Showing papers on "Random effects model published in 2001"

Generalized, Linear, and Mixed Models

Abstract: Preface. Preface to the First Edition. 1. Introduction. 1.1 Models. 1.2 Factors, Levels, Cells, Effects And Data. 1.3 Fixed Effects Models. 1.4 Random Effects Models. 1.5 Linear Mixed Models (Lmms). 1.6 Fixed Or Random? 1.7 Inference. 1.8 Computer Software. 1.9 Exercises. 2. One-Way Classifications. 2.1 Normality And Fixed Effects. 2.2 Normality, Random Effects And MLE. 2.3 Normality, Random Effects And REM1. 2.4 More On Random Effects And Normality. 2.5 Binary Data: Fixed Effects. 2.6 Binary Data: Random Effects. 2.7 Computing. 2.8 Exercises. 3. Single-Predictor Regression. 3.1 Introduction. 3.2 Normality: Simple Linear Regression. 3.3 Normality: A Nonlinear Model. 3.4 Transforming Versus Linking. 3.5 Random Intercepts: Balanced Data. 3.6 Random Intercepts: Unbalanced Data. 3.7 Bernoulli - Logistic Regression. 3.8 Bernoulli - Logistic With Random Intercepts. 3.9 Exercises. 4. Linear Models (LMs). 4.1 A General Model. 4.2 A Linear Model For Fixed Effects. 4.3 Mle Under Normality. 4.4 Sufficient Statistics. 4.5 Many Apparent Estimators. 4.6 Estimable Functions. 4.7 A Numerical Example. 4.8 Estimating Residual Variance. 4.9 Comments On The 1- And 2-Way Classifications. 4.10 Testing Linear Hypotheses. 4.11 T-Tests And Confidence Intervals. 4.12 Unique Estimation Using Restrictions. 4.13 Exercises. 5. Generalized Linear Models (GLMs). 5.1 Introduction. 5.2 Structure Of The Model. 5.3 Transforming Versus Linking. 5.4 Estimation By Maximum Likelihood. 5.5 Tests Of Hypotheses. 5.6 Maximum Quasi-Likelihood. 5.7 Exercises. 6. Linear Mixed Models (LMMs). 6.1 A General Model. 6.2 Attributing Structure To VAR(y). 6.3 Estimating Fixed Effects For V Known. 6.4 Estimating Fixed Effects For V Unknown. 6.5 Predicting Random Effects For V Known. 6.6 Predicting Random Effects For V Unknown. 6.7 Anova Estimation Of Variance Components. 6.8 Maximum Likelihood (Ml) Estimation. 6.9 Restricted Maximum Likelihood (REMl). 6.10 Notes And Extensions. 6.11 Appendix For Chapter 6. 6.12 Exercises. 7. Generalized Linear Mixed Models. 7.1 Introduction. 7.2 Structure Of The Model. 7.3 Consequences Of Having Random Effects. 7.4 Estimation By Maximum Likelihood. 7.5 Other Methods Of Estimation. 7.6 Tests Of Hypotheses. 7.7 Illustration: Chestnut Leaf Blight. 7.8 Exercises. 8. Models for Longitudinal data. 8.1 Introduction. 8.2 A Model For Balanced Data. 8.3 A Mixed Model Approach. 8.4 Random Intercept And Slope Models. 8.5 Predicting Random Effects. 8.6 Estimating Parameters. 8.7 Unbalanced Data. 8.8 Models For Non-Normal Responses. 8.9 A Summary Of Results. 8.10 Appendix. 8.11 Exercises. 9. Marginal Models. 9.1 Introduction. 9.2 Examples Of Marginal Regression Models. 9.3 Generalized Estimating Equations. 9.4 Contrasting Marginal And Conditional Models. 9.5 Exercises. 10. Multivariate Models. 10.1 Introduction. 10.2 Multivariate Normal Outcomes. 10.3 Non-Normally Distributed Outcomes. 10.4 Correlated Random Effects. 10.5 Likelihood Based Analysis. 10.6 Example: Osteoarthritis Initiative. 10.7 Notes And Extensions. 10.8 Exercises. 11. Nonlinear Models. 11.1 Introduction. 11.2 Example: Corn Photosynthesis. 11.3 Pharmacokinetic Models. 11.4 Computations For Nonlinear Mixed Models. 11.5 Exercises. 12. Departures From Assumptions. 12.1 Introduction. 12.2 Misspecifications Of Conditional Model For Response. 12.3 Misspecifications Of Random Effects Distribution. 12.4 Methods To Diagnose And Correct For Misspecifications. 12.5 Exercises. 13. Prediction. 13.1 Introduction. 13.2 Best Prediction (BP). 13.3 Best Linear Prediction (BLP). 13.4 Linear Mixed Model Prediction (BLUP). 13.5 Required Assumptions. 13.6 Estimated Best Prediction. 13.7 Henderson's Mixed Model Equations. 13.8 Appendix. 13.9 Exercises. 14. Computing. 14.1 Introduction. 14.2 Computing Ml Estimates For LMMs. 14.3 Computing Ml Estimates For GLMMs. 14.4 Penalized Quasi-Likelihood And Laplace. 14.5 Exercises. Appendix M: Some Matrix Results. M.1 Vectors And Matrices Of Ones. M.2 Kronecker (Or Direct) Products. M.3 A Matrix Notation. M.4 Generalized Inverses. M.5 Differential Calculus. Appendix S: Some Statistical Results. S.1 Moments. S.2 Normal Distributions. S.3 Exponential Families. S.4 Maximum Likelihood. S.5 Likelihood Ratio Tests. S.6 MLE Under Normality. References. Index.

