Adjusting for differential misclassification in multilevel models: the relationship between child exposure to smoke and cognitive development

Misclassification is found in many of the variables used in social sciences and, in practice, tends to be ignored in statistical analyses, and this can lead to biased results. This paper shows how to correct for differential misclassification in multilevel models and illustrates the extent to which this changes fixed and random parameter estimates. Reliability studies on self-reported behaviour of pregnant women suggest that there may be differential misclassification related to smoking and, thus, to child exposure to smoke. Models are applied to the Millennium Cohort Study data. The response variable is the child cognitive development assessed by the British Ability Scales at 3years of age and explanatory variables are child exposure to smoke and family income. The proposed method allows a correction for misclassification when the specificity and sensitivity are known, and the assessment of potential biases occurring in the multilevel model parameter estimates if a validation data sample is not available, which is often the case.