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Showing papers in "Biometrika in 1999"


Journal ArticleDOI
TL;DR: In this paper, the authors derived an adjusted repeated-imputation degree of freedom, ν m, with the following properties: for fixed m and estimated fraction of missing information, the adjusted degree increases in ν com.
Abstract: An appealing feature of multiple imputation is the simplicity of the rules for combining the multiple complete-data inferences into a final inference, the repeated-imputation inference (Rubin, 1987). This inference is based on a t distribution and is derived from a Bayesian paradigm under the assumption that the complete-data degrees of freedom, ν com , are infinite, but the number of imputations, m, is finite. When ν com is small and there is only a modest proportion of missing data, the calculated repeated-imputation degrees of freedom, ν m , for the t reference distribution can be much larger than ν com , which is clearly inappropriate. Following the Bayesian paradigm, we derive an adjusted degrees of freedom, ν m , with the following three properties: for fixed m and estimated fraction of missing information, ν m monotonically increases in ν com ; ν m is always less than or equal to ν com ; and ν m equals ν m when ν com is infinite. A small simulation study demonstrates the superior frequentist performance when using ν m rather than ν m .

684 citations


Journal ArticleDOI
TL;DR: In this paper, an extended generalised linear model is introduced for joint modelling of the vectors of predictors for the mean and covariance subsuming the joint modelling strategy for mean and variance heterogeneity, Gabriel's antedependence models, Dempster's covariance selection models and the class of graphical models.
Abstract: SUMMARY We provide unconstrained parameterisation for and model a covariance using covariates. The Cholesky decomposition of the inverse of a covariance matrix is used to associate a unique unit lower triangular and a unique diagonal matrix with each covariance matrix. The entries of the lower triangular and the log of the diagonal matrix are unconstrained and have meaning as regression coefficients and prediction variances when regressing a measurement on its predecessors. An extended generalised linear model is introduced for joint modelling of the vectors of predictors for the mean and covariance subsuming the joint modelling strategy for mean and variance heterogeneity, Gabriel's antedependence models, Dempster's covariance selection models and the class of graphical models. The likelihood function and maximum likelihood estimators of the covariance and the mean parameters are studied when the observations are normally distributed. Applications to modelling nonstationary dependence structures and multivariate data are discussed and illustrated using real data. A graphical method, similar to that based on the correlogram in time series, is developed and used to identify parametric models for nonstationary covariances.

597 citations


Journal ArticleDOI
TL;DR: In this article, a spatio-temporal Kalman filter is proposed for space-time prediction with dimension reduction and uses a statistical model that is temporally dynamic and spatially descriptive.
Abstract: SUMMARY Many physical/biological processes involve variability over both space and time. As a result of difficulties caused by large datasets and the modelling of space, time and spatiotemporal interactions, traditional space-time methods are limited. In this paper, we present an approach to space-time prediction that achieves dimension reduction and uses a statistical model that is temporally dynamic and spatially descriptive. That is, it exploits the unidirectional flow of time, in an autoregressive framework, and is spatially 'descriptive' in that the autoregressive process is spatially coloured. With the inclusion of a measurement equation, this formulation naturally leads to the development of a spatio-temporal Kalman filter that achieves dimension reduction in the analysis of large spatio-temporal datasets. Unlike other recent space-time Kalman filters, our model also allows a nondynamic spatial component. The method is applied to a dataset of near-surface winds over the topical Pacific ocean. Spatial predictions with this dataset are improved by considering the additional non-dynamic spatial process. The improvement becomes more pronounced as the signal-to-noise ratio decreases.

428 citations


Journal ArticleDOI
TL;DR: In this article, the combined impact of all-or-none compliance and subsequent missing outcomes can have on the estimation of the intention-to-treat effect of assignment in randomised studies.
Abstract: SUMMARY We study the combined impact that all-or-none compliance and subsequent missing outcomes can have on the estimation of the intention-to-treat effect of assignment in randomised studies. In this setting, a standard analysis, which drops subjects with missing outcomes and ignores compliance information, can be biased for the intention-to-treat effect. To address all-or-none compliance that is followed by missing outcomes, we construct a new estimation procedure for the intention-to-treat effect that maintains good randomisation-based properties under more plausible, nonignorable noncompliance and nonignorable missing-outcome conditions: the 'compound exclusion restriction' on the effect of assignment and the 'latent ignorability' of the missing data mechanism. We present both theoretical results and a simulation study. Moreover, we show how the two key concepts of compound exclusion and latent ignorability are relevant in more complicated settings, such as right censoring of a time-to-event outcome.

