Classical Latent Variable Models for Medical Research
Statistical Methods in Medical Research 2008; 17: 5–32 Classical latent variable models for medical research Sophia Rabe-Hesketh Graduate School of Education and Graduate Group in Biostatistics, University of California, Berkeley, USA and Institute of Education, University of London, London, UK and Anders Skrondal Department of Statistics and The Methodology Institute, London School of Economics, London, UK and Division of Epidemiology, Norwegian Institute of Public Health, Oslo, Norway Latent variable models are commonly used in medical statistics, although often not referred to under this name. In this paper we describe classical latent variable models such as factor analysis, item response theory,latent class models and structural equation models. Their usefulness in medical research is demon- strated using real data. Examples include measurement of forced expiratory flow,measurement of physical disability, diagnosis of myocardial infarction and modelling the determinants of clients’ satisfaction with counsellors’ interviews. 1 Introduction Latent variable modelling has become increasingly popular in medical research. By latent variable model we mean any model that includes unobserved random variables which can alternatively be thought of as random parameters. Examples include factor, item response, latent class, structural equation, mixed effects and frailty models. Areas of application include longitudinal analysis1, survival analysis2, meta-analysis3, disease mapping4, biometrical genetics5, measurement of constructs such as quality of life6, diagnostic testing7, capture–recapture models8, covariate measurement error models9 and joint models for longitudinal data and dropout.10 Starting at the beginning of the 20th century, ground breaking work on latent vari- able modelling took place in psychometrics.11–13 The utility of these models in medical research has only quite recently been recognized and it is perhaps not surprising that med- ical statisticians tend to be unaware of the early,and indeed contemporary,psychometric literature.
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