Assessing measurement error in surveys using latent class analysis: application to self-reported illicit drug use in data from the Iranian Mental Health Survey

Latent class analysis (LCA) is a method of assessing and correcting measurement error in surveys. The local independence assumption in LCA assumes that indicators are independent from each other condition on the latent variable. Violation of this assumption leads to unreliable results. We explored this issue by using LCA to estimate the prevalence of illicit drug use in the Iranian Mental Health Survey. The following three indicators were included in the LCA models: five or more instances of using any illicit drug in the past 12 months (indicator A), any use of any illicit drug in the past 12 months (indicator B), and the self-perceived need of treatment services or having received treatment for a substance use disorder in the past 12 months (indicator C). Gender was also used in all LCA models as a grouping variable. One LCA model using indicators A and B, as well as 10 different LCA models using indicators A, B, and C, were fitted to the data. The three models that had the best fit to the data included the following correlations between indicators: (AC and AB), (AC), and (AC, BC, and AB). The estimated prevalence of illicit drug use based on these three models was 28.9%, 6.2% and 42.2%, respectively. None of these models completely controlled for violation of the local independence assumption. In order to perform unbiased estimations using the LCA approach, the factors violating the local independence assumption (behaviorally correlated error, bivocality, and latent heterogeneity) should be completely taken into account in all models using well-known methods.