392 citations


Journal ArticleDOI
TL;DR: A hyper inverse Wishart prior distribution on the concentration matrix for each given graph is considered, containing only the elements for which the corresponding element of the inverse is nonzero, allowing all computations to be performed locally, at the clique level, which is a clear advantage for the analysis of large and complex datasets.
Abstract: We propose a methodology for Bayesian model determination in decomposable graphical Gaussian models. To achieve this aim we consider a hyper inverse Wishart prior distribution on the concentration matrix for each given graph. To ensure compatibility across models, such prior distributions are obtained by marginalisation from the prior conditional on the complete graph. We explore alternative structures for the hyperparameters of the latter, and their consequences for the model. Model determination is carried out by implementing a reversible jump Markov chain Monte Carlo sampler. In particular, the dimension-changing move we propose involves adding or dropping an edge from the graph. We characterise the set of moves which preserve the decomposability of the graph, giving a fast algorithm for maintaining the junction tree representation of the graph at each sweep. As state variable, we use the incomplete variance-covariance matrix, containing only the elements for which the corresponding element of the inverse is nonzero. This allows all computations to be performed locally, at the clique level, which is a clear advantage for the analysis of large and complex datasets. Finally, the statistical and computational performance of the procedure is illustrated by mean of both artificial and real datasets.

287 citations


Journal ArticleDOI
TL;DR: The authors used reversible jump Markov chain Monte Carlo (MCMCMC) methods to calculate posterior probabilities of hierarchical, graphical or decomposable log-linear models for high-dimensional contingency tables.
Abstract: We use reversible jump Markov chain Monte Carlo methods (Green, 1995) to develop strategies for calculating posterior probabilities of hierarchical, graphical or decomposable log-linear models for high-dimensional contingency tables. Even for tables of moderate size, these sets of models may be very large. The choice of suitable prior distributions for model parameters is also discussed in detail, and two examples are presented. For the first example, a three-way table, the model probabilities calculated using our reversible jump approach are compared with model probabilities calculated exactly or by using an alternative approximation. The second example is a six-way contingency table for which exact methods are infeasible, because of the large number of possible models. We identify the most probable hierarchical, graphical and decomposable models, and compare the results with alternatives approaches.

190 citations


Journal ArticleDOI
TL;DR: In this article, two different approaches to nonparametric regression are considered: simex, simulation-extrapolation, and regression spline based methods, where the error-prone predictor has a distribution of a mixture of normals with an unknown number of components, and uses regression splines.
Abstract: Summary In many regression applications the independent variable is measured with error. When this happens, conventional parametric and nonparametric regression techniques are no longer valid. We consider two diVerent approaches to nonparametric regression. The first uses the simex, simulation-extrapolation, method and makes no assumption about the distribution of the unobserved error-prone predictor. For this approach we derive an asymptotic theory for kernel regression which has some surprising implications. Penalised regression splines are also considered for fixed number of known knots. The second approach assumes that the error-prone predictor has a distribution of a mixture of normals with an unknown number of components, and uses regression splines. Simulations illustrate the results.

186 citations


Journal ArticleDOI
TL;DR: In this article, a nonparametric estimator for the multivariate distribution function of the gap times between successive events when the follow-up time is subject to right censoring is presented.
Abstract: Summary In many follow-up studies, each subject can potentially experience a series of events, which may be repetitions of essentially the same event or may be events of entirely diVerent natures. This paper provides a simple nonparametric estimator for the multivariate distribution function of the gap times between successive events when the follow-up time is subject to right censoring. The estimator is consistent and, upon proper normalisation, converges weakly to a zero-mean Gaussian process with an easily estimated covariance function. Numerical studies demonstrate that both the distribution function estimator and its covariance function estimator perform well for practical sample sizes. An application to a colon cancer study is presented.

186 citations


Journal ArticleDOI
TL;DR: In this paper, the authors consider likelihood-based inference from multivariate regression models with independent Student-t errors and uncover some very intruiging pitfalls of both Bayesian and classical methods on the basis of point observations.
Abstract: We consider likelihood-based inference from multivariate regression models with independent Student-t errors. Some very intruiging pitfalls of both Bayesian and classical methods on the basis of point observations are uncovered. Bayesian inference may be precluded as a consequence of the coarse nature of the data. Global maximization of the likelihood function is a vacuous exercise since the likelihood function is unbounded as we tend to the boundary of the parameter space. A Bayesian analysis on the basis of set observations is proposed and illustrated by several examples.

