Robust bootstrap estimates in heteroscedastic semi-varying coefficient models and applications in analyzing Australia CPI data

This article deals with the estimation of the parametric component, which is of primary interest, in the heteroscedastic semi-varying coefficient models. Based on the bootstrap technique, we present a procedure for estimating the parameters, which can provide a reliable approximation to the asymptotic distribution of the profile least-square (PLS) estimator. Furthermore, a bootstrap-type estimator of covariance matrix is developed, which is proved to be a consistent estimator of the covariance matrix. Moreover, some simulation experiments are conducted to evaluate the finite sample performance for the proposed methodology. Finally, the Australia CPI dataset is analyzed to demonstrate the application of the methods.     

Reversible jump Markov chain Monte Carlo algorithms for Bayesian variable selection in logistic mixed models

In this article, to reduce computational load in performing Bayesian variable selection, we used a variant of reversible jump Markov chain Monte Carlo methods, and the Holmes and Held (HH) algorithm, to sample model index variables in logistic mixed models involving a large number of explanatory variables. Furthermore, we proposed a simple proposal distribution for model index variables, and used a simulation study and real example to compare the performance of the HH algorithm with our proposed and existing proposal distributions. The results show that the HH algorithm with our proposed proposal distribution is a computationally efficient and reliable selection method.     

Conditional covariance penalties for mixed models

The prediction error for mixed models can have a conditional or a marginal perspective depending on the research focus. We introduce a novel conditional version of the optimism theorem for mixed models linking the conditional prediction error to covariance penalties for mixed models. Different possibilities for estimating these conditional covariance penalties are introduced. These are bootstrap methods, cross-validation, and a direct approach called Steinian. The behavior of the different estimation techniques is assessed in a simulation study for the binomial-, the t-, and the gamma distribution and for different kinds of prediction error. Furthermore, the impact of the estimation techniques on the prediction error is discussed based on an application to undernutrition in Zambia.     

Joint models for mixed categorical outcomes: a study of HIV risk perception and disease status in Mozambique

Two types of bivariate models for categorical response variables are introduced to deal with special categories such as ‘unsure’ or ‘unknown’ in combination with other ordinal categories, while taking additional hierarchical data structures into account. The latter is achieved by the use of different covariance structures for a trivariate random effect. The models are applied to data from the INSIDA survey, where interest goes to the effect of covariates on the association between HIV risk perception (quadrinomial with an ‘unknown risk’ category) and HIV infection status (binary). The final model combines continuation-ratio with cumulative link logits for the risk perception, together with partly correlated and partly shared trivariate random effects for the household level. The results indicate that only age has a significant effect on the association between HIV risk perception and infection status. The proposed models may be useful in various fields of application such as social and biomedical sciences, epidemiology and public health.     

Robust Bayesian nonlinear mixed‐effects modeling of time to positivity in tuberculosis trials

Early phase 2 tuberculosis (TB) trials are conducted to characterize the early bactericidal activity (EBA) of anti‐TB drugs. The EBA of anti‐TB drugs has conventionally been calculated as the rate of decline in colony forming unit (CFU) count during the first 14 days of treatment. The measurement of CFU count, however, is expensive and prone to contamination. Alternatively to CFU count, time to positivity (TTP), which is a potential biomarker for long‐term efficacy of anti‐TB drugs, can be used to characterize EBA. The current Bayesian nonlinear mixed‐effects (NLME) regression model for TTP data, however, lacks robustness to gross outliers that often are present in the data. The conventional way of handling such outliers involves their identification by visual inspection and subsequent exclusion from the analysis. However, this process can be questioned because of its subjective nature. For this reason, we fitted robust versions of the Bayesian nonlinear mixed‐effects regression model to a wide range of TTP datasets. The performance of the explored models was assessed through model comparison statistics and a simulation study. We conclude that fitting a robust model to TTP data obviates the need for explicit identification and subsequent “deletion” of outliers but ensures that gross outliers exert no undue influence on model fits. We recommend that the current practice of fitting conventional normal theory models be abandoned in favor of fitting robust models to TTP data.     

Assessment of individual bioequivalence using sufficient bootstrap procedure

This paper proposes a sufficient bootstrap method, which uses only the unique observations in the resamples, to assess the individual bioequivalence under 2 × 4 randomized crossover design. The finite sample performance of the proposed method is illustrated by extensive Monte Carlo simulations as well as a real‐experimental data set, and the results are compared with those obtained by the traditional bootstrap technique. Our records reveal that the proposed method is a good competitor or even better than the classical percentile bootstrap confidence limits.     

Modelling of connected processes

The problem of comparing, contrasting and combining information from different sets of data is an enduring one in many practical applications of statistics. A specific problem of combining information from different sources arose in integrating information from three different sets of data generated by three different sampling campaigns at the input stage as well as at the output stage of a grey-water treatment process. For each stage, a common process trend function needs to be estimated to describe the input and output material process behaviours. Once the common input and output process models are established, it is required to estimate the efficiency of the grey-water treatment method. A synthesized tool for modelling different sets of process data is created by assembling and organizing a number of existing techniques: (i) a mixed model of fixed and random effects, extended to allow for a nonlinear fixed effect, (ii) variogram modelling, a geostatistical technique, (iii) a weighted least squares regression embedded in an iterative maximum-likelihood technique to handle linear/nonlinear fixed and random effects and (iv) a formulation of a transfer-function model for the input and output processes together with a corresponding nonlinear maximum-likelihood method for estimation of a transfer function. The synthesized tool is demonstrated, in a new case study, to contrast and combine information from connected process models and to determine the change in one quality characteristic, namely pH, of the input and output materials of a grey-water filtering process.