Standard multiple imputation of survey data didn’t perform better than simple substitution in enhancing an administrative dataset: the example of self-rated health in England

Background Health surveys provide a rich array of information but on relatively small numbers of individuals and evidence suggests that they are becoming less representative as response levels fall. Routinely collected administrative data offer more extensive population coverage but typically comprise fewer health topics. We explore whether data combination and multiple imputation of health variables from survey data is a simple and robust way of generating these variables in the general population. Methods We use the UK Integrated Household Survey and the English 2011 population census both of which included self-rated general health. Setting aside the census self-rated health data we multiply imputed self-rated health responses for the census using the survey data and compared these with the actual census results in 576 unique groups defined by age, sex, housing tenure and geographic region. Results Compared with original census data across the groups, multiply imputed proportions of bad or very bad self-rated health were not a markedly better fit than those simply derived from the survey proportions. Conclusion While multiple imputation may have the potential to augment population data with information from surveys, further testing and refinement is required.

Multiple imputation to balance unbalanced designs for two-way analysis of variance

A balanced ANOVA design provides an unambiguous interpretation of the F-tests, and has more power than an unbalanced design. In earlier literature, multiple imputation was proposed to create balance in unbalanced designs, as an alternative to Type-III sum of squares. In the current simulation study we studied four pooled statistics for multiple imputation, namely D₀, D₁, D₂, and D₃ in unbalanced data, and compared them with Type-III sum of squares. Statistics D₁ and D₂ generally performed best regarding Type-I error rates, and had power rates closest to that of Type-III sum of squares. Additionally, for the interaction, D₁ produced power rates higher than Type-III sum of squares. For multiply imputed datasets D₁ and D₂ may be the best methods for pooling the results in multiply imputed datasets, and for unbalanced data, D₁ might be a good alternative to Type-III sum of squares regarding the interaction.

Pooling methods for likelihood ratio tests in multiply imputed data sets

Likelihood ratio tests (LRTs) are a popular tool for comparing statistical models. However, missing data are also common in empirical research, and multiple imputation (MI) is often used to deal with them. In multiply imputed data, there are multiple options for conducting LRTs, and new methods are still being proposed. In this article, we compare all available methods in multiple simulations covering applications in linear regression, generalized linear models, and structural equation modeling (SEM). In addition, we implemented these methods in an R package, and we illustrate its application in an example analysis concerned with the investigation of measurement invariance.

Much ado about nothing: Multiple imputation to balance unbalanced designs for two-way analysis of variance

In earlier literature, multiple imputation was proposed to create balance in unbalanced designs, as an alternative to Type III sum of squares in two-way ANOVA. In the current simulation study we studied four pooled statistics for multiple imputation, namely D₀, D₁, D₂, and D₃ in unbalanced data, and compared these statistics with Type III sum of squares. Statistics D₀ and D₂ generally performed best regarding Type-I error rates, and had power rates closest to that of Type III sum of squares. However, none of the statistics produced power rates higher than Type III sum of squares. The results lead to the conclusion that for multiply imputed datasets D₀ and D₂ may be the best methods for pooling the results of multiparameter estimates in multiply imputed datasets, and that for unbalanced data, Type III sum of square is to be preferred over using multiple imputation in obtaining ANOVA results.

Finite Sample Inference for Multiply Imputed Synthetic Data under a Multiple Linear Regression Model

In this article, we develop finite sample inference based on multiply imputed synthetic data generated under the multiple linear regression model. We consider two methods of generating the synthetic data, namely posterior predictive sampling and plug-in sampling. Simulation results are presented to confirm that the proposed methodology performs as the theory predicts and to numerically compare the proposed methodology with the current state-of-the-art procedures for analysing multiply imputed partially synthetic data. AMS 2000 subject classification: 62F10, 62F25, 62J05