181 citations


Journal ArticleDOI
TL;DR: The authors derived general expressions for the magnitude of the bias due to errors in the response and showed that, unless both the sensitivity and specificity are very high, ignoring errors in responses will yield highly biased covariate effect estimators.
Abstract: SUMMARY Methods that ignore errors in binary responses yield biased estimators of the associations of covariates with response. This paper derives general expressions for the magnitude of the bias due to errors in the response and shows that, unless both the sensitivity and specificity are very high, ignoring errors in the responses will yield highly biased covariate effect estimators. When the true, error-free response follows a generalised linear model and misclassification probabilities are known and independent of covariate values, responses observed with error also follow such a model with a modified link function. We describe a simple method to obtain consistent estimators of covariate effects and associated errors in this case, and derive an expression for the asymptotic relative efficiency of covariate effect estimators from the correct likelihood for the responses with errors with respect to estimates based on the true, error-free responses. This expression shows that errors in the response can lead to substantial losses of information about covariate effects. Data from a study on infection with human papilloma virus among women and simulation studies motivate this work and illustrate the findings.

180 citations


Journal ArticleDOI
TL;DR: This paper investigates the use of working parameters in the contexts of Markov chain Monte Carlo, in particular in the context of Tanner & Wong's (1987) data augmentation algorithm, via a theoretical study of two working-parameter approaches, the conditional augmentation approach and the marginal augmentation approaches.
Abstract: Data augmentation, sometimes known as the method of auxiliary variables, is a powerful tool for constructing optimisation and simulation algorithms. In the context of optimisation, Meng & van Dyk (1997, 1998) reported several successes of the 'working parameter' approach for constructing efficient data-augmentation schemes for fast and simple EM-type algorithms. This paper investigates the use of working parameters in the context of Markov chain Monte Carlo, in particular in the context of Tanner & Wong's (1987) data augmentation algorithm, via a theoretical study of two working-parameter approaches, the conditional augmentation approach and the marginal augmentation approach. Posterior sampling under the univariate t model is used as a running example, which particularly illustrates how the marginal augmentation approach obtains a fast-mixing positive recurrent Markov chain by first constructing a nonpositive recurrent Markov chain in a larger space.

Journal ArticleDOI
TL;DR: In this paper, the authors consider a Bayesian hierarchical linear mixed model where the fixed effects have a vague prior such as a constant prior and the random effect follows a class of CAR(1) models including those whose joint prior distribution of the regional effects is improper.
Abstract: SUMMARY We examine properties of the conditional autoregressive model, or CAR( 1) model, which is commonly used to represent regional effects in Bayesian analyses of mortality rates. We consider a Bayesian hierarchical linear mixed model where the fixed effects have a vague prior such as a constant prior and the random effect follows a class of CAR(1) models including those whose joint prior distribution of the regional effects is improper. We give sufficient conditions for the existence of the posterior distribution of the fixed and random effects and variance components. We then prove the necessity of the conditions and give a one-way analysis of variance example where the posterior may or may not exist. Finally, we extend the result to the generalised linear mixed model, which includes as a special case the Poisson log-linear model commonly used in disease mapping.

Journal ArticleDOI
TL;DR: In a previous work as discussed by the authors, we presented a biometric authentication system based on the Web of Science Record created on 2006-04-21, modified on 2017-05-12.
Abstract: Reference STAT-ARTICLE-1999-001doi:101093/biomet/864929View record in Web of Science Record created on 2006-04-21, modified on 2017-05-12

Journal ArticleDOI
TL;DR: In this paper, a class of estimating equations for case-cohort sampling, each depending on a different estimator of the population distribution, are derived, which lead naturally to simple estimators that improve on Prentice's pseudolikelihood estimator.
Abstract: Prentice (1986) proposed the case-cohort design and studied a pseudolikelihood estimator of regression parameters in Cox's model. We derive a class of estimating equations for case-cohort sampling, each depending on a different estimator of the population distribution, which lead naturally to simple estimators that improve on Prentice's pseudolikelihood estimator. We also discuss an equivalence between case-control and case-cohort sampling in terms of the estimation of regression parameters in Cox's model.