Marginal Likelihood From the Metropolis–Hastings Output

Abstract: This article provides a framework for estimating the marginal likelihood for the purpose of Bayesian model comparisons. The approach extends and completes the method presented in Chib (1995) by overcoming the problems associated with the presence of intractable full conditional densities. The proposed method is developed in the context of MCMC chains produced by the Metropolis–Hastings algorithm, whose building blocks are used both for sampling and marginal likelihood estimation, thus economizing on prerun tuning effort and programming. Experiments involving the logit model for binary data, hierarchical random effects model for clustered Gaussian data, Poisson regression model for clustered count data, and the multivariate probit model for correlated binary data, are used to illustrate the performance and implementation of the method. These examples demonstrate that the method is practical and widely applicable.

Meta-analysis of correlation coefficients: A Monte Carlo comparison of fixed- and random-effects methods.

Abstract: The efficacy of the Hedges and colleagues, Rosenthal-Rubin, and Hunter-Schmidt methods for combining correlation coefficients was tested for cases in which population effect sizes were both fixed and variable. After a brief tutorial on these meta-analytic methods, the author presents two Monte Carlo simulations that compare these methods for cases in which the number of studies in the meta-analysis and the average sample size of studies were varied. In the fixed case the methods produced comparable estimates of the average effect size; however, the HunterSchmidt method failed to control the Type I error rate for the associated significance tests. In the variable case, for both the Hedges and colleagues and HunterSchmidt methods, Type I error rates were not controlled for meta-analyses including 15 or fewer studies and the probability of detecting small effects was less than .3. Some practical recommendations are made about the use of meta-analysis .

Is catch-per-unit-effort proportional to abundance?

Abstract: We compiled 297 series of catch-per-unit-effort (CPUE) and independent abundance data (as estimated by research trawl surveys) and used observation error and random effects models to test the hypot...

A comparison of statistical methods for meta-analysis.

Abstract: Meta-analysis may be used to estimate an overall effect across a number of similar studies. A number of statistical techniques are currently used to combine individual study results. The simplest of these is based on a fixed effects model, which assumes the true effect is the same for all studies. A random effects model, however, allows the true effect to vary across studies, with the mean true effect the parameter of interest. We consider three methods currently used for estimation within the framework of a random effects model, and illustrate them by applying each method to a collection of six studies on the effect of aspirin after myocardial infarction. These methods are compared using estimated coverage probabilities of confidence intervals for the overall effect. The techniques considered all generally have coverages below the nominal level, and in particular it is shown that the commonly used DerSimonian and Laird method does not adequately reflect the error associated with parameter estimation, especially when the number of studies is small.

