References in this section are not meant to be comprehensive. Instead, a selection of useful overviews, mostly books, are listed. Section 1.2 also includes some more specific references which are cited in Section 4 but which are not themselves about multiple-group modelling.
Fienberg (1980): A concise summary of models for categorical data, with a focus on log-linear models for contingency tables.
Agresti (2002): A comprehensive overview of methods of categorical data analysis.
Skrondal and Rabe-Hesketh (2004): Theory and examples of a wide range of latent variable models, corresponding mostly to the very broad class of Generalized Linear Latent and Mixed Models (GLLAMM), plus some models which are not accommodated within that class.
Bartholomew et al. (2011): The theory of the various families of latent variable models previously discussed separately in the literature, embedded in a general framework (referred to as General Linear Latent Variable Model, GLLVM).
Bollen (1989): A comprehensive overview of linear structural equation models.
Langeheine and Rost (1988): An edited volume on both latent class and latent trait models, including some chapters on comparisons between the two.
Hagenaars and McCutcheon (2002): An edited volume on latent class models, including various extensions developed relatively recently.
Goodman (2002): On overview of latent class models, plus extended examples of sensitivity to identifiability restrictions in otherwise nonidentified models. (A chapter in Hagenaars and McCutcheon (2002).)
Stocking and Lord (1982): IRT models fitted to several distinct samples. Thus the estimated item parameters are not directly comparable, because fitted models imply different scales for the latent traits. The paper presents a method of scaling the initial estimated item parameters so that they are more comparable. In other words (although these terms are nto used in the paper), the method essentially estimates trait means and variances under the assumption of (approximate) measurement equivalence.
Andrich (1988): A concise overview of Rasch models (focusing on the simple logistic model for binary items) and their use for measurement.
Langeheine and Rost (1988): See Section 1.2.3.
Edelen and Reeve (2007): Overview of the use of IRT models for questionnaire development. Extended example, using an ordinal model for 19-item depression scale. Useful references, e.g. to publications which discuss differential item function and methods of model selection.
van de Vijver and Leung (1997): Overview of methodology of cross-cultural research, with emphasis on cross-cultural psychology. Discussions of measurement equivalence and analysis of it using both simple item bias analyses and methods item response theory.
Harkness et al. (2003): Overview of the methodology of cross-national surveys, from design to analysis. Includes good discussions of equivalence of measurement and comparability of findings.
Saris and Gallhofer (2007): Design of survey questions in general. In Chapter 16, discussion of measurement equivalence in cross-national surveys, expressed in terms of linear structural equation models.
Jowell et al. (2007): Design and procedures of the European Social Survey, plus substantive analyses of three examples.
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