Journal ArticleDOI
TL;DR: In this article, a simple general formula for approximating the p-value for testing a scalar parameter in the presence of nuisance parameters is described, covering both frequentist and Bayesian contexts and does not require explicit nuisance parameterisation.
Abstract: SUMMARY We describe a simple general formula for approximating the p-value for testing a scalar parameter in the presence of nuisance parameters. The formula covers both frequentist and Bayesian contexts and does not require explicit nuisance parameterisation. Implementation is discussed in terms of computer algebra packages. Examples are given and the relationship to Barndorff-Nielsen's approximation is discussed.

Journal ArticleDOI
TL;DR: In this article, a simple maximum partial likelihood method for deriving the semiparametric maximum likelihood estimator is proposed, and a discussion of assumptions under which the selection bias model is identifiable and uniquely estimable is presented.
Abstract: SUMMARY The following problem is treated: given s possibly selection biased samples from an unknown distribution function, and assuming that the sampling rule weight functions for each of the samples are mathematically specified up to a common unknown finite-dimensional parameter, how can we use the data to estimate the unknown parameters? We propose a simple maximum partial likelihood method for deriving the semiparametric maximum likelihood estimator. A discussion of assumptions under which the selection bias model is identifiable and uniquely estimable is presented. We motivate the need for the methodology by discussing the generalised logistic regression model (Gilbert, Self & Ashby, 1998), a semiparametric selection bias model which is useful for assessing from vaccine trial data how the efficacy of an HIV vaccine varies with characteristics of the exposing virus. We show through simulations and an example that the maximum likelihood estimator in the generalised logistic regression model has satisfactory finite-sample properties.

Journal ArticleDOI
TL;DR: In this article, the authors show that even though the Liang-Zeger approach in many situations yields consistent estimators for the regression parameters, these estimators are usually inefficient as compared to the regression estimators obtained by using the independence estimating equations approach.
Abstract: SUMMARY Liang & Zeger (1986) introduced a generalised estimating equations approach based on a 'working' correlation matrix to obtain consistent and efficient estimators of regression parameters in the class of generalised linear models for repeated measures data. As demonstrated by Crowder (1995), because of the uncertainty of definition of the working correlation matrix, the Liang-Zeger approach may in some cases lead to a complete breakdown of the estimation of the regression parameters. In this paper we show that, even though the Liang-Zeger approach in many situations yields consistent estimators for the regression parameters, these estimators are usually inefficient as compared to the regression estimators obtained by using the independence estimating equations approach.

Journal ArticleDOI
TL;DR: In this paper, a partially linear single-index model is proposed to explore the relation between the response y and the stochastic explanatory vector variable X beyond the linear approximation, which is a well-known approach in multidimensional cases.
Abstract: Aiming to explore the relation between the response y and the stochastic explanatory vector variable X beyond the linear approximation, we consider the single-index model, which is a well-known approach in multidimensional cases. Specifically, we extend the partially linear single-index model to take the form y = β 0 T X + o(0 0 T X) + e, where e is a random variable with Ee = 0 and var(e) = σ 2 , unknown, β 0 and θ o are unknown parametric vectors and o(.) is an unknown real function. The model is also applicable to nonlinear time series analysis. In this paper, we propose a procedure to estimate the model and prove some related asymptotic results. Both simulated and real data are used to illustrate the results.

Journal ArticleDOI
TL;DR: In this paper, a non-stationary state space model for multivariate longitudinal count data driven by a latent gamma Markov process is proposed, where the Poisson counts are assumed to be conditionally independent given the latent process.
Abstract: SUMMARY We propose a nonstationary state space model for multivariate longitudinal count data driven by a latent gamma Markov process. The Poisson counts are assumed to be conditionally independent given the latent process, both over time and across categories. We consider a regression model where time-varying covariates may enter via either the Poisson model or the latent gamma process. Estimation is based on the Kalman smoother, and we consider analysis of residuals from both the Poisson model and the latent process. A reanalysis of Zeger's (1988) polio data shows that the choice between a stationary and nonstationary model is crucial for the correct assessment of the evidence of a long-term decrease in the rate of U.S. polio infection.

Journal ArticleDOI
TL;DR: In this paper, a test for missing completely at random is proposed to help decide whether or not we should adjust estimating equations to correct the possible bias introduced by a missing-data mechanism that is not missing at random.
Abstract: We consider inference from generalised estimating equations when data are incomplete. A test for missing completely at random is proposed to help decide whether or not we should adjust estimating equations to correct the possible bias introduced by a missing-data mechanism that is not missing completely at random. Likelihood ratio tests have been introduced to test the missing completely at random hypothesis (Fuchs, 1982; Little, 1988). For the estimating equation setting, following the basic idea of Little (1988), we propose a Wald-type test based on an information decomposition and recombination procedure, which also provides an alternative method for estimating parameters. One application of the test is to assess the adequacy of the marginal generalised estimating equation for longitudinal data with missing values. Simulations are done to evaluate its performance.

