These pages provide information about and resources from the research project “Latent Variable Modelling of Categorical Data: Tools of Analysis for Cross-National Surveys” (LCAT for short) at the Departments of Statistics and Methodology of the London School of Economics and Political Science (LSE). The project was funded in 2010-12 by the UK Economic and Social Research Council (ESRC), under its Comparative Cross-National Research Methods initiative. The funding period has now ended, but our work on topics of the project continues and materials are still being added to these pages.

Overview of the project

In surveys many concepts are too complex to be captured or “measured” by a single question, so batteries of several questions are used to measure such underlying (latent) concepts. Statistical latent variable models are used to represent measurement of concepts by multiple questions and analyse the relations among the concepts. Furthermore, “multi-group” versions of such models can be used to answer questions about comparisons between different groups, in our project in particular different countries in cross-national surveys where the same questions (translated into the local languages) are asked of respondents in different countries.

But a pressing challenge in cross-national survey research is the comparability or equivalence of such measurement across countries, i.e. the issue of whether a survey question “works the same way” in all of the countries? If it does not, any comparisons between countries may be distorted, since observed differences may be artefacts of measurement. While survey designers use a variety of techniques, such as advanced translation procedures, to check the meaning of items across countries, the issue of non-equivalence of measurement continues to be a concern. There is a need for complementary statistical methods for examining the equivalence of survey questions and of derived latent concepts.

We are developing tools of latent variable modelling for cross-national survey data. In particular, we are examining methods which correctly account for the fact that typical survey questions are categorical in nature, meaning that the respondents answer them by selecting one of a small set of fixed response options. Latent variable models for categorical data are known as latent class and latent trait models. While much is known about other methods which are strictly speaking only appropriate for the analysis of continuous-level survey data (especially linear factor analysis and structural equation modelling), little work has been done on analysis of international surveys using tools specifically designed for survey questions that yield categorical data.

By drawing upon the researchers’ expertise in both statistics and substantive social science, the project involves an interplay between statistical modelling and the analysis of real survey data to ensure the practical applicability of the work. The aims of the project are to:

  1. provide advice and examples, which are accessible to all survey researchers, of how to use statistical latent trait and latent class models to analyse cross-national survey data, to examine equivalence of survey questions and to find answers to substantive research questions;
  2. examine the general properties of the models and methods of comparing them, using both mathematical and simulation techniques, and analyses of real survey data; and
  3. provide practical guidelines to survey users about what may be done in different situations of measurement equivalence, and how such choices affect conclusions about the substantively interesting research questions.

The methodological work of the project is tested and illustrated in the context of cross-national comparisons in three substantive areas that the researchers specialise in (i) confidence in criminal justice systems, (ii) public attitudes towards science and technology, and (iii) individual-level characteristics of civil society.

To enable a wide range of potential users to learn from the project, we have provided two-day training workshops for PhD students and survey researchers across the UK. Other information and training materials are provided on this website.