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Showing papers on "Random effects model published in 1992"


Book
01 Jan 1992
TL;DR: In this paper, the authors present an AMMI data set and compare AMMI with other statistical models, such as ANOVA, PCA, SHMM, and SHMM Shifted Multiplicative Models.
Abstract: Preface. 1. Introduction. The Yield-Trial Experiment. Research Purposes (Accurate Estimates. Reliable Selections. Insightful Models. Efficient Designs). A Brief History. Conclusions. Summary. 2. Basic Statistical Concepts. Four Opportunities for Accuracy. Mathematical Notation. Populations and Samples. Treatment Design and Experimental Design. Pattern, Noise and Error. Prediction and Postdiction (Definitions. Statistical Assessment. Model Criteria and Choice. Fixed and Random Effects. Levels of Prediction. Agricultural Progress). Interaction. A Dubious Dogma. Summary. 3. AMMI and Related Models. AMMI Data. Treatment Means Model. ANOVA Additive Model. Linear Regression Model. PCA Multiplicative Model. AMMI Additive and Multiplicative Model. SHMM Shifted Multiplicative Model. Other Statistical Models. Model Comparisons. Summary. 4. Estimation. Assigning Degrees of Freedom (Structural df. Pure Noise df. Pattern Plus Noise df. Choosing an Accounting). Postdictive Accuracy. Predictive Accuracy. Imputing Missing Data (Interaction Absent: ANOVA. Interaction Present: EM-AMMI). Inspecting AMMI Residuals. Empirical Evidence of Accuracy. Selecting the Best AMMI Model. Summary. 5. Selection. Order Statistics. A Soybean Example. Selection Systems (Simulation of Selection Strategies. The Numbers Game and Noise Game. The Interaction Game. Practical Selection Systems). Corn and Wheat Examples. Summary. 6. Modeling. Biplots for Model Diagnosis. Modeling Interactions. Mapping Genotypes. Understanding Locations. Defining Mega-environments. Causal Explanations. Applications (Physical Sciences. Engineering. Social Sciences. Medicine and Pharmacology. Business). Summary. 7. Efficient Experiments. Research Costs and Benefits. Partitioning Research Resources (Combining Information. Analysis of Experimental Designs. The Selection Triathlon). Statistical Expectations. Open Questions (Optimal Selection Strategies. Heritability. Stability and Dependability. Value-Added Seed). Summary. 8. Conclusions. References. Index.

641 citations



Journal ArticleDOI
TL;DR: In this paper, the authors considered a survival experiment where individuals within a certain subset of the population share a common, unobservable, random frailty and used an EM algorithm based on profile likelihood construction to estimate the fixed and random effects.
Abstract: Consider a survival experiment where individuals within a certain subset of the population share a common, unobservable, random frailty. Such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households. Suppose that if the frailty, omega, is known, the Cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate. Assuming tht the random frailties follow a gamma distribution, estimates of the fixed and random effects are obtained by using an EM algorithm based on a profile likelihood construction. The method developed is applied to the Framingham Heart Study to examine the risks of smoking and cholesterol levels, adjusting for potential random effects.

430 citations


Journal ArticleDOI
TL;DR: In this paper, a model of the selection