Bayesian inference for generalized additive mixed models based on Markov random field priors

Abstract: Most regression problems in practice require flexible semiparametric forms of the predictor for modelling the dependence of responses on covariates. Moreover, it is often necessary to add random effects accounting for overdispersion caused by unobserved heterogeneity or for correlation in longitudinal or spatial data. We present a unified approach for Bayesian inference via Markov chain Monte Carlo (MCMC) simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as usual covariates with fixed effects, metrical covariates with nonlinear effects, unstructured random effects, trend and seasonal components in longitudinal data and spatial covariates are all treated within the same general framework by assigning appropriate priors with different forms and degrees of smoothness. The approach is particularly appropriate for discrete and other fundamentally non-Gaussian responses, where Gibbs sampling techniques developed for Gaussian models cannot be applied, but it also works well for Gaussian responses. We use the close relation between nonparametric regression and dynamic or state space models to develop posterior sampling procedures, based on Markov random field priors. They include recent Metropolis-Hastings block move algorithms for dynamic generalized linear models and extensions for spatial covariates as building blocks. We illustrate the approach with a number of applications that arose out of consulting cases, showing that the methods are computionally feasible also in problems with many covariates and large data sets.

A Two-Part Random-Effects Model for Semicontinuous Longitudinal Data

Abstract: A semicontinuous variable has a portion of responses equal to a single value (typically 0) and a continuous, often skewed, distribution among the remaining values. In cross-sectional analyses, variables of this type may be described by a pair of regression models; for example, a logistic model for the probability of nonzero response and a conditional linear model for the mean response given that it is nonzero. We extend this two-part regression approach to longitudinal settings by introducing random coefficients into both the logistic and the linear stages. Fitting a two-part random-effects model poses computational challenges similar to those found with generalized linear mixed models. We obtain maximum likelihood estimates for the fixed coefficients and variance components by an approximate Fisher scoring procedure based on high-order Laplace approximations. To illustrate, we apply the technique to data from the Adolescent Alcohol Prevention Trial, examining reported recent alcohol use for students in g...

Analyzing variety by environment data using multiplicative mixed models and adjustments for spatial field trend.

Abstract: The recommendation of new plant varieties for commercial use requires reliable and accurate predictions of the average yield of each variety across a range of target environments and knowledge of important interactions with the environment. This information is obtained from series of plant variety trials, also known as multi-environment trials (MET). Cullis, Gogel, Verbyla, and Thompson (1998) presented a spatial mixed model approach for the analysis of MET data. In this paper we extend the analysis to include multiplicative models for the variety effects in each environment. The multiplicative model corresponds to that used in the multivariate technique of factor analysis. It allows a separate genetic variance for each environment and provides a parsimonious and interpretable model for the genetic covariances between environments. The model can be regarded as a random effects analogue of AMMI (additive main effects and multiplicative interactions). We illustrate the method using a large set of MET data from a South Australian barley breeding program.

Bayesian approaches to modeling the conditional dependence between multiple diagnostic tests

Abstract: Many analyses of results from multiple diagnostic tests assume the tests are statistically independent conditional on the true disease status of the subject. This assumption may be violated in practice, especially in situations where none of the tests is a perfectly accurate gold standard. Classical inference for models accounting for the conditional dependence between tests requires that results from at least four different tests be used in order to obtain an identifiable solution, but it is not always feasible to have results from this many tests. We use a Bayesian approach to draw inferences about the disease prevalence and test properties while adjusting for the possibility of conditional dependence between tests, particularly when we have only two tests. We propose both fixed and random effects models. Since with fewer than four tests the problem is nonidentifiable, the posterior distributions are strongly dependent on the prior information about the test properties and the disease prevalence, even with large sample sizes. If the degree of correlation between the tests is known a priori with high precision, then our methods adjust for the dependence between the tests. Otherwise, our methods provide adjusted inferences that incorporate all of the uncertainty inherent in the problem, typically resulting in wider interval estimates. We illustrate our methods using data from a study on the prevalence of Strongyloides infection among Cambodian refugees to Canada.

