Research

Missing data and multiple imputation

Multiple imputation is one of the standard answers to incomplete data, and for well-behaved data it is more or less a solved problem. My work concerns the cases where it is not.

What the standard models assume, and when that fails

The imputation models built into the common software assume convenient functional forms such as multivariate normality and homoscedasticity. Research data frequently supply neither:

Counts. Variables that count events — delinquent acts, relapses, doctor visits — are discrete, bounded below by zero, often overdispersed, and often carry far more zeros than any single count distribution predicts. Imputing them under a normal model yields values that cannot occur, and the software that exists rarely goes beyond Poisson. The countimp package supplies thirteen count families: Poisson and negative binomial, their zero-inflated and hurdle variants, zero-truncated, right-censored and bounded counts, and Conway–Maxwell–Poisson for counts that are underdispersed — most of them with multilevel versions.

Skewed and heteroscedastic data. Where the shape of the conditional distribution changes with the predictors, a single conditional mean model is the wrong object. Quantile-regression-based imputation and, more recently, quantile forests estimate the whole conditional distribution instead.

Small samples. Predictive mean matching needs suitable donors. In the sample sizes common in psychological and medical research there may be few — or none. Which donor selection strategy is used stops being a detail and starts determining the result.

Clustered and panel data. Missingness occurs at every level: in outcomes, in level-1 and level-2 predictors, sometimes in the group identifier itself. Interaction terms and non-linear associations built from incomplete predictors are a further problem, and the available solutions are not equally robust when assumptions are violated.

Where this leads

The practical question behind all of it is the same: how much can an imputation model be misspecified before the inferences drawn from it stop being trustworthy — and which robust alternatives hold up when it is? Most of the papers below answer some version of that question by Monte Carlo simulation, and then apply the method to data where the assumptions really are violated: corporal punishment data, juvenile delinquency panels, victimisation surveys.

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