Semiparametric Mixed Model Research Articles

Semiparametric Inference in Generalized Mixed Effects Models

Summary The paper presents a study of the generalized partially linear model including random effects in its linear part. We propose an estimator that combines likelihood approaches for mixed effects models, with kernel methods. Following the methodology of Härdle and co-workers, we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model. The critical values are estimated by using a bootstrap procedure. The asymptotic theory for the methods is provided, as are the results of a simulation study. These verify the feasibility and the excellent behaviour of the methods for samples of even moderate size. The usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in Galicia, Spain.

Modelling Price Paths in On-Line Auctions: Smoothing Sparse and Unevenly Sampled Curves by Using Semiparametric Mixed Models

Summary On-line auctions pose many challenges for the empirical researcher, one of which is the effective and reliable modelling of price paths. We propose a novel way of modelling price paths in eBay's on-line auctions by using functional data analysis. One of the practical challenges is that the functional objects are sampled only very sparsely and unevenly. Most approaches rely on smoothing to recover the underlying functional object from the data, which can be difficult if the data are irregularly distributed. We present a new approach that can overcome this challenge. The approach is based on the ideas of mixed models. Specifically, we propose a semiparametric mixed model with boosting to recover the functional object. As well as being able to handle sparse and unevenly distributed data, the model also results in conceptually more meaningful functional objects. In particular, we motivate our method within the framework of eBay's on-line auctions. On-line auctions produce monotonic increasing price curves that are often correlated across auctions. The semiparametric mixed model accounts for this correlation in a parsimonious way. It also manages to capture the underlying monotonic trend in the data without imposing model constraints. Our application shows that the resulting functional objects are conceptually more appealing. Moreover, when used to forecast the outcome of an on-line auction, our approach also results in more accurate price predictions compared with standard approaches. We illustrate our model on a set of 183 closed auctions for Palm M515 personal digital assistants.

Semiparametric Mixed Model for Longitudinal Image Data

SYNOPTIC ABSTRACTThis paper is concerned with analyzing the image data with repeated measurement. Modeling the complex spatial variability in medical images can enhance the inference for comparing treatments and examining the time evolution. We propose a semiparametric mixed regression model that combines the robustness of a low-rank spline method with the efficiency of likelihood-based parameter estimation. In the convenient framework of a linear mixed model, we decompose pattern variation by using the Karhunen-Loève expansion of a spatial random process. Additional spatial covariates, the time variable and other experimental factors are easily accommodated in the linear predictor, which enables comprehensive analyses underlying spatial patterns. The back-fitting algorithm and the smoothing parameter selections are investigated by simulation for our semiparametric model. We illustrate our method through application to data from a clinical study of neuromuscular electrical stimulation effects on the seating interface pressures for patients with spinal cord injury.

Semiparametric Inference in Generalized Mixed Effects Models

The paper presents a study of the generalized partially linear model including random effects in its linear part. We propose an estimator that combines like-lihood approaches for mixed effects models, with kernel methods. Following the methodology of Hardle et al (1998), we introduce a test for the hypothesis of a parametric mixed effects model against the alternative of a semiparametric mixed effects model. The critical values are estimated using a bootstrap procedure. The asymptotic theory for the methods is provided, as are the results of a simulation study. These verify the feasibility and the excellent behavior of the methods for samples of even moderate size. The usefulness of the methodology is illustrated with an application in which the objective is to estimate forest coverage in Galicia, Spain.

Semiparametric Mixed Models for Increment-Averaged Data With Application to Carbon Sequestration in Agricultural Soils

Adoption of conservation tillage practice in agriculture offers the potential to mitigate greenhouse gas emissions. Studies comparing conservation tillage methods to traditional tillage pair fields under the two management systems and obtain soil core samples from each treatment. Cores are divided into multiple increments, and matching increments from one or more cores are aggregated and analyzed for carbon stock. These data represent not the actual value at a specific depth, but rather the total or average over a depth increment. A semiparametric mixed model is developed for such increment-averaged data. The model uses parametric fixed effects to represent covariate effects, random effects to capture correlation within studies, and an integrated smooth function to describe effects of depth. The depth function is specified as an additive model, estimated with penalized splines using standard mixed model software. Smoothing parameters are automatically selected using restricted maximum likelihood. The methodology is applied to the problem of estimating a change in carbon stock due to a change in tillage practice.

