Regression modeling of zero-inflated functional data

Music City Center 

Zero-inflated functional data appear when an excessive number of zeros are recorded for some functional variables due to the threshold of detection limits. To analyze this kind of data we propose a two part mixed-effects functional regression model. The first part models the probability function of the functional response taking nonzero values via a mixed-effects functional logistic regression model. The second part models the log-transformed true response function by a mixed-effects functional linear model. We use smoothing splines to estimate both the fixed and random effect functions. The estimation procedures for the two parts are respectively penalized quasi-likelihood and a REML-based EM algorithm. Extensive simulations are presented to evaluate the numerical performance of our method. We also apply the method to a Northwestern ICU study to investigate the relationship between total calcium and albumin measurements in repeated blood tests during each of the multiple ICU visits of a patient. Results show that the proposed approach effectively handles zero inflation while recovering the functional relationship between the variables of interest.

Zero-inflated functional data

Functional regression model

Mixed-effects model

Penalized quasi-likelihood

REML based EM algorithm 

Section on Nonparametric Statistics