Incorporating prior theory in covariance structure analysis: A bayesian approach

A Bayesian approach to the testing of competing covariance structures is developed. The method provides approximate posterior probablities for each model under consideration without prior specification of individual parameter distributions. The method is based on ayesian updating using cross-validated pseudo-likelihoods. Given that the observed variables are the samefor all competing models, the approximate posterior probabilities may be obtained easily from the chi square values and other known constants, using only a hand calculator. The approach is illustrated using and example which illustrates how the prior probabilities can alter the results concerning which model specification is preferred.     

Nonconvergence,improper solutions,and starting values in lisrel maximum likelihood estimation

In the framework of a robustness study on maximum likelihood estimation with LISREL three types of problems are dealt with: nonconvergence, improper solutions, and choice of starting values. The purpose of the paper is to illustrate why and to what extent these problems are of importance for users of LISREL. The ways in which these issues may affect the design and conclusions of robustness research is also discussed.     

Statistical consistency and hypothesis testing for nonmetric multidimensional scaling

The properties of nonmetric multidimensional scaling (NMDS) are explored by specifying statistical models, proving statistical consistency, and developing hypothesis testing procedures. Statistical models with errors in the dependent and independent variables are described for quantitative and qualitative data. For these models, statistical consistency often depends crucially upon how error enters the model and how data are collected and summarized (e.g., by means, medians, or rank statistics). A maximum likelihood estimator for NMDS is developed, and its relationship to the standard Shepard-Kruskal estimation method is described. This maximum likelihood framework is used to develop a method for testing the overall fit of the model.     

SERIOUS DELINQUENT BEHAVIOR AS PART OF A SIGNIFICANTLY HANDICAPPING CONDITION: CURES AND SUPPORTIVE ENVIRONMENTS

The past 20 years have been productive ones for the field of applied behavior analysis. A brief review of our own efforts during this period reveals that we have accomplished several but not all of our goals for the Teaching-Family approach. In this context, we note that the setting of realistic and appropriate goals is important for the field and for society. Moreover, we suggest that the realistic goal for some persons with serious delinquent behavior may be extended supportive and socializing treatment rather than permanent cure from conventional short-term treatment programs. We base this suggestion on the accumulating evidence that serious delinquent behavior may often be part of a significantly disabling and durable condition that consists of multiple antisocial and dysfunctional behaviors, often runs in families, and robustly eludes effective short-term treatment. Like other significant disabilities such as retardation, autism, and blindness, the effects of this condition may be a function of an interaction of environmental and constitutional variables. We argue that our field has the wherewithal to construct effective and humane long-term supportive environments for seriously delinquent youths. In this regard, we explore the dimensions, rationales, logistics, and beginnings of a new treatment direction that involves long-term supportive family treatment. We contend that such supportive families may be able to provide long, perhaps even lifetime, socializing influences through models, values, and contingencies that seem essential for developing and maintaining prosocial behavior in these high-risk youths.     

On structural equation modeling with data that are not missing completely at random

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.The research of the first author was supported by grant No. SES-8312583 from the National Science Foundation and by a Spencer Foundation grant. We wish to thank Chuen-Rong Chan for drawing the path diagram.     

Latent trait models and dichotomization of graded responses

This paper discusses thecompatibility of the polychotomous Rasch model with dichotomization of the response continuum. It is argued that in the case of graded responses, the response categories presented to the subject are essentially an arbitrary polychotomization of the response continuum, ranging for example from total rejection or disagreement to total acceptance or agreement of an item or statement. Because of this arbitrariness, the measurement outcome should be independent of the specific polychotomization applied, for example, presenting a specific multicategory response format should not affect the measurement outcome. When such is the case, the original polychotomous model is called compatible with dichotomization.A distinction is made between polychotomization or dichotomization before the fact, that is, in constructing the response format, and polycho- or dichotomization after the fact, for example in dichotomizing existing graded response data.It is shown that, at least in case of dichotomization after-the-fact, the polychotomous Rasch model is not compatible with dichotomization, unless a rather special condition of the model parameters is met. Insofar as it may be argued that dichotomization before the fact is not essentially different from dichotomization after the fact, the value of the unidimensional polychotomous Rasch model is consequently questionable. The impact of our conclusion on related models is also discussed.     

A note on the computation of the second-order derivatives of the elementary symmetric functions in the rasch model

Jansen (1984) gave explicit formulas for the computation of the second-order derivatives of the elementary symmetric functions. But they are only applicable to those pairs of items which have unequal parameters. It is shown here that for equal parameters similar explicit formulas do exist, too, facilitating the application of the Newton-Raphson procedure to estimate the parameters in the Rasch model and related models according to the conditional maximum likelihood principle.The author wishes to thank the reviewers for their helpful comments on an earlier draft of this paper.     

Estimation for structural equation models with missing data

A direct method in handling incomplete data in general covariance structural models is investigated. Asymptotic statistical properties of the generalized least squares method are developed. It is shown that this approach has very close relationships with the maximum likelihood approach. Iterative procedures for obtaining the generalized least squares estimates, the maximum likelihood estimates, as well as their standard error estimates are derived. Computer programs for the confirmatory factor analysis model are implemented. A longitudinal type data set is used as an example to illustrate the results.This research was supported in part by Research Grant DAD1070 from the U.S. Public Health Service. The author is indebted to anonymous reviewers for some very valuable suggestions. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

Sense of community improves community participation in Chinese residential communities: The mediating role of sense of community responsibility and prosocial tendencies

Community participation is essential for community development and enhancing quality of life. Several studies have focused on the relationship between sense of community (SOC) and community participation in organizational settings. Guided by the community experiences framework, this study aims to examine how a SOC improves community participation in Chinese residential communities. Moreover, the study aims to assess the mediating role of SOC responsibility (SOC-R) and prosocial tendencies in that relationship. A sample of 433 residents completed questionnaires regarding their SOC, sense of community responsibility, prosocial tendencies, and community participation. Using a linear regression model, we found that a SOC can positively predict the level of community participation. Mediation effect analysis revealed that a SOC-R mediated the relationship between SOC and community participation. In addition, prosocial tendencies mediated the association between the SOC and community participation. Using multiple mediation analysis, we found that SOC-R and prosocial tendencies mediated the link between a SOC and community participation in a sequential manner. The findings of this study complement existing research by uncovering the mechanism underlying the relationship between a SOC and community participation.