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Panel count data describes aggregated counts of recurrent events observed atdiscrete time points. To understand dynamics of health behaviors, the field ofquantitative behavioral research has evolved to increasingly rely upon panelcount data collected via multiple self reports, for example, about frequenciesof smoking using in-the-moment surveys on mobile devices. However, missingreports are common and present a major barrier to downstream statisticallearning. As a first step, under a missing completely at random assumption(MCAR), we propose a simple yet widely applicable functional EM algorithm toestimate the counting process mean function, which is of central interest tobehavioral scientists. The proposed approach wraps several popular panel countinference methods, seamlessly deals with incomplete counts and is robust tomisspecification of the Poisson process assumption. Theoretical analysis of theproposed algorithm provides finite-sample guarantees by expanding parametric EMtheory to our general non-parametric setting. We illustrate the utility of theproposed algorithm through numerical experiments and an analysis of smokingcessation data. We also discuss useful extensions to address deviations fromthe MCAR assumption and covariate effects.

A Robust Functional EM Algorithm for Incomplete Panel Count Data