A maximum likelihood method for latent class regression involving a censored dependent variable

The standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored. This model is generalized by developing a conditional mixture, maximum likelihood method for latent class censored regression. The proposed method simultaneously estimates separate regression functions and subject membership in K latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The proposed method is illustrated via a consumer psychology application.     

Charting the process of change: A primer on survival analysis

Survival analysis is a powerful and useful technique for understanding qualitative change. This article provides a practical, nontechnical introduction to the use of survival analysis for social scientists. Important issues in using survival analysis are discussed, including research design, data preparation and management, and data analysis. Attendance data from a self-helf organization are used to illustrate common survival analysis tasks such as describing the overall survival and hazard functions, examining covariate effects, and modeling the form of the hazard function over time. An appendix that discusses the strengths and weaknesses of current survival analysis computer programs is included. Editor's note: Edward Seidman served as action editor for this article while serving as Associate Editor for Methodology.I thank William Davidson, Susan Englund, Bruce Rapkin, Kurt Ribisl, and three anonymous reviewers for their helpful comments on earlier drafts. The example data presented here were collected with the support of an NIMH grant (MH37390) awarded to Julian Rappaport and Ed Seidman.     

Swedish translations of the Suicide Probability Scale, Perceived Social Support from Friends and Family Scales, and the Scale for Interpersonal Behavior: A reliability analysis

The Suicide Probability Scale (SPS), the Perceived Social Support (PSS) from Friends (PSS-Fr) and Family (PSS-Fa) scales, and the Scale for Interpersonal Behavior (SIB) were translated into Swedish and their reliability was estimated in a university student sample. The reliability coefficients indicated that both subscales and the total scales of the SPS, PSS, and SIB possess highly adequate reliabilities. The intercorrelations among the subscales and between the subscales and the total scales were found to be highly significant. The results of the study supported the use of SPS, PSS-Fr and PSS-Fa, and the SIB as reliable methods for assessing suicide risk, perceived social support from friends and family, and assertive behavior.     

Category discrimination by pigeons using five polymorphous features

Eight pigeons were trained to discriminate between sets of color photographs of natural scenes. The scenes differed along five two-valued dimensions (site, weather, camera distance, camera orientation, and camera height), and all combinations of the feature values were used. One value of each dimension was designated as positive, and slides containing three or more positive feature values were members of the positive stimulus set. Thus, each feature had an equal, low, correlation with reinforcement, and all features had zero correlations with each other. Seven of the 8 pigeons learned this discrimination, and their responding came under the control of all five features. Within the positive and negative stimulus sets, response rates were higher to stimuli that contained more positive feature values. Once discrimination had been achieved, reversal training was given using a subset of the slides. In this subset, only a single feature was correlated with reinforcement. All pigeons learned this reversal successfully and generalized it to additional photographs with the same feature content. After reversal, the original reinforcement contingencies were reinstated, and training was continued using all the slides except those that had been used in reversal. Reversal generalized to these slides to some extent. Analysis of the response rates to individual slides showed that, compared with prereversal training, only the feature that had been subjected to reversal contingencies showed a reversed correlation with response rate. The remaining features showed the same correlation with response rate as they had before reversal training. Thus, reversal on some members of a category following category discrimination training led to generalization to stimuli within the category that were not involved in the reversal, but not to features that were not reversed. It is therefore inappropriate to refer to the pigeons as learning a concept.     

Three-term contingency patterns in mother-child verbal interactions during first-language acquisition

Selections from a large longitudinal data set of verbal interactions between a mother and her child are presented. Two sets of three-term contingency sequences that seemed to reflect maternal rewards and corrections were noted. Both the antecedents as well as the immediate consequences of maternal interventions are presented to explore training and learning processes. The observed frequencies of three-step sequences are compared to those expected based upon Markov-chain logic to substantiate the patterning of the interactions. Behavioral conceptualizations of the learning process are supported by these analyses, although their sufficiency is questioned. It is suggested that maternal rewards and corrections should be integrated with perceptual, cognitive, and social learning conceptualizations in a skill-learning approach to explain the complexity of language transmission and acquisition processes.     

The many null distributions of person fit indices

This paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fittingitems may be removed, this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting ofk symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called ability parameter, although our results are equally valid for Rasch scales measuring other attributes.As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.The authors express their gratitude to the reviewers and to many colleagues for comments on an earlier version.     

Interpreting canonical correlation analysis through biplots of structure correlations and weights

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis. The plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biplots may be interpreted.     

New lower and upper bounds for communality in factor analysis

We derive several relationships between communalities and the eigenvalues for ap ×p correlation matrix under the usual factor analysis model. For suitable choices ofj, _j (), where _j () is thej-th largest eigenvalue of , provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - _p () improves on the use of squared mulitiple correlation coefficient as a lower bound.This research was done while the second author was at Tokyo Institute of Technology.     

Type A behaviour in pre-school children: Interrater reliability, stability over six months and subcomponents

Type A behaviour was measured in 250 boys and 245 girls (ages 3-7) using a Swedish version of Matthews' Youth Test for Health (MYTH). In addition, speech and voice characteristics (speed, loudness, response latency) were measured. Each child was independently rated by two play group leaders and measurements were repeated after a six month interval. Interrater reliability (first session) was 0.76 for both sexes and did not change with the age of the child. Boys obtained significantly (p less than 0.0001) higher scores than girls. Correlations over the six month period were 0.64 and 0.60 (p less than 0.001) for the two possible combinations of different raters and slightly higher (0.75 and 0.68, p less than 0.001) when the same rater was used. Two components of Type A behaviour were identified from a factor analysis of the data: impatience and competitiveness, and they accounted for 57% of the total variance. As for the total scale, boys obtained significantly higher scores than girls on both subscales. Scores on the competitiveness scale increased systematically with age. Speech and voice characteristics correlated significantly with Type A scores (total Type A behaviour: r = 0.50, using different raters, and 0.71, using the same raters, p less than 0.001) and, once again, boys obtained significantly (p less than 0.001) higher scores than girls. The results are in close agreement with the American findings from the original scale. It was concluded that the scale provides a reliable and valid instrument for measuring Type A or Type A-like behaviours in pre-school children.     

Continuous and discrete latent structure models for item response data

Relations are examined between latent trait and latent class models for item response data. Conditions are given for the two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes, and methods are presented for relating latent class models to factor models for dichotomized variables. Results are illustrated using data from the Law School Admission Test, previously analyzed by several authors.