Testing homogeneity in clustered (longitudinal) count data regression model with over-dispersion

Clustered (longitudinal) count data arise in many bio-statistical practices in which a number of repeated count responses are observed on a number of individuals. The repeated observations may also represent counts over time from a number of individuals. One important problem that arises in practice is to test homogeneity within clusters (individuals) and between clusters (individuals). As data within clusters are observations of repeated responses, the count data may be correlated and/or over-dispersed. For over-dispersed count data with unknown over-dispersion parameter we derive two score tests by assuming a random intercept model within the framework of (i) the negative binomial mixed effects model and (ii) the double extended quasi-likelihood mixed effects model (Lee and Nelder, 2001). These two statistics are much simpler than a statistic derived by Jacqmin-Gadda and Commenges (1995) under the framework of the over-dispersed generalized linear model. The first statistic takes the over-dispersion more directly into the model and therefore is expected to do well when the model assumptions are satisfied and the other statistic is expected to be robust. Simulations show superior level property of the statistics derived under the negative binomial and double extended quasi-likelihood model assumptions. A data set is analyzed and a discussion is given.     

Reference priors for linear models with general covariance structures

We develop a new class of reference priors for linear models with general covariance structures. A general Markov chain Monte Carlo algorithm is also proposed for implementing the computation. We present several examples to demonstrate the results: Bayesian penalized spline smoothing, a Bayesian approach to bivariate smoothing for a spatial model, and prior specification for structural equation models.     

A Note on Generalized Functional Linear Model and Its Application

Motivated by a biomarker study for colorectal neoplasia, we consider generalized functional linear models where the functional predictors are measured with errors at discrete design points. Assuming that the true functional predictor and the slope function are smooth, we investigate a two-step estimating procedure where both the true functional predictor and the slope function are estimated through spline smoothing. The operating characteristics of the proposed method are derived; the usefulness of the proposed method is illustrated by a simulation study as well as data analysis for the motivating colorectal neoplasia study.     

Multivariate temporal disaggregation with cross-sectional constraints

Multivariate temporal disaggregation deals with the historical reconstruction and nowcasting of economic variables subject to temporal and contemporaneous aggregation constraints. The problem involves a system of time series that are related not only by a dynamic model but also by accounting constraints. The paper introduces two fundamental (and realistic) models that implement the multivariate best linear unbiased estimation approach that has potential application to the temporal disaggregation of the national accounts series. The multivariate regression model with random walk disturbances is most suitable to deal with the chained linked volumes (as the nature of the national accounts time series suggests); however, in this case the accounting constraints are not binding and the discrepancy has to be modeled by either a trend-stationary or an integrated process. The tiny, compared with other driving disturbances, size of the discrepancy prevents maximum-likelihood estimation to be carried out, and the parameters have to be estimated separately. The multivariate disaggregation with integrated random walk disturbances is suitable for the national accounts aggregates expressed at current prices, in which case the accounting constraints are binding.     

A step-by-step algorithm for combining diagnostic tests

Combining data of several tests or markers for the classification of patients according to their health status for assigning better treatments is a major issue in the study of diseases such as cancer. In order to tackle this problem, several approaches have been proposed in the literature. In this paper, a step-by-step algorithm for estimating the parameters of a linear classifier that combines several measures is considered. The optimization criterion is to maximize the area under the receiver operating characteristic curve. The algorithm is applied to different simulated data sets and its performance is evaluated. Finally, the method is illustrated with a prostate cancer staging database.     

Leverage analysis for linear mixed models

We consider a generalized leverage matrix useful for the identification of influential units and observations in linear mixed models and show how a decomposition of this matrix may be employed to identify high leverage points for both the marginal fitted values and the random effect component of the conditional fitted values. We illustrate the different uses of the two components of the decomposition with a simulated example as well as with a real data set.     

Bootstrap in functional linear regression

We have considered the functional linear model with scalar response and functional explanatory variable. One of the most popular methodologies for estimating the model parameter is based on functional principal components analysis (FPCA). In recent literature, weak convergence for a wide class of FPCA-type estimates has been proved, and consequently asymptotic confidence sets can be built. In this paper, we have proposed an alternative approach in order to obtain pointwise confidence intervals by means of a bootstrap procedure, for which we have obtained its asymptotic validity. Besides, a simulation study allows us to compare the practical behaviour of asymptotic and bootstrap confidence intervals in terms of coverage rates for different sample sizes.     

Spline-backfitted kernel smoothing of partially linear additive model

A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the data spline smoothing and kernel smoothing consecutively. Simulation experiments with both moderate and large number of variables confirm the asymptotic results. Application to the Boston housing data serves as a practical illustration of the method.     

Asymptotic expansion for nonparametric M-estimator in a nonlinear regression model with long-memory errors

We consider asymptotic expansion of the nonparametric M-estimator in a fixed-design nonlinear regression model when the errors are generated by long-memory linear processes. Under mild conditions, we show that the nonparametric M-estimator is first-order equivalent to the Nadaraya-Watson (NW) estimator, which implies that the nonparametric M-estimator has the same asymptotic distribution as that of the NW estimator. Furthermore, we study the second-order asymptotic expansion of the nonparametric M-estimator and show that the difference between the nonparametric M-estimator and the NW estimator has a limiting distribution after suitable standardization. The nature of the limiting distribution depends on the range of long-memory parameter α. We also compare the finite sample behavior of the two estimators through a numerical example when the errors are long-memory.     

Modeling longitudinal binomial responses: implications from two dueling paradigms

The generalized estimating equations (GEEs) and generalized linear mixed-effects model (GLMM) are the two most popular paradigms to extend models for cross-sectional data to a longitudinal setting. Although the two approaches yield well-interpreted models for continuous outcomes, it is quite a different story when applied to binomial responses. We discuss major modeling differences between the GEE- and GLMM-derived models by presenting new results regarding the model-driven differences. Our results show that GLMM induces some artifacts in the marginal models at assessment times, making it inappropriate when applied to such responses from real study data. The different interpretations of parameters resulting from the conceptual difference between the two modeling approaches also carry quite significant implications and ramifications with respect to data and power analyses. Although a special case involving a scale difference in parameters between GEE and GLMM has been noted in the literature, its implications in real data analysis has not been thoroughly addressed. Further, this special case has a very limited covariate structure and does not apply to most real studies, especially multi-center clinical trials. The new results presented fill a substantial gap in the literature regarding the model-driven differences between the two dueling paradigms.