Streamlined variance calculations for semiparametric mixed models

Semiparametric mixed model analysis benefits from variability estimates such as standard errors of effect estimates and variability bars to accompany curve estimates. We show how the underlying variance calculations can be done extremely efficiently compared with the direct naïve approach. These streamlined calculations are linear in the number of subjects, representing a two orders of magnitude improvement.

A semi‐parametric Bayesian approach to average bioequivalence

Bioequivalence assessment is an issue of great interest. Development of statistical methods for assessing bioequivalence is an important area of research for statisticians. Bioequivalence is usually determined based on the normal distribution. We relax this assumption and develop a semi-parametric mixed model for bioequivalence data. The proposed method is quite flexible and practically meaningful. Our proposed method is based on a mixture normal distribution and a non-parametric Bayesian approach using a Dirichlet process mixture prior. A numerical example illustrates the use of our procedure.

Variance component testing in semiparametric mixed models

It is of considerable interest to test for heteroscedasticity in statistical studies. In this paper, we investigate such a problem under the framework of a semiparametric mixed model. A score test is proposed for the hypothesis that all the variance components are zero. We establish the asymptotic property of the test, and examine its performance in a simulation study. The test is illustrated with the analysis of a longitudinal study of measurements of serum creatinine.

An estimation method for the semiparametric mixed effects model.

A semiparametric mixed effects regression model is proposed for the analysis of clustered or longitudinal data with continuous, ordinal, or binary outcome. The common assumption of Gaussian random effects is relaxed by using a predictive recursion method (Newton and Zhang, 1999) to provide a nonparametric smooth density estimate. A new strategy is introduced to accelerate the algorithm. Parameter estimates are obtained by maximizing the marginal profile likelihood by Powell's conjugate direction search method. Monte Carlo results are presented to show that the method can improve the mean squared error of the fixed effects estimators when the random effects distribution is not Gaussian. The usefulness of visualizing the random effects density itself is illustrated in the analysis of data from the Wisconsin Sleep Survey. The proposed estimation procedure is computationally feasible for quite large data sets.

Micro-models of criminal careers: A synthesis of the criminal careers and life course approaches via semiparametric mixed poisson regression models, with empirical applications

Much recent research and debate in criminology have centered around how to conceptualize and model longitudinal sequences of delinquent and criminal acts committed by individuals. Two approaches dominate this controversy. One originates in thecriminal careers paradigm, which emphasizes a potentialheterogeneity of offending groups in the general population—thus leading to a distinction between incidence and prevalence of criminal offending, a focus on the onset, persistence, and desistence of criminal careers, and the possibility that criminals are a distinctive group with constant high rates of offending. Another approach places criminal events within a broader context ofstudies of the life course by explicitly substituting the conceptualization of “social events” for that of “criminal careers”. With respect to analytical models, this approach emphasizes a potentialheterogeneity of offenders with respect to order of criminal events from first to second to higher orders and thus suggests an analysis of the “risks” or “hazards” of offending by order of offense. Some extant commentaries on the criminal careers and life course approaches to conceptualizing and modeling longitudinal sequences of delinquent and criminal events committed by individuals have emphasized their differences and incompatibilities. In contrast, we apply recently developed semiparametric mixed Poisson regression techniques to develop conditions under which the two conceptual/modeling approaches are formally equivalent. We also modify the semiparametric mixed Poisson regression model of criminal careers to incorporate information on order of the delinquent/criminal event and develop an empirical application. This modification demonstrates the complementarity of the criminal careers and life course approaches, even though they have somewhat different foci.

A Comparison of Poisson, Negative Binomial, and Semiparametric Mixed Poisson Regression Models

Specifications and moment properties of the univariate Poisson and negative binomial distributions are briefly reviewed and illustrated. Properties and limitations of the corresponding poisson and negative binomial (gamma mixtures of Poissons) regression models are described. It is shown how a misspecification of the mixing distribution of a mixed Poisson model to accommodate hidden heterogeneity ascribable to unobserved variables—although not affecting the consistency of maximum likelihood estimators of the Poisson mean rate parameter or its regression parameterization—can lead to inflated t ratios of regression coefficients and associated incorrect inferences. Then the recently developed semiparametric maximum likelihood estimator for regression models composed of arbitrary mixtures of Poisson processes is specified and further developed. It is concluded that the semiparametric mixed Poisson regression model adds considerable flexibility to Poisson-family regression models and provides opportunities for interpretation of empirical patterns not available in the conventional approaches.