Multiple imputation in functional regression with applications to EEG data in a depression study
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Methods for estimating parameters in functional regression models require complete data on both the response and the predictors. However, in many applications, complete data are not available for all subjects. While many methods are available to handle missingness in data sets with all scalar variables, no such methods exist for data sets that include functional variables. We propose an approach that is an extension of multiple imputation by chained equations (fregMICE). fregMICE handles both scalar and functional variables as predictors in the imputation models as well as scalar and functional outcomes that need to be imputed. We also propose an extension to Rubin's Rules that can be used to pool estimates from the multiply imputed data sets and conduct valid inference. Simulation results suggest that the proposed methods are superior to both complete case analysis and mean imputation in the context of estimating parameters in functional regression models. We employ the proposed methods in fitting a functional regression model for the relationship between major depressive disorder and frontal asymmetry curves derived from electroencephalography.
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