Multilevel models are invaluable in area-level research for investigating the impact of context on health outcomes. Frequently datasets are collected which include sparse levels of data and published studies of household-level effects on mental health often contain many single response households. This results in the household level being sparse. The effect of this sparsity on the validity of results from a multilevel model investigating mental health has not been investigated to date. The aim of the work is to determine the impacts of including and excluding a sparse household level in a multilevel analysis.

Three-level datasets were simulated with known variance structure in order to imitate individuals nested within households nested within areas. The relative importance of the household level, sample size and level of sparseness were all varied in order to assess their impact on multilevel modelling. An outcome measure was simulated based on the variance structure, as well as an individual-level predictor of this outcome. Hierarchical models were fitted to these data using the R programming language.

Variance component estimates for three-level null models were unbiased for most levels of sparseness. Under extreme sparseness conditions (average number of respondents per household < 1.5) the variability of the household and individual level variance components increased. Excluding the household level resulted in most of that level's variation being attributed to the individual level.

Sparseness can reduce variance component estimation precision and so caution should be exercised when interpreting these models.