On the stationary distribution of iterative imputations

Abstract

Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling problem with relatively simple univariate regressions. In this paper, we begin to characterize the stationary distributions of iterative imputations and their statistical properties. More precisely, when the conditional models are compatible (defined in the text), we give a set of sufficient conditions under which the imputation distribution converges in total variation to the posterior distribution of a Bayesian model. When the conditional models are incompatible but are valid, we show that the combined imputation estimator is consistent. arXiv:1012.2902v2 [math.ST] 3 Apr 2012 imputation algorithms are not well understood. Even if, as we would prefer, the fitting of each imputation model and the imputations themselves are performed using conditional Bayesian inference, the stationary distribution of the algorithm (if it exists) does not in general correspond to Bayesian inference on any specified multivariate distribution. Key questions are: (1) Under what conditions does the algorithm converge to a stationary distribution? (2) What statistical properties does the procedure admit given that a unique stationary distribution exists?Regarding the first question, researchers have long known that the Markov chain may be nonrecurrent ("blowing up" to infinity or drifting like a nonstationary random walk), even if each of

The impact of missing data on analyses of a time-dependent exposure in a longitudinal cohort: a simulation study

“…The slight bias observed in analysis (a) may be a result of the imputation model being semi-compatible with the analysis model (i.e. the exposure of interest in the analysis model is change in waist circumference, however, waist circumference at wave 2 is imputed in the imputation model) [41]. We decided to impute waist circumference at wave 2 instead of change in waist circumference in order to represent the real epidemiological analysis (i.e.…”

Handling Missing Data in Matched Case-Control Studies Using Multiple Imputation

“…Otherwise, FCS is less theoretically justified, but there is much evidence that it works well in terms of approximate unbiasedness of parameter and variance estimates and coverage of confidence intervals (van Buuren, 2012;Hughes et al, 2014;Lee and Carlin, 2010). An important theoretical result was given by Liu et al (2014). They defined the set of conditional models to be compatible with a joint model if, for each conditional model and every possible set of parameter values for that model, there exists a set of parameter values for the joint model such that the conditional and joint models imply the same distribution for the dependent variable of that conditional model.…”

Simulations Test Impact Of Education, Employment, And Income Improvements On Minority Patients With Mental Illness

“…Therefore, the estimated population mean of the outcome is $Y^{\ast \ast }=\frac{{\sum }_i{Y}_i{W}_i^{\ast \ast }}{{\sum }_i{W}_i^{\ast \ast }}$. The effect of augmenting the social determinant (income, education or employment) on variable X I is then the difference between Y** and Y*, that is, E = Y** − Y*. The missing data are imputed by the method of multiple imputation via chain equations through the mi package in R. 3 In particular, we create 10 imputations. The variances of the complete data estimators are estimated by the Bootstrap method described in Rust and Rao (1996).…”

“…The missing data are imputed by the method of multiple imputation via chain equations through the mi package in R. 3 In particular, we create 10 imputations. The variances of the complete data estimators are estimated by the Bootstrap method described in Rust and Rao (1996).…”