Clifford C. Clogg

Statistical Methods for Comparing Regression Coefficients Between Models

Statistical methods are developed for comparing regression coefficients between models in the setting where one of the models is nested in the other. Comparisons of this kind are of interest whenever two explanations of a given phenomenon are specified as linear models. In this case, researchers should ask whether the coefficients associated with a given set of predictors change in a significant way when other predictors or covariates are added as controls. Simple calculations based on quantities provided by routines for regression analysis can be used to obtain the standard errors and other statistics that are required. Results are also given for the class of generalized linear models (e.g., logistic regression, log-linear models, etc.). We recommend fundamental change in strategies for model comparison in social research as well as modifications in the presentation of results from regression or regression-type models.

Handbook of statistical modeling for the social and behavioral sciences

Casual Inference in the Social and Behavioral Sciences. Missing Data. Specification and Estimation of Mean Structures. The Analysis of Contingency Tables. Latent Class Models. Panel Analysis for Metric Data. Panel Analysis for Qualitative Variables. Analysis of Event Histories. Random Coefficient Models. Index.

Latent Structure Analysis of a Set of Multidimensional Contingency Tables

Abstract Statistical methods are introduced for latent structure analysis of a set of two or more multidimensional contingency tables. Three basic classes of models are considered: (a) models that assume complete homogeneity across tables, (b) models that allow partial homogeneity across tables, and (c) models that allow complete heterogeneity. Methods are presented for testing whether these models are congruent with the data in the tables and for assessing the significance of differences among the tables in the estimated parameters. To illustrate the wide applicability of these models and methods, we present analyses of two quite different sets of data.

Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis

Abstract The Rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects, leading to the failure of the usual likelihood methodology. Both conditional-likelihood methods and mixture-model techniques have been used to circumvent these problems. In this article, we show that these seemingly unrelated analyses are in fact closely linked to each other, despite dramatic structural differences between the classes of models implied by each approach. We show that the finite-mixture model for J dichotomous items having T latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if T ≥ (J + 1)/2. Unconditional maximum likelihood estimators for the finite-mixture model can be viewed as Keifer-Wolfowitz estimators for the random-effects version of the Rasch model. Latent-class versions of the model are especially attractive when T is...

Statistical Models for Ordinal Variables.

Preliminaries The Linear-by-Linear Interaction Model Association Models for Two-Way Tables The ANOAS Approach Other Models for Two-Way Tables Symmetry-Type Models Multiple Dimensions of Association Bivariate Association in Multiple Groups Logit-Type Regression Models for Ordinal Dependent Variables

Multiple Imputation of Industry and Occupation Codes in Census Public-use Samples Using Bayesian Logistic Regression

Abstract We describe methods used to create a new Census data base that can be used to study comparability of industry and occupation classification systems. This project represents the most extensive application of multiple imputation to date, and the modeling effort was considerable as well—hundreds of logistic regressions were estimated. One goal of this article is to summarize the strategies used in the project so that researchers can better understand how the new data bases were created. Another goal is to show how modifications of maximum likelihood methods were made for the modeling and imputation phases of the project. To multiply-impute 1980 census-comparable codes for industries and occupations in two 1970 census public-use samples, logistic regression models were estimated with flattening constants. For many of the regression models considered, the data were too sparse to support conventional maximum likelihood analysis, so some alternative had to be employed. These methods solve existence and ...

Some Models for the Analysis of Association in Multiway Cross-Classifications Having Ordered Categories

Abstract Goodman recently presented a class of models for the analysis of association between two discrete, ordinal variables. The association was measured in terms of the odds ratios in 2 × 2 subtables formed from adjacent rows and adjacent columns of the cross-classification, and models were devised that allowed the odds ratios to depend on an overall effect, on row effects, on column effects, and on other effects. This article presents some generalizations of this approach appropriate for multiway cross-classifications, including (a) models for the analysis of conditional association, (b) models for the analysis of partial association, and (c) models for the analysis of symmetric association. Three cross-classifications are analyzed with these models and methods, and rather simple interpretations of the association in each are provided.

Some Common Problems in Log-Linear Analysis

Several problems often encountered in research using log-linear models for categorical response variables are discussed. The issues covered are (a) determining the degrees of freedom for a model, (b) analyzing sparse data, (c) analyzing weighted data, (d) modeling rates, and (e) interpreting results.

Mismatch between occupation and schooling: A prevalence measure, recent trends and demographic analysis

This paper deals with the mismatch between occupation and schooling attainment, the imbalance between occupation-specific demand for labor and schooling-level-specific labor supply. A framework for measuring the prevalence of mismatch is given, and a simple index derived from it gives plausible results and robust inferences about differentials and time trend. This approach can be applied to existing data, yields comprehensive and current social indicators, and can be used with a minimum number of assumptions. Trends for the U.S. labor force over the 1969–1980 interval are examined. Results show that there has been a dramatic and general increase in mismatch prevalence. Various demographic explanations of mismatch trends are examined.

Analysis of Sets of Two-Way Contingency Tables Using Association Models

Abstract A class of models is introduced for the analysis of group differences in the association between two discrete variables. The RC(M) association model for two-way tables is reviewed, and alternative weighting systems for identifying interaction parameters are presented. This model is generalized for the setting where a two-way contingency table is available for two or more groups. Various restricted models can be used to examine possible sources of intergroup heterogeneity in the association. These sources pertain to heterogeneity in the intrinsic association and/or in the scores for the row and column variables. The importance of weights used to identify the row and column scores is emphasized. A classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here.