Locally dependent latent class models with covariates: an application to under‐age drinking in the USA

Summary. Under‐age drinking is a long‐standing public health problem in the USA and the identification of underage drinkers suffering alcohol‐related problems has been difficult by using diagnostic criteria that were developed in adult populations. For this reason, it is important to characterize patterns of drinking in adolescents that are associated with alcohol‐related problems. Latent class analysis is a statistical technique for explaining heterogeneity in individual response patterns in terms of a smaller number of classes. However, the latent class analysis assumption of local independence may not be appropriate when examining behavioural profiles and could have implications for statistical inference. In addition, if covariates are included in the model, non‐differential measurement is also assumed. We propose a flexible set of models for local dependence and differential measurement that use easily interpretable odds ratio parameterizations while simultaneously fitting a marginal regression model for the latent class prevalences. Estimation is based on solving a set of second‐order estimating equations. This approach requires only specification of the first two moments and allows for the choice of simple ‘working’ covariance structures. The method is illustrated by using data from a large‐scale survey of under‐age drinking. This new approach indicates the effectiveness of introducing local dependence and differential measurement into latent class models for selecting substantively interpretable models over more complex models that are deemed empirically superior.