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Nonparametric Mixed-Effects Density Regression


Conditional density provides the most informative summary of the relationship between independent and dependent variables. It enables us to examine the overall shapes of densities as well as summary characteristics such as quantiles and modes. Repeated measures designs are widely used in many areas such as agriculture, education and pharmaceutical sciences. The data from repeated measures designs are correlated. We develop a nonparametric method for conditional density estimation for repeated measures data. Specifically we propose nonparametric mixed-efffects density regression (NMDR) models. The NMDR models allow us to estimate conditional densities with fewer constraints on the form of densities when data are correlated. The models may be constructed using Smoothing Spline ANOVA (SS ANOVA) methods. Penalized marginal likelihood is used to estimate the density function as well as parameters. We use the stochastic approximation algorithm (SAA) with Newton-Raphson method for optimization, and Markov chain Monte Carlo (MCMC) for approximating integrals. An example from speech science is provided to illustrate the utility of our model.

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