A refined method for the meta-analysis of controlled clinical trials with binary outcome.

Abstract: For the meta-analysis of controlled clinical trials with binary outcome a test statistic for testing an overall treatment effect is proposed, which is based on a refined estimator for the variance of the treatment effect estimator usually used in the random-effects model of meta-analysis. In simulation studies it is shown that the proposed test keeps the prescribed significance level much better than the commonly used tests in the fixed-effects and random-effects model, respectively. Moreover, when using the test it is not necessary to choose between fixed effects and random effects approaches in advance. The proposed method applies in the same way to the analysis of a controlled multi-centre study with binary outcome, including a possible interaction between drugs and centres.

General Growth Mixture Modeling for Randomized Preventive Interventions

Abstract: This paper proposes growth mixture modeling to assess intervention effects in longitudinal randomized trials. Growth mixture modeling represents unobserved hetero-geneity among the subjects using a finite mixture random effects model. The methodology allows one to examine the impact of an intervention on subgroups characterized by different types of growth trajectories. Such modeling is informative when examining effects on populations that contain individuals who have normative growth as well as non-normative growth. The analysis identi?es subgroup membership and allows theory-based modeling of intervention effects in the different subgroups. An example is presented concerning a randomized intervention in Baltimore public schools aimed at reducing aggressive classroom behavior, where only students who were initially more aggressive showed benefits from the intervention.

Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions

Abstract: SUMMARY Hierarchical generalised linear models are developed as a synthesis of generalised linear models, mixed linear models and structured dispersions. We generalise the restricted maximum likelihood method for the estimation of dispersion to the wider class and show how the joint fitting of models for mean and dispersion can be expressed by two interconnected generalised linear models. The method allows models with (i) any combination of a generalised linear model distribution for the response with any conjugate distribution for the random effects, (ii) structured dispersion components, (iii) different link and variance functions for the fixed and random effects, and (iv) the use of quasilikelihoods in place of likelihoods for either or both of the mean and dispersion models. Inferences can be made by applying standard procedures, in particular those for model checking, to components of either generalised linear model. We also show by numerical studies that the new method gives an efficient estimation procedure for substantial class of models of practical importance. Likelihood-type inference is extended to this wide class of models in a unified way.

Assessment of Actual Significance Levels for Covariate Effects in NONMEM

Abstract: The objectives of this study were to assess the difference between actual and nominal significance levels, as judged by the likelihood ratio test, for hypothesis tests regarding covariate effects using NONMEM, and to study what factors influence these levels. Also, a strategy for obtaining closer agreement between nominal and actual significance levels was investigated. Pharmacokinetic (PK) data without covariate relationships were simulated from a one compartment iv bolus model for 50 individuals. Models with and without covariate relationships were then fitted to the data, and differences in the objective function values were calculated. Alterations were made to the simulation settings; the structural and error models, the number of individuals, the number of samples per individual and the covariate distribution. Different estimation methods in NONMEM were also tried. In addition, a strategy for estimating the actual significance levels for a specific data set, model and parameter was investigated using covariate randomization and a real data set. Under most conditions when the first-order (FO) method was used, the actual significance level for including a covariate relationship in a model was higher than the nominal significance level. Among factors with high impact were frequency of sampling and residual error magnitude. The use of the first-order conditional estimation method with interaction (FOCE-INTER) resulted in close agreement between actual and nominal significance levels. The results from the covariate randomization procedure of the real data set were in agreement with the results from the simulation study. With the FO method the actual significance levels were higher than the nominal, independent of the covariate type, but depending on the parameter influenced. When using FOCE-INTER the actual and nominal levels were similar. The most important factors influencing the actual significance levels for the FO method are the approximation of the influence of the random effects in a nonlinear model, a heteroscedastic error structure in which an existing interaction between interindividual and residual variability is not accounted for in the model, and a lognormal distribution of the residual error which is approximated by a symmetric distribution. Estimation with FOCE–INTER and the covariate randomization procedure provide means to achieve agreement between nominal and actual significance levels.

