Dalei Yu

Conditional Akaike information criterion for generalized linear mixed models

In this study, a model identification instrument to determine the variance component structure for generalized linear mixed models (glmms) is developed based on the conditional Akaike information (cai). In particular, an asymptotically unbiased estimator of the cai (denoted as caicc) is derived as the model selection criterion which takes the estimation uncertainty in the variance component parameters into consideration. The relationship between bias correction and generalized degree of freedom for glmms is also explored. Simulation results show that the estimator performs well. The proposed criterion demonstrates a high proportion of correct model identification for glmms. Two sets of real data (epilepsy seizure count data and polio incidence data) are used to illustrate the proposed model identification method.

Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models

ABSTRACT Considering model averaging estimation in generalized linear models, we propose a weight choice criterion based on the Kullback–Leibler (KL) loss with a penalty term. This criterion is different from that for continuous observations in principle, but reduces to the Mallows criterion in the situation. We prove that the corresponding model averaging estimator is asymptotically optimal under certain assumptions. We further extend our concern to the generalized linear mixed-effects model framework and establish associated theory. Numerical experiments illustrate that the proposed method is promising.

Influence diagnostics in meta‐regression model

This paper studies the influence diagnostics in meta-regression model including case deletion diagnostic and local influence analysis. We derive the subset deletion formulae for the estimation of regression coefficient and heterogeneity variance and obtain the corresponding influence measures. The DerSimonian and Laird estimation and maximum likelihood estimation methods in meta-regression are considered, respectively, to derive the results. Internal and external residual and leverage measure are defined. The local influence analysis based on case-weights perturbation scheme, responses perturbation scheme, covariate perturbation scheme, and within-variance perturbation scheme are explored. We introduce a method by simultaneous perturbing responses, covariate, and within-variance to obtain the local influence measure, which has an advantage of capable to compare the influence magnitude of influential studies from different perturbations. An example is used to illustrate the proposed methodology.

Adjusted quasi-maximum likelihood estimator for mixed regressive, spatial autoregressive model and its small sample bias

Under flexible distributional assumptions, the adjusted quasi-maximum likelihood ( adqml ) estimator for mixed regressive, spatial autoregressive model is studied in this paper. The proposed estimation method accommodates the extra uncertainty introduced by the unknown regression coefficients. Moreover, the explicit expressions of theoretical/feasible second-order-bias of the adqml estimator are derived and the difference between them is investigated. The feasible second-order-bias corrected adqml estimator is then designed accordingly for small sample setting. Extensive simulation studies are conducted under both normal and non-normal situations, showing that the quasi-maximum likelihood ( qml ) estimator suffers from large bias when the sample size is relatively small in comparison to the number of regression coefficients and such bias can be effectively eliminated by the proposed adqml estimation method. The use of the method is then demonstrated in the analysis of the Neighborhood Crimes Data.

Multilevel cumulative logistic regression model with random effects

A multilevel model for ordinal data in generalized linear mixed models (GLMM) framework is developed to account for the inherent dependencies among observations within clusters. Motivated by a data set from the British Social Attitudes Panel Survey (BSAPS), the random district effects and respondent effects are incorporated into the linear predictor to accommodate the nested clusterings. The fixed (random) effects are estimated (predicted) by maximizing the penalized quasi likelihood (PQL) function, whereas the variance component parameters are obtained via the restricted maximum likelihood (REML) estimation method. The model is employed to analyze the BSAPS data. Simulation studies are conducted to assess the performance of estimators.

Robust REML estimation for k-component Poisson mixture with random effects: application to the epilepsy seizure count data and urinary tract infections data

A robust version of residual maximum likelihood estimation for Poisson log-linear mixed model is developed, and the method is extended to k-component Poisson mixture with random effects. The method not only provides the robust estimators for the fixed effects and variance component parameters but also gives the robust prediction of random effects. Simulation results show that the proposed method is effective in limiting the impact of outliers under different data contamination schemes. The method is adopted to analyze the epilepsy seizure count data and the urinary tract infections data, which are deemed to contain several potential outliers. The results show that the proposed method provides better goodness of fit to the data and demonstrate the effect of the robust tuning mechanism.

Robust estimation and confidence interval in meta-regression models

Meta-analysis provides a quantitative method for combining results from independent studies with the same treatment. However, existing estimation methods are sensitive to the presence of outliers in the datasets. In this paper we study the robust estimation for the parameters in meta-regression, including the between-study variance and regression parameters. Huber’s rho function and Tukey’s biweight function are adopted to derive the formulae of robust maximum likelihood (ML) estimators. The corresponding algorithms are developed. The asymptotic confidence interval and second-order-corrected confidence interval are investigated. Extensive simulation studies are conducted to assess the performance of the proposed methodology, and our results show that the robust estimators are promising and outperform the conventional ML and restricted maximum likelihood estimators when outliers exist in the dataset. The proposed methods are applied in three case studies and the results further support the eligibility of our methods in practical situations.

Statistical Inference on Progressive Type-II Censored Data from Extreme-value Distribution

We conduct statistical inference on data collected from extreme-value distribution under a progressive Type-II censoring scheme in this paper. By converting the extreme-value model into a Wei bull model, the computation of the maximum likelihood estimator (MLE) for model parameters can be greatly simplified. The bias, variance and covariance of the MLEs under various censoring schemes are investigated. Besides, based on the asymptotic normality of these MLEs, the coverage probability for some defined pivotal quantities and the average length of the confidence interval for model parameters are also provided. The properties of the derived censoring schemes are evaluated by a numerical study. The results show that in order to get satisfying performance in respect to bias, variance, coverage probability and average length of confidence intervals, a moderate or large number of failures are required. Furthermore, a sensitivity study is also employed to evaluate the robustness of our suggested approach, which shows that it is rather robust and the simulation results can be easily reproduced.

Information Based Model Selection Criterion for Binary Response Generalized Linear Mixed Models

Conditional Akaike information criterion is derived within the framework of conditional-likelihood-based method for binary response generalized linear mixed models. The criterion essentially is the asymptotically unbiased estimator of conditional Akaike information based on maximum likelihood estimator. The proposed criterion is adopted to address the model selection problems in binary response generalized linear mixed models. Comparing with other Monte-Carlo EM based methods, conditional Akaike information criterion is more flexible and computationally attractive. Simulations show that the performance of the proposed criterion is in general promising. The use of the criterion is demonstrated in the analysis of the chronic asthmatic patients data.