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244
Nonlinear Models for Repeated Measurement Data
, 1995
"... Nonlinear mixed effects models for data in the form of continuous, repeated measurements on each of a number of individuals, also known as hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individualspecific characteristics. This framework first enjoyed wid ..."
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Cited by 144 (4 self)
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Nonlinear mixed effects models for data in the form of continuous, repeated measurements on each of a number of individuals, also known as hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individualspecific characteristics. This framework first enjoyed widespread attention within the statistical research community in the late 1980s, and the 1990s saw vigorous development of new methodological and computational techniques for these models, the emergence of generalpurpose software, and broad application of the models in numerous substantive fields. This article presents an overview of the formulation, interpretation, and implementation of nonlinear mixed effects models and surveys recent advances and applications.
Bayesian measures of model complexity and fit
 Journal of the Royal Statistical Society, Series B
, 2002
"... [Read before The Royal Statistical Society at a meeting organized by the Research ..."
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Cited by 132 (2 self)
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[Read before The Royal Statistical Society at a meeting organized by the Research
Modelbased Geostatistics
 Applied Statistics
, 1998
"... Conventional geostatistical methodology solves the problem of predicting the realised value of a linear functional of a Gaussian spatial stochastic process, S(x), based on observations Y i = S(x i ) + Z i at sampling locations x i , where the Z i are mutually independent, zeromean Gaussian random v ..."
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Cited by 96 (4 self)
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Conventional geostatistical methodology solves the problem of predicting the realised value of a linear functional of a Gaussian spatial stochastic process, S(x), based on observations Y i = S(x i ) + Z i at sampling locations x i , where the Z i are mutually independent, zeromean Gaussian random variables. We describe two spatial applications for which Gaussian distributional assumptions are clearly inappropriate. The first concerns the assessment of residual contamination from nuclear weapons testing on a South Pacific island, in which the sampling method generates spatially indexed Poisson counts conditional on an unobserved spatially varying intensity of radioactivity; we conclude that a coventional geostatistical analysis oversmooths the data and underestimates the spatial extremes of the intensity. The second application provides a description of spatial variation in the risk of campylobacter infections relative to other enteric infections in part of North Lancashire and South C...
Implementing approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations: A manual for the inlaprogram
, 2008
"... Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemp ..."
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Cited by 79 (16 self)
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Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalised) linear models, (generalised) additive models, smoothingspline models, statespace models, semiparametric regression, spatial and spatiotemporal models, logGaussian Coxprocesses, geostatistical and geoadditive models. In this paper we consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with nonGaussian response variables. The posterior marginals are not available in closed form due to the nonGaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, both in terms of convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations
Bayesian inference for generalized additive mixed models based on markov random field priors
 C
, 2001
"... Summary. Most regression problems in practice require ¯exible 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 lo ..."
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Cited by 63 (19 self)
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Summary. Most regression problems in practice require ¯exible 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 uni®ed approach for Bayesian inference via Markov chain Monte Carlo simulation in generalized additive and semiparametric mixed models. Different types of covariates, such as the usual covariates with ®xed 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 Markov random ®eld priors with different forms and degrees of smoothness. We applied the approach in several casestudies and consulting cases, showing that the methods are also computationally feasible in problems with many covariates and large data sets. In this paper, we choose two typical applications.
Categorical Data Analysis: Away from ANOVAs (transformation or not) and towards Logit Mixed Models
"... This paper identifies several serious problems with the widespread use of ANOVAs for the analysis of categorical outcome variables such as forcedchoice variables, questionanswer accuracy, choice in production (e.g. in syntactic priming research), et cetera. I show that even after applying the arc ..."
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Cited by 62 (6 self)
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This paper identifies several serious problems with the widespread use of ANOVAs for the analysis of categorical outcome variables such as forcedchoice variables, questionanswer accuracy, choice in production (e.g. in syntactic priming research), et cetera. I show that even after applying the arcsinesquareroot transformation to proportional data, ANOVA can yield spurious results. I discuss conceptual issues underlying these problems and alternatives provided by modern statistics. Specifically, I introduce ordinary logit models (i.e. logistic regression), which are wellsuited to analyze categorical data and offer many advantages over ANOVA. Unfortunately, ordinary logit models do not include random effect modeling. To address this issue, I describe mixed logit models (Generalized Linear Mixed Models for binomially distributed outcomes, Breslow & Clayton, 1993), which combine the advantages of ordinary logit models with the ability to account for random subject and item effects in one step of analysis. Throughout the paper, I use a psycholinguistic data set to compare the different statistical methods.
Hierarchical SpatioTemporal Mapping of Disease Rates
 Journal of the American Statistical Association
, 1996
"... Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with sociodemographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or oth ..."
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Cited by 51 (7 self)
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Maps of regional morbidity and mortality rates are useful tools in determining spatial patterns of disease. Combined with sociodemographic census information, they also permit assessment of environmental justice, i.e., whether certain subgroups suffer disproportionately from certain diseases or other adverse effects of harmful environmental exposures. Bayes and empirical Bayes methods have proven useful in smoothing crude maps of disease risk, eliminating the instability of estimates in lowpopulation areas while maintaining geographic resolution. In this paper we extend existing hierarchical spatial models to account for temporal effects and spatiotemporal interactions. Fitting the resulting highlyparametrized models requires careful implementation of Markov chain Monte Carlo (MCMC) methods, as well as novel techniques for model evaluation and selection. We illustrate our approach using a dataset of countyspecific lung cancer rates in the state of Ohio during the period 19681988...
Inference in Generalized Additive Mixed Models Using Smoothing Splines
, 1999
"... this paper, we propose generalized additive mixed models (GAMMs), which are an additive extension of generalized linear mixed models in the spirit of Hastie and Tibshirani (1990). This new class of models uses additive nonparametric functions to model covariate effects while accounting for overdispe ..."
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Cited by 45 (4 self)
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this paper, we propose generalized additive mixed models (GAMMs), which are an additive extension of generalized linear mixed models in the spirit of Hastie and Tibshirani (1990). This new class of models uses additive nonparametric functions to model covariate effects while accounting for overdispersion and correlation by adding random effects to the additive predictor. GAMMs encompass nested and crossed designs and are applicable to clustered, hierarchical and spatial data. We estimate the nonparametric functions using smoothing splines, and jointly estimate the smoothing parameters and the variance components using marginal quasilikelihood. This marginal quasilikelihood approach is an extension of the restricted maximum likelihood approach used by Wahba (1985) and Kohn, et al. (1991) in the classical nonparametric regression model (Kohn, et al. 1991, eq 2.1), and by Zhang, et al. (1998) in Gaussian nonparametric mixed models, where they treated the smoothing parameter as an extra variance component. In view of numerical integration often required by maximizing the objective functions, double penalized quasilikelihood (DPQL) is proposed to make approximate inference. Frequentist and Bayesian inferences are compared. A key feature of the proposed method is that it allows us to make systematic inference on all model components of GAMMs within a unified parametric mixed model framework. Specifically, our estimation of the nonparametric functions, the smoothing parameters and the variance components in GAMMs can proceed by fitting a working GLMM using existing statistical software, which iteratively fits a linear mixed model to a modified dependent variable. When the data are sparse (e.g., binary), the DPQL estimators of the variance components are found to be subject t...
Conditional prior proposals in dynamic models
 SCANDINAVIAN JOURNAL OF STATISTICS
, 1999
"... Dynamic models extend state space models to nonnormal observations. This paper suggests a specific hybrid MetropolisHastings algorithm as a simple device for Bayesian inference via Markov chain Monte Carlo in dynamic models. Hastings proposals from the (conditional) prior distribution of the unk ..."
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Cited by 33 (3 self)
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Dynamic models extend state space models to nonnormal observations. This paper suggests a specific hybrid MetropolisHastings algorithm as a simple device for Bayesian inference via Markov chain Monte Carlo in dynamic models. Hastings proposals from the (conditional) prior distribution of the unknown, timevarying parameters are used to update the corresponding full conditional distributions. It is shown through simulated examples that the methodology has optimal performance in situations where the prior is relatively strong compared to the likelihood. Typical examples include smoothing priors for categorical data. A specific blocking strategy is proposed to ensure good mixing and convergence properties of the simulated Markov chain. It is also shown that the methodology is easily extended to robust transition models using mixtures of normals. The applicability is illustrated with an analysis of a binomial and a binary time series, known in the literature.
Geoadditive Models
, 2000
"... this paper is a recent article on modelbased geostatistics by Diggle, Tawn and Moyeed (1998) where pure kriging (i.e. no covariates) is the focus. Our paper inherits some of its aspects: modelbased and with mixed model connections. In particular the comment by Bowman (1998) in the ensuing discussi ..."
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Cited by 33 (1 self)
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this paper is a recent article on modelbased geostatistics by Diggle, Tawn and Moyeed (1998) where pure kriging (i.e. no covariates) is the focus. Our paper inherits some of its aspects: modelbased and with mixed model connections. In particular the comment by Bowman (1998) in the ensuing discussion suggested that additive modelling would be a worthwhile extension. This paper essentially follows this suggestion. However, this paper is not the first to combine the notions of geostatistics and additive modelling. References known to us are Kelsall and Diggle (1998), Durban Reguera (1998) and Durban, Hackett, Currie and Newton (2000). Nevertheless, we believe that our approach has a number of attractive features (see (1)(4) above), not all shared by these references. Section 2 describes the motivating application and data in detail. Section 3 shows how one can express additive models as a mixed model, while Section 4 does the same for kriging and merges the two into the geoadditive model. Issues concerning the amount of smoothing are discussed in Section 5 and inferential aspects are treated in Section 6. Our analysis of the Upper Cape Cod reproductive data is presented in Section 7. Section 8 discusses extension to the generalised context.We close the paper with some disussion in Section 9. 2 Description of the application and data