A comparison of approaches for assessing covariate effects in latent class analysis


  • Jon E Heron University of Bristol
  • Tim J Croudace University of Dundee
  • Edward D Barker King’s College London
  • Kate Tilling University of Bristol




ALSPAC, latent class analysis, trajectories, bias, three-step


Mixture modelling is a commonly used technique for describing longitudinal patterns of change, often with the aim of relating the resulting trajectory membership to a set of earlier risk factors. When determining these covariate effects, a three-step approach is often preferred as it is less computationally intensive and also avoids the situation where each new covariate can influence the measurement model, thus subtly changing the outcome under study. Recent simulation work has demonstrated that estimates obtained using three-step models are likely to be biased, particular when classification quality (entropy) is poor. Using both simulated data and empirical data from a large United Kingdom(UK)-based cohort study we contrast the performance of a range of commonly used three-step techniques. Bias in parameter estimates and their precision were determined and compared to new bias-adjusted three-step methods that have recently become available. The bias-adjusted three-step procedures were markedly less biased than the simpler three-step methods. Proportional Maximum Likelihood (ML), with its complex-sampling robust estimation, suffered from negligible bias across a range of values of entropy. Whilst entropy was related to bias for all methods considered, there was evidence that class-separation for each pairwise comparison may also play an important role. Under some circumstances a standard three-step method may provide unbiased covariate effects, however on the basis of these results we would recommend the use of bias-adjusted three-step estimation over these standard methods.

Author Biographies

Jon E Heron, University of Bristol

Senior Research Fellow
School and Social and Community Medicine

Tim J Croudace, University of Dundee

Chair in Applied Health ResearchUniversity of Dundee , School of Nursing and Midwifery

Edward D Barker, King’s College London

Department of Psychology

Kate Tilling, University of Bristol

Professor of Medical Statistics 
School of Social and Community Medicine


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