A Diagnostic Test for the Mixing Distribution in a Generalised Linear Mixed Model

We introduce a diagnostic test for the mixing distribution in a generalised linear mixed model. The test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimates of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-square distribution under the null hypothesis that the mixing distribution is correctly specified. For the important special case of the logistic regression model with random intercepts, we evaluate via simulation the power of the test in finite samples under several alternative distributional forms for the mixing distribution. We illustrate the method by applying it to data from a clinical trial investigating the effects of hormonal contraceptives in women.

PSPLINE: Stata module providing a penalized spline scatterplot smoother based on linear mixed model technology

Pspline uses xtmixed to fit a penalized spline regression and plots the smoothed function. Additional covariates can be specified to adjust the smooth and plot partial residuals.

A zero-augmented gamma mixed model for longitudinal data with many zeros

In many occupational safety interventions, the objective is to reduce the injury incidence as well as the mean claims cost once injury has occurred. The claims cost data within a period typically contain a large proportion of zero observations (no claim). The distribution thus comprises a point mass at 0 mixed with a non-degenerate parametric component. Essentially, the likelihood function can be factorized into two orthogonal components. These two components relate respectively to the effect of covariates on the incidence of claims and the magnitude of claims, given that claims are made. Furthermore, the longitudinal nature of the intervention inherently imposes some correlation among the observations. This paper introduces a zero-augmented gamma random effects model for analysing longitudinal data with many zeros. Adopting the generalized linear mixed model (GLMM) approach reduces the original problem to the fitting of two independent GLMMs. The method is applied to evaluate the effectiveness of a workplace risk assessment teams program, trialled within the cleaning services of a Western Australian public hospital.

Probe-specific mixed-model approach to detect copy number differences using multiplex ligation-dependent probe amplification (MLPA)

Background: MLPA method is a potentially useful semi-quantitative method to detect copy number alterations in targeted regions. In this paper, we propose a method for the normalization procedure based on a non-linear mixed-model, as well as a new approach for determining the statistical significance of altered probes based on linear mixed-model. This method establishes a threshold by using different tolerance intervals that accommodates the specific random error variability observed in each test sample.Results: Through simulation studies we have shown that our proposed method outperforms two existing methods that are based on simple threshold rules or iterative regression. We have illustrated the method using a controlled MLPA assay in which targeted regions are variable in copy number in individuals suffering from different disorders such as Prader-Willi, DiGeorge or Autism showing the best performace.Conclusion: Using the proposed mixed-model, we are able to determine thresholds to decide whether a region is altered. These threholds are specific for each individual, incorporating experimental variability, resulting in improved sensitivity and specificity as the examples with real data have revealed.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.

Finite mixture regression model with random effects: application to neonatal hospital length of stay

A two-component mixture regression model that allows simultaneously for heterogeneity and dependency among observations is proposed. By specifying random effects explicitly in the linear predictor of the mixture probability and the mixture components, parameter estimation is achieved by maximising the corresponding best linear unbiased prediction type log-likelihood. Approximate residual maximum likelihood estimates are obtained via an EM algorithm in the manner of generalised linear mixed model (GLMM). The method can be extended to a g-component mixture regression model with the component density from the exponential family, leading to the development of the class of finite mixture GLMM. For illustration, the method is applied to analyse neonatal length of stay (LOS). It is shown that identification of pertinent factors that influence hospital LOS can provide important information for health care planning and resource allocation. (C) 2002 Elsevier Science B.V. All rights reserved.

She’s a femme fatale: low-density larval development produces good disease vectors

Two hypotheses for how conditions for larval mosquitoes affect vectorial capacity make opposite predictions about the relationship of adult size and frequency of infection with vector-borne pathogens. Competition among larvae produces small adult females. The competition-susceptibility hypothesis postulates that small females are more susceptible to infection and predicts frequency of infection should decrease with size. The competition-longevity hypothesis postulates that small females have lower longevity and lower probability of becoming competent to transmit the pathogen and thus predicts frequency of infection should increase with size. We tested these hypotheses for Aedes aegypti in Rio de Janeiro, Brazil, during a dengue outbreak. In the laboratory, longevity increases with size, then decreases at the largest sizes. For field-collected females, generalised linear mixed model comparisons showed that a model with a linear increase of frequency of dengue with size produced the best Akaike’s information criterion with a correction for small sample sizes (AICc). Consensus prediction of three competing models indicated that frequency of infection increases monotonically with female size, consistent with the competition-longevity hypothesis. Site frequency of infection was not significantly related to site mean size of females. Thus, our data indicate that uncrowded, low competition conditions for larvae produce the females that are most likely to be important vectors of dengue. More generally, ecological conditions, particularly crowding and intraspecific competition among larvae, are likely to affect vector-borne pathogen transmission in nature, in this case via effects on longevity of resulting adults. Heterogeneity among individual vectors in likelihood of infection is a generally important outcome of ecological conditions impacting vectors as larvae.

Biometrical analysis and selection of tetraploid progenies of Panicum maximum using mixed model methods

The objectives of this work were to estimate the genetic and phenotypic parameters and to predict the genetic and genotypic values of the selection candidates obtained from intraspecific crosses in Panicum maximum as well as the performance of the hybrid progeny of the existing and projected crosses. Seventy-nine intraspecific hybrids obtained from artificial crosses among five apomictic and three sexual autotetraploid individuals were evaluated in a clonal test with two replications and ten plants per plot. Green matter yield, total and leaf dry matter yields and leaf percentage were evaluated in five cuts per year during three years. Genetic parameters were estimated and breeding and genotypic values were predicted using the restricted maximum likelihood/best linear unbiased prediction procedure (REML/BLUP). The dominant genetic variance was estimated by adjusting the effect of full-sib families. Low magnitude individual narrow sense heritabilities (0.02-0.05), individual broad sense heritabilities (0.14-0.20) and repeatability measured on an individual basis (0.15-0.21) were obtained. Dominance effects for all evaluated characteristics indicated that breeding strategies that explore heterosis must be adopted. Less than 5% increase in the parameter repeatability was obtained for a three-year evaluation period and may be the criterion to determine the maximum number of years of evaluation to be adopted, without compromising gain per cycle of selection. The identification of hybrid candidates for future cultivars and of those that can be incorporated into the breeding program was based on the genotypic and breeding values, respectively. The prediction of the performance of the hybrid progeny, based on the breeding values of the progenitors, permitted the identification of the best crosses and indicated the best parents to use in crosses.

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119-130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model. (C) 2007 Elsevier B.V. All rights reserved.

Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups

This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

Likelihood prediction for generalized linear mixed models under covariate uncertainty

This paper presents the techniques of likelihood prediction for the generalized linear mixed models. Methods of likelihood prediction is explained through a series of examples; from a classical one to more complicated ones. The examples show, in simple cases, that the likelihood prediction (LP) coincides with already known best frequentist practice such as the best linear unbiased predictor. The paper outlines a way to deal with the covariate uncertainty while producing predictive inference. Using a Poisson error-in-variable generalized linear model, it has been shown that in complicated cases LP produces better results than already know methods.