Rolf Langeheine

Latent trait and latent class models

and Overview.- I Latent Trait Theory.- 1 Measurement Models for Ordered Response Categories.- 2 Testing a Latent Trait Model.- 3 Latent Trait Models with Indicators of Mixed Measurement Level.- II Latent Class Theory.- 4 New Developments in Latent Class Theory.- 5 Log-Linear Modeling, Latent Class Analysis, or Correspondence Analysis: Which Method Should Be Used for the Analysis of Categorical Data?.- 6 A Latent Class Covariate Model with Applications to Criterion-Referenced Testing.- III Comparative Views of Latent Traits and Latent Classes.- 7 Test Theory with Qualitative and Quantitative Latent Variables.- 8 Latent Class Models for Measuring.- Chaffer 9 Comparison of Latent Structure Models.- IV Application Studies.- 10 Latent Variable Techniques for Measuring Development.- 11 Item Bias and Test Multidimensionality.- 12 On a Rasch-Model-Based Test for Noncomputerized Adaptive Testing.- 13 Systematizing the Item Content in Test Design.

Bootstrapping Goodness-of-Fit Measures in Categorical Data Analysis

When sparse data have to be fitted to a log-linear or latent class model, one cannot use the theoretical chi-square distribution to evaluate model fit, because with sparse data the observed cross-table has too many cells in relation to the number of observations to use a distribution that only holds asymptotically. The choice of a theoretical distribution is also difficult when model-expected frequencies are 0 or when model probabilities are estimated 0 or 1. The authors propose to solve these problems by estimating the distribution of a fit measure, using bootstrap methods. An algorithm is presented for estimating this distribution by drawing bootstrap samples from the model-expected proportions, the so-called nonnaive bootstrap method. For the first time the method is applied to empirical data of varying sparseness, from five different data sets. Results show that the asymptotic chi-square distribution is not at all valid for sparse data.

A Unifying Framework for Markov Modeling in Discrete Space and Discrete Time

The focus of this article is on Markov models for the analysis of panel data and, more specifically, on data obtained from repeated measurements of one categorical variable at several consecutive points in time. We first review developments in the field that attack the two main problems of the simple Markov model. The Mixed Markov model extends the simple model by allowing for population heterogeneity; the Latent Markov model incorporates measurement error and latent change into the simple model. Second, we present the more general Latent Mixed Markov model and show how both the Mixed Markov model and the Latent Markov model, as well as several more specific models, relate to this more general model. Finally, we reanalyze the Los Angeles panel data on depression with a focus on stability and change.

A Typology of Students' Interest in Physics and the Distribution of Gender and Age within Each Type.

This paper deals with the identification of qualitatively different types of interest in physics among students in the 12‐16 age range in Germany. Using the statistical tool of mixed‐Rasch analysis three groups of students with distinctly different interest patterns were identified. The three types are characterized in terms of preferred interest pattern, age and gender distribution, preferences over other subjects and physics‐related self‐concept. The consequences for physics education are discussed.

Latent change in recurrent choice data

This paper introduces dynamic latent-class models for the analysis and interpretation of stability and change in recurrent choice data. These latent-class models provide a nonparametric representation of individual taste differences. Changes in preferences are modeled by allowing for individual-level transitions from one latent class to another over time. The most general model facilitates a saturated representation of class membership changes. Several special cases are presented to obtain a parsimonious description of latent change mechanisms. An easy to implement EM algorithm is derived for parameter estimation. The approach is illustrated by a detailed analysis of a purchase incidence data set.

New Developments in Latent Class Theory

A feature common to most models considered in the first part of this book may be easily depicted by Figure 1. In latent trait models, the point of departure is a set of manifest categorical variables (indicators, items, say A, B, and C), which may be related to each other in some way (cf. the curved lines). The crucial assumption now is that these relationships are conceived as being due to some continuous latent variable X. That is, if the model holds, the relationships between the manifest variables will vanish and the structure will be depicted by the straight lines going from X to A, B, and C. Several people, however, have questioned whether this procedure is advisable in all instances. Latent trait models strive for a relatively sophisticated scaling property of the latent variable (most models aim at least at an interval scale) which often remains unused for subsequent interpretation of the data. In fact, we are often simply interested in certain groups or types of persons (see Rost, Chapter 7, this volume), that means that we need no more than a categorical or nominal latent variable. This is exactly what latent class models assume.

Manifest and Latent Markov Chain Models for Categorical Panel Data

The starting point of this paper is a 3 × 3 × 3 table of repeated behavior ratings of children, which has been previously analyzed by Plewis (1981) using manifest discrete time and continuous time Markov chain models. Potential reasons for the ubiquitous misfit of the manifest discrete time Markov chain model are outlined. It is proposed, instead, to make use of more recent developments in latent discrete time Markov chain modeling that simultaneously address the main problems of heterogeneity, measurement error, stationarity, and order effects.

Statistical evaluation of measures of fit in the Lingoes-Borg procrustean individual differences scaling

PINDIS, as recently presented by Lingoes and Borg [1978] not only marks the latest development within the scope of individual differences scaling, but, may be of benefit in some closely related topics, such as target analysis. Decisions on whether the various models available from PINDIS fit fallible data are relatively arbitrary, however, since a statistical theory of the fit measures is lacking. Using Monte Carlo simulation, expected fit measures as well as some related statistics were therefore obtained by scaling sets of 4(4)24 random configurations of 5(5)30 objects in 2, 3, and 4 dimensions (individual differences case) and by fitting one random configuration to a fixed random target for 5(5)30 objects in 2, 3, and 4 dimensions (target analysis case). Applications are presented.

State Mastery Learning: Dynamic Models for Longitudinal Data:

Macready & Dayton (1980) showed that state mas tery models are handled optimally within the general latent class framework for data from a single time point. An extension of this idea is presented here for longitudinal data obtained from repeated measure ments across time. The static approach is extended using multiple-indicator Markov chain models. The approach presented here emphasizes the dynamic as pects of the process of change, such as growth, decay, and stability. The general approach is presented, and models with purely categorical and ordered categorical states and several extensions of these models are dis cussed. Problems of estimation, identification, assess ment of model fit, and hypothesis testing associated with these models also are discussed. The applicability of these models is demonstrated using data from a lon gitudinal study on solving arithmetic word problems. The advantages and disadvantages of using the ap proach presented here are discussed. Index terms: arithmetic word problems, dynamic latent class mod els, latent class models, longitudinal categorical data, Markov models, state mastery models.

Struktur und Veränderung des Interesses an Physik bei Schülern der 6. bis 10. Klassenstufe

Zusammenfassung. Es werden die Ergebnisse einer bundesweiten Befragung zur Entwicklung des Interesses an den Inhalten des Schulfaches Physik referiert. In einer kombinierten Quer- und Langsschnittstudie wurden insgesamt uber 6000 Schuler mit einem umfangreichen Fragebogen zu ihrem Physikinteresse und anderen lern- und leistungsbezogenen Variablen befragt. Dabei wird eine Analysemethode eingesetzt (das Mixed Rasch Modell), welche es gestattet, gleichzeitig qualitative Unterschiede zwischen den Schulern hinsichtlich der Interessenstruktur und quantitative Unterschiede in der Interessenstarke zu berucksichtigen. Es ergeben sich zunachst gebietsspezifische Interessentypen, die sich jedoch als relativ stabil uber die Inhaltsgebiete der Physik erweisen. Interessenstruktur und Interessenintensitat werden hinsichtlich ihrer Abhangigkeit von Geschlecht und Alter analysiert und interpretiert. Dabei zeigt sich, das die Entwicklung des Interesses an Physik primar durch eine Veranderung der Interessenstruktur zu kennz...