Efficient Algorithms for Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t Distribution

Abstract: Linear mixed-effects models are frequently used to analyze repeated measures data, because they model flexibly the within-subject correlation often present in this type of data. The most popular linear mixed-effects model for a continuous response assumes normal distributions for the random effects and the within-subject errors, making it sensitive to outliers. Such outliers are more problematic for mixed-effects models than for fixed-effects models, because they may occur in the random effects, in the within-subject errors, or in both, making them harder to be detected in practice. Motivated by a real dataset from an orthodontic study, we propose a robust hierarchical linear mixed-effects model in which the random effects and the within-subject errors have multivariate t-distributions, with known or unknown degrees-of-freedom, which are allowed to vary with groups of subjects. By using a gamma-normal hierarchical structure, our model allows the identification and classification of both types of outliers,...

A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error

Abstract: SUMMARY A common objective in longitudinal studies is to characterise the relationship between a failure time process and time-independent and time-dependent covariates. Timedependent covariates are generally available as longitudinal data collected periodically during the course of the study. We assume that these data follow a linear mixed effects model with normal measurement error and that the hazard of failure depends both on the underlying random effects describing the covariate process and other time-independent covariates through a proportional hazards relationship. A routine assumption is that the random effects are normally distributed; however, this need not hold in practice. Within this framework, we develop a simple method for estimating the proportional hazards model parameters that requires no assumption on the distribution of the random effects. Large-sample properties are discussed, and finite-sample performance is assessed and compared to competing methods via simulation.

Misspecified maximum likelihood estimates and generalised linear mixed models

Abstract: SUMMARY We investigate the impact of model violations on the estimate of a regression coefficient in a generalised linear mixed model. Specifically, we evaluate the asymptotic relative bias that results from incorrect assumptions regarding the random effects. We compare the impact of model violation for two parameterisations of the regression model. Substantial bias in the conditionally specified regression point estimators can result from using a simple random intercepts model when either the random effects distribution depends on measured covariates or there are autoregressive random effects. A marginally specified regression structure that is estimated using maximum likelihood is much less susceptible to bias resulting from random effects model misspecification.

Linear mixed models with flexible distributions of random effects for longitudinal data.

Abstract: Normality of random effects is a routine assumption for the linear mixed model, but it may be unrealistic, obscuring important features of among-individual variation. We relax this assumption by approximating the random effects density by the seminonparameteric (SNP) representation of Gallant and Nychka (1987, Econometrics 55, 363-390), which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior, controlled by a user-chosen tuning parameter. An advantage is that the marginal likelihood may be expressed in closed form, so inference may be carried out using standard optimization techniques. We demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality, and we illustrate the approach via simulation and using longitudinal data from the Framingham study.

Jointly Modeling Longitudinal and Event Time Data With Application to Acquired Immunodeficiency Syndrome

Abstract: In many clinical and epidemiologic studies, periodically measured disease markers are used to monitor progression to the onset of disease. Motivated by a study of CD4 counts in men infected with human immunodeficiency virus (HIV) at risk for acquired immunodeficiency syndrome (AIDS), we developed a joint model for analysis of both longitudinal and event time data. We use a longitudinal model for continuous data that incorporates a mean structure dependent on covariates, a random intercept, a stochastic process, and measurement error. A central component of the longitudinal model is an integrated Ornstein–Uhlenbeck stochastic process, which represents a family of covariance structures with a random effects model and Brownian motion as special cases. The regression model for the event time data is a proportional hazards model that includes the longitudinal marker as a time-dependent variable and other covariates. A Markov chain Monte Carlo algorithm was developed for fitting the joint model. The joint model...

Item Analysis by the Hierarchical Generalized Linear Model.

Abstract: The hierarchical generalized linear model (HGLM) is presented as an explicit, two-level formulation of a multilevel item response model. In this paper, it is shown that the HGLM is equivalent to the Rasch model and that, characteristic of the HGLM, person ability can be expressed in the form of random effects rather than parameters. The two-level item analysis model is presented as a latent regression model with person-characteristic variables. Furthermore, it is shown that the two-level HGLM model can be extended to a three-level latent regression model that permits investigation of the variation of students' performance across groups, such as is found in classrooms and schools, and of the interactive effect of person-and group-characteristic variables.

On tests of the overall treatment effect in meta-analysis with normally distributed responses.

Abstract: For the meta-analysis of controlled clinical trials or epidemiological studies, in which the responses are at least approximately normally distributed, a refined test for the hypothesis of no overall treatment effect is proposed. The test statistic is based on a direct estimation function for the variance of the overall treatment effect estimator. As outcome measures, the absolute and the standardized difference between means are considered. In simulation studies it is shown that the proposed test keeps the prescribed significance level very well in contrast to the commonly used tests in the fixed effects and random effects model, respectively, which can become very liberal. Furthermore, just for using the proposed test it is not necessary to choose between the fixed effects and the random effects approach in advance.

Meta-analysis of continuous outcome data from individual patients.

Abstract: Meta-analyses using individual patient data are becoming increasingly common and have several advantages over meta-analyses of summary statistics. We explore the use of multilevel or hierarchical models for the meta-analysis of continuous individual patient outcome data from clinical trials. A general framework is developed which encompasses traditional meta-analysis, as well as meta-regression and the inclusion of patient-level covariates for investigation of heterogeneity. Unexplained variation in treatment differences between trials is considered as random. We focus on models with fixed trial effects, although an extension to a random effect for trial is described. The methods are illustrated on an example in Alzheimer's disease in a classical framework using SAS PROC MIXED and MLwiN, and in a Bayesian framework using BUGS. Relative merits of the three software packages for such meta-analyses are discussed, as are the assessment of model assumptions and extensions to incorporate more than two treatments.

Missing responses in generalised linear mixed models when the missing data mechanism is nonignorable

Abstract: SUMMARY We propose a method for estimating parameters in the generalised linear mixed model with nonignorable missing response data and with nonmonotone patterns of missing data in the response variable. We develop a Monte Carlo EM algorithm for estimating the parameters in the model via the Gibbs sampler. For the normal random effects model, we derive a novel analytical form for the E- and M-steps, which is facilitated by integrating out the random effects. This form leads to a computationally feasible and extremely efficient Monte Carlo EM algorithm for computing maximum likelihood estimates and standard errors. In addition, we propose a very general joint multinomial model for the missing data indicators, which can be specified via a sequence of one-dimensional conditional distributions. This multinomial model allows for an arbitrary correlation structure between the missing data indicators, and has the potential of reducing the number of nuisance parameters. Real datasets from the International Breast Cancer Study Group and an environmental study involving dyspnoea in cotton workers are presented to illustrate the proposed methods.

Improved estimation procedures for multilevel models with binary response: a case-study

Abstract: Summary. During recent years, analysts have been relying on approximate methods of inference to estimate multilevel models for binary or count data. In an earlier study of random-intercept models for binary outcomes we used simulated data to demonstrate that one such approximation, known as marginal quasi-likelihood, leads to a substantial attenuation bias in the estimates of both fixed and random effects whenever the random effects are non-trivial. In this paper, we fit three-level randomintercept models to actual data for two binary outcomes, to assess whether refined approximation procedures, namely penalized quasi-likelihood and second-order improvements to marginal and penalized quasi-likelihood, also underestimate the underlying parameters. The extent of the bias is assessed by two standards of comparison: exact maximum likelihood estimates, based on a Gauss-Hermite numerical quadrature procedure, and a set of Bayesian estimates, obtained from Gibbs sampling with diffuse priors. We also examine the effectiveness of a parametric bootstrap procedure for reducing the bias. The results indicate that second-order penalized quasi-likelihood estimates provide a considerable improvement over the other approximations, but all the methods of approximate inference result in a substantial underestimation of the fixed and random effects when the random effects are sizable. We also find that the parametric bootstrap method can eliminate the bias but is computationally very intensive.

Series Estimation of Partially Linear Panel Data Models with Fixed Eects

Abstract: This paper considers the problem of estimating a partially linear semiparametric fixed eects panel data model with possible endogeneity. Using the series method, we establish the root N normality result for the estimator of the parametric component, and we show that the unknown function can be consistently estimated at the standard nonparametric rate.

Are Points in Tennis Independent and Identically Distributed? Evidence from a Dynamic Binary Panel Data Model

Abstract: This article tests whether points in tennis are independent and identically distributed (iid). We model the probability of winning a point on service and show that points are neither independent nor identically distributed: winning the previous point has a positive effect on winning the current point, and at “important” points it is more difficult for the server to win the point than at less important points. Furthermore, the weaker a player, the stronger are these effects. Deviations from iid are small, however, and hence the iid hypothesis will still provide a good approximation in many cases. The results are based on a large panel of matches played at Wimbledon 1992–1995, in total almost 90,000 points. Our panel data model takes into account the binary character of the dependent variable, uses random effects to capture the unobserved part of a player's quality, and includes dynamic explanatory variables.

Multinomial logit random effects models

Abstract: This article presents a general approach for logit random effects modelling of clustered ordinal and nominal responses. We review multinomial logit random effects models in a unified form as multivariate generalized linear mixed models. Maximum likelihood estimation utilizes adaptive Gauss-Hermite quadrature within a quasi-Newton maximization algorithm. For cases in which this is computationally infeasible, we generalize a Monte Carlo EM algorithm. We also generalize a pseudo-likelihood approach that is simpler but provides poorer approximations for the likelihood. Besides the usual normality structure for random effects, we also present a semi-parametric approach treating the random effects in a non-parametric manner. An example comparing reviews of movie critics uses adjacent-categories logit models and a related baseline-category logit model.

Zero‐inflated Poisson regression with random effects to evaluate an occupational injury prevention programme

Abstract: This study presents a zero-inflated Poisson regression model with random effects to evaluate a manual handling injury prevention strategy trialled within the cleaning services department of a 600 bed public hospital between 1992 and 1995. The hospital had been experiencing high annual rates of compensable injuries of which over 60 per cent were attributed to manual handling. The strategy employed Workplace Risk Assessment Teams (WRATS) that utilized a workplace risk identification, assessment and control approach to manual handling injury hazard reduction. The WRATS programme was an intervention trial, covering the 1988-1995 financial years. In the course of compiling injury counts, it was found that the data exhibited an excess of zeros, in the context that the majority of cleaners did not suffer any injuries. This phenomenon is typical of data encountered in the occupational health discipline. We propose a zero-inflated random effects Poisson regression model to analyse such longitudinal count data with extra zeros. The WRATS intervention and other concomitant information on individual cleaners are considered as fixed effects in the model. The results provide statistical evidence showing the value of the WRATS programme. In addition, the methods can be applied to assess the effectiveness of intervention trials on populations at high risk of manual handling injury or indeed of injury from other hazards.

Tutorial in Biostatistics: Evaluating the impact of ‘critical periods’ in longitudinal studies of growth using piecewise mixed effects models

Abstract: Recent developments in modern multivariate methods provide applied researchers with the means to address many important research questions that arise in studies with repeated measures data collected on individuals over time. One such area of applied research is focused on studying change associated with some event or critical period in human development. This tutorial deals with the use of the general linear mixed model for regression analysis of correlated data with a two-piece linear function of time corresponding to the pre- and post-event trends. The model assumes a continuous outcome is linearly related to a set of explanatory variables, but allows for the trend after the event to be different from the trend before it. This task can be accomplished using a piecewise linear random effects model for longitudinal data where the response depends upon time of the event. A detailed example that examines the influence of menarche on changes in body fat accretion will be presented using data from a prospective study of 162 girls measured annually from approximately age 10 until 4 years post menarche.