Generalized additive partial linear models for analyzing correlated data

Local influence diagnostics in elliptical multilevel models

Local influence diagnostics for elliptical multilevel models are proposed in this paper. This class of models involves the use of continuous symmetric distributions, including heavy-tailed error models, and the normal distribution as a particular case. Maximum likelihood estimation and features related to the fitting and model assumptions are discussed. Finally, local influence measures under different perturbation schemes are developed and applied to fit real data under the normal, Student- t and power exponential distributions.

Semiparametric partial linear modeling of risk factors for ear infections: the Early Childhood Longitudinal Study

The Early Childhood Longitudinal Study-Kindergarten Class of 2010-2011 (ECLS-K:2011) ascertained timing of ear infections within age specified intervals and parent's/caregiver's report of medically diagnosed hearing loss. In this nationally representative, school-based sample of children followed from kindergarten entry through fifth grade, academic performance in reading, mathematics, and science was assessed longitudinally. Prior investigations of this ECLS-K:2011 cohort showed that age has a non-linear, monotonically increasing functional relationship with academic performance. Because of this knowledge, a semiparametric partial linear model is proposed, in which the effect of age is modeled by an unknown monotonically increasing function along with other regression parameters. The parameters are estimated by a semiparametric maximum likelihood estimator. A test of a constant effect of age is also proposed. Simulation studies are conducted to evaluate the performance of the proposed method, as compared with the commonly used linear model; the former outperforms the latter based on several criteria. We then analyzed ECLS-K:2011 data to compare results of the partial linear parametric model estimation with that of classical linear regression models.

GMM Estimation of a Partially Linear Additive Spatial Error Model

This article presents a partially linear additive spatial error model (PLASEM) specification and its corresponding generalized method of moments (GMM). It also derives consistency and asymptotic normality of estimators for the case with a single nonparametric term and an arbitrary number of nonparametric additive terms under some regular conditions. In addition, the finite sample performance for our estimates is assessed by Monte Carlo simulations. Lastly, the proposed method is illustrated by analyzing Boston housing data.