Journal ArticleDOI
TL;DR: In this article, a truncation-adaptable criterion is proposed, and the uniformly-minimum-variance estimator among all truncationadaptable unbiased estimators is found.
Abstract: It is shown that, in a group sequential test about the drift 0 of a Brownian motion X(t) stopped at time T, the sufficient statistic (T,X(T)) is not complete for 0. There exist infinitely many unbiased estimators of 0 and none has uniformly minimum variance. A truncation-adaptable criterion is proposed, and the uniformly-minimum-variance estimator among all truncation-adaptable unbiased estimators is found. This estimator is identical to estimators of Ferebee (1983) and Emerson & Fleming (1990).

Journal ArticleDOI
TL;DR: In this paper, a data-perturbation method for reducing bias of a wide variety of density estimators, in univariate, multivariate, spatial and spherical data settings, is introduced.
Abstract: We introduce a data-perturbation method for reducing bias of a wide variety of density estimators, in univariate, multivariate, spatial and spherical data settings. The method involves 'sharpening' the data by making them slightly more clustered than before, and then computing the estimator in the usual way, but from the sharpened data rather than the original data. The transformation depends in a simple, explicit way on the smoothing parameter employed for the density estimator, which may be based on classical kernel methods, orthogonal series, histosplines, singular integrals or other linear or approximately-linear methods. Bias is reduced by an order of magnitude, at the expense of a constant-factor increase in variance.

Journal ArticleDOI
TL;DR: In this paper, the authors combine the approaches of marked point processes and deformable template models to handle scenes containing variable numbers of objects of different types, using reversible jump Markov chain Monte Carlo methods for inference.
Abstract: This paper addresses the task of locating and identifying an unknown number of objects of different types in an image. Baddeley & Van Lieshout (1993) advocate marked point processes as object priors, whereas Grenander & Miller (1994) use deformable template models. In this paper elements of both approaches are combined to handle scenes containing variable numbers of objects of different types, using reversible jump Markov chain Monte Carlo methods for inference (Green, 1995). The naive application of these methods here leads to slow mixing and we adapt the model and algorithm in tandem in proposing three strategies to deal with this. The first two expand the model space by introducing an additional 'unknown' object type and the idea of a variable resolution template. The third strategy, utilising the first two, augments the algorithm with classes of updates which provide intuitive transitions between realisations containing different numbers of cells by splitting or merging nearby objects.

Journal ArticleDOI
TL;DR: In this article, the authors developed both graphical and numerical techniques for checking the adequacy of the gamma frailty model for multivariate failure time data, based on the posterior expectation of the frailty given the observable data.
Abstract: SUMMARY Multivariate failure time data arise when the sample consists of clusters and each cluster contains several dependent failure times. The semiparametric gamma frailty model (Vaupel, Manton & Stallard, 1979; Clayton, 1978; Oakes, 1982) for multivariate failure times characterises the intracluster dependence by the gamma frailty distribution while allowing the marginal distributions to be unspecified. This paper develops both graphical and numerical techniques for checking the adequacy of this model. The proposed techniques are based on the posterior expectation of the frailty given the observable data. Two examples from genetics are provided.

Journal ArticleDOI
TL;DR: In this paper, a modified balanced repeated replication method using gentler perturbation of weights is proposed to avoid extreme replicate estimates, which is extended to the case of imputation for item nonresponse.
Abstract: SUMMARY Balanced repeated replication, commonly used to estimate the variances of nonlinear estimators from stratified sampling designs, can run into problems in estimating a ratio of small domain totals or in the case of poststratification or unit nonresponse adjustment involving ratio weighting within cells if some cell sizes are small. This problem is mainly caused by a sharp perturbation of the weights to construct replicate estimates. To avoid extreme replicate estimates, Robert Fay proposed a modified balanced repeated replication method using gentler perturbation of weights. Theoretical properties of the modified method are studied here. The method is extended to the case of imputation for item nonresponse. Both smooth and nonsmooth estimators are studied.

Journal ArticleDOI
TL;DR: In this paper, the authors consider the choice of explanatory variables in multivariate linear regression and employ a nonconjugate proper prior distribution for the parameters of the regression model, extending the standard normal-inverse Wishart by adding a component of error which is unexplainable by any number of predictor variables, thus avoiding the determinism identified by Dawid.
Abstract: We consider the choice of explanatory variables in multivariate linear regression. Our approach balances prediction accuracy against costs attached to variables:in a multivariate version of a decision theory approach pioneered by Lindley (1968). We also employ a non-conjugate proper prior distribution for the parameters of the regression model, extending the standard normal-inverse Wishart by adding a component of error which is unexplainable by any number of predictor variables, thus avoiding the determinism identified by Dawid (1988). Simulated annealing and fast updating algorithms are used to search for good subsets when there are very many regressors. The technique is illustrated on a near infrared spectroscopy example involving 39 observations and 300 explanatory variables. This demonstrates the effectiveness of multivariate regression as opposed to separate univariate regressions. It also emphasises that within a Bayesian framework more variables than observations can be utilised.

Journal ArticleDOI
TL;DR: In this paper, a recursive approximation based on one-step posterior predictive distributions is proposed to obtain solutions of the self-consistency equations from a non-Bayesian perspective.
Abstract: SUMMARY The mixture of Dirichlet processes posterior that arises in nonparametric Bayesian analysis has been analysed most effectively using Markov chain Monte Carlo. As a computationally simple alternative, we introduce a recursive approximation based on one-step posterior predictive distributions. Asymptotic calculations provide theoretical support for this approximation, and we investigate its actual behaviour in several numerical examples. From a non-Bayesian perspective, this new recursion may be used to obtain solutions of the self-consistency equations.

Journal ArticleDOI
TL;DR: In this article, an information criterion is proposed for detecting the configuration of the true parameters with the simple order restriction, which can also be applied for detecting a changepoint in a sequence of parameters with a monotone trend.
Abstract: Suppose we have independent random samples from each of k populations specified by scalar-valued, unknown parameters θ 1 ,...,θ k satisfying the simple order restriction θ 1 ≤...≤ θ k . Our concern is to seek distinct parameters among θ 1 θ k based on the data. To find a configuration of distinct parameters among the 0's, one may consider employing Akaike's information criterion (Akaike, 1973). However, the criterion is not appropriate for the order-restricted maximum likelihood estimator of θ = (θ 1 ,..., θ k ), since the normality or the asymptotic normality of the estimator is not valid. In this paper an information criterion is proposed for detecting the configuration of the true parameters with the simple order restriction. This method may also be applied for detecting a changepoint in a sequence of parameters with a monotone trend. A Monte Carlo study indicates that our new criterion is effective, compared to Akaike's information criterion, for detecting the configuration of normal means satisfying the simple order restriction.

Journal ArticleDOI
TL;DR: In this paper, the authors consider parameter estimation for certain random set models for image data and discuss one method based on likelihoods for small subsets of the data, which leads to a weighted version of the basic approach.
Abstract: SUMMARY We consider parameter estimation for certain random set models for image data. For the spatial models considered here, a full likelihood-based approach to this problem is often difficult, since the likelihood generally cannot be computed for images of typical size. This has motivated the consideration of various less computationally demanding parameter estimation techniques. We discuss one method based on likelihoods for small subsets of the data. Consideration of the basic technique within the framework of the theory of estimating functions leads to a weighted version of the basic approach. Results of a simulation study are reported for some variants of the Boolean model and excursion sets of random fields. The methods are illustrated for some data on the spatial incidence of heather.

Journal ArticleDOI
TL;DR: In this article, a semiparametric additive time-varying regression model for longitudinal data recorded at irregular intervals is proposed, which allows the influence of each covariate to vary separately with time.
Abstract: In previous work we have studied a nonparametric additive time-varying regression model for longitudinal data recorded at irregular intervals. The model allows the influence of each covariate to vary separately with time. For small datasets, however, only a limited number of covariates may be handled in this way. In this paper, we introduce a semiparametric regression model for longitudinal data. The influence of some of the covariates varies nonparametrically with time while the effect of the remaining covariates are constant. No smoothing is necessary in the estimation of the parametric terms of the model. Asymptotics are derived using martingale techniques for the cumulative regression functions, which are much easier to estimate and study than the regression functions themselves. The approach is applied to longitudinal data from the Copenhagen Study Group for Liver Diseases (Schlichting et al., 1983).