In addition, he reviews log-linear models, latent trait models, and a number of restricted latent class models in detail as well as for the estimation of parameters for these models.

This volume is based on an international conference held at the Institute for Science Education (IPN) in Kiel in August 1985. The IPN is a national research institute for science education of the Federal Republic of Germany associated with the University of Kiel. The aim of this conference-to treat latent trait and latent class models under comparative points of view as well as under application aspects-was realized in many stimulating contributions and very different ways. We asked the authors of these papers to work out their contributions for publication here, not only because many of the papers present new material, but also because the time is ripe for a comprehen sive volume, working up the widespread literature of the past ten years in this field. We have tried to compile a volume that will be of interest to statistically oriented researchers in a variety of disciplines, including psychology, sociology, education, political science, epidemiology, and the like. Although the chapters assume a reasonably high level of methodo logical sophistication, we hope that the book will find its way into advanced courses in the above fields. We are grateful to the IPN for organizing the conference, to our contributors for their untiring efforts in revising their chapters for publication, and to the staff of Plenum Publishing Corporation for helping to make this book a reality.

What is latent class analysis? If you asked that question thirty or forty years ago you would have gotten a different answer than you would today. Closer to its time of inception, latent class analysis was viewed primarily as a categorical data analysis technique, often framed as a factor analysis model where both the measured variable indicators and underlying latent variables are categorical. Today, however, it rests within much broader mixture and diagnostic modeling framework, integrating measured and latent variables that may be categorical and/or continuous, and where latent classes serve to define the subpopulations for whom many aspects of the focal measured and latent variable model may differ. For latent class analysis to take these developmental leaps required contributions that were methodological, certainly, as well as didactic. Among the leaders on both fronts was C. Mitchell “Chan” Dayton, at the University of Maryland, whose work in latent class analysis spanning several decades helped the method to expand and reach its current potential. The current volume in the Center for Integrated Latent Variable Research (CILVR) series reflects the diversity that is latent class analysis today, celebrating work related to, made possible by, and inspired by Chan’s noted contributions, and signaling the even more exciting future yet to come.

This book provides methods and applications of latent class analysis, and the following topics are taken up in the focus of discussion: basic latent structure models in a framework of generalized linear models, exploratory latent class analysis, latent class analysis with ordered latent classes, a latent class model approach for analyzing learning structures, the latent Markov analysis for longitudinal data, and path analysis with latent class models. The maximum likelihood estimation procedures for latent class models are constructed via the expectation–maximization (EM) algorithm, and along with it, latent profile and latent trait models are also treated. Entropy-based discussions for latent class models are given as advanced approaches, for example, comparison of latent classes in a latent class cluster model, assessing latent class models, path analysis, and so on. In observing human behaviors and responses to various stimuli and test items, it is valid to assume they are dominated by certain factors. This book plays a significant role in introducing latent structure analysis to not only young researchers and students studying behavioral sciences, but also to those investigating other fields of scientific research.

Applied Latent Class Analysis introduces several innovations in latent class analysis to a wider audience of researchers. Many of the world's leading innovators in the field of latent class analysis contributed essays to this volume, each presenting a key innovation to the basic latent class model and illustrating how it can prove useful in situations typically encountered in actual research.

Few guidelines exist for selecting from the one and three-parameter logistic latent trait models. This study explored fit of empirical data to these two models in terms of degree of violation of model assumptions. Specifically, unidimensionality, guessing, and equality of item discrimination indices were examined. Additionally, fit statistics were explored for data which varied in both sample size and test length. Chi square statistics were used to compare fit of distributions of observed number-right scores to number right scores predicted from latent trait theory. Using the mean of the conditional distribution of number-right scores for a given ability level as the criterion, the Rasch (one-parameter) model was generally found to be superior in fit to data than the three-parameter model for the five data sets utilized in the study. Fit of data to both models improved as the number of items or persons increased. When short tests were constructed from the data such that item discriminations displayed a broad range, better fit was found for the three-parameter model. Improvement in fit for both models was found for data fulfilling the assumption of unidimensionality. Keywords: Latent trait theory, Cognition, Mathematical models, Psychological tests, Aptitude tests. (SDW).