stanford, CA. Helpful comments by the editor and three anonymous reviewers are gratefully acknowledged.