Measuring Change in Latent Subgroups Using Dichotomous Data: Unconditional, Conditional, and Semiparametric Maximum Likelihood Estimation

Abstract Changes in dichotomous data caused by treatments can be analyzed by means of the so-called linear logistic model with relaxed assumptions (LLRA). In contrast to models of the Rasch type, the LLRA allows incidental multidimensional parameters describing the response behavior of the subjects so that each observable criterion used for assessing the changes is governed by its own subject parameter. Because generalizability of the treatment effects over subjects and criteria is scientifically desirable, statistical tests for this desideratum play an important role in practical situations. Whereas generalizability over the criteria can easily be tested, generalizability over subjects can be tested only by stratifying the sample according to some further observable subject variables. However, one cannot be sure to detect nongeneralizability over the subjects by this method with certainty. Therefore, the mixture LLRA is proposed that allows directly unobservable types of subjects reacting differently on ...

[1]  G. H. Fischer,et al.  Logistic latent trait models with linear constraints , 1983 .

[2]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[3]  Dean Follmann,et al.  Consistent estimation in the rasch model based on nonparametric margins , 1988 .

[4]  Anton K. Formann,et al.  Constrained latent class models: Theory and applications , 1985 .

[5]  Gerhard H. Fischer,et al.  A measurement model for the effect of mass-media , 1972 .

[6]  B. Lindsay,et al.  Semiparametric Estimation in the Rasch Model and Related Exponential Response Models, Including a Simple Latent Class Model for Item Analysis , 1991 .

[7]  Gerhard H. Fischer,et al.  An irt-based model for dichotomous longitudinal data , 1989 .

[8]  I. Plewis.  A comparison of approaches to the analysis of longitudinal categoric data , 1981 .

[9]  Gerhard H. Fischer,et al.  An extension of the rating scale model with an application to the measurement of change , 1991 .

[10]  Norman Verhelst,et al.  Maximum Likelihood Estimation in Generalized Rasch Models , 1986 .

[11]  Georg Rasch,et al.  Probabilistic Models for Some Intelligence and Attainment Tests , 1981, The SAGE Encyclopedia of Research Design.

[12]  G G Koch,et al.  A general methodology for the analysis of experiments with repeated measurement of categorical data. , 1977, Biometrics.

[13]  N Breslow,et al.  Regression analysis of the log odds ratio: a method for retrospective studies. , 1976, Biometrics.

[14]  Education Division.  Studies in social psychology in World War II , 1949 .

[15]  R. Rust,et al.  Incorporating prior theory in covariance structure analysis: A bayesian approach , 1989 .

[16]  Anton K. Formann,et al.  Linear Logistic Latent Class Analysis , 1982 .

[17]  J. Kiefer,et al.  CONSISTENCY OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN THE PRESENCE OF INFINITELY MANY INCIDENTAL PARAMETERS , 1956 .

[18]  A. Formann.  Linear Logistic Latent Class Analysis for Polytomous Data , 1992 .

[19]  G. H. Fischer,et al.  An extension of the partial credit model with an application to the measurement of change , 1994 .

[20]  G. H. Fischer,et al.  Applying the principles of specific objectivity and of generalizability to the measurement of change , 1987 .

[21]  Henk Kelderman,et al.  Item bias detection using loglinear irt , 1989 .

[22]  C. Harris.  Problems in measuring change , 1965 .

[23]  N Mantel,et al.  Models for complex contingency tables and polychotomous dosage response curves. , 1966, Biometrics.

[24]  Ronald C. Serlin,et al.  Tests and contrasts for comparing change parameters for a multiple sample McNemar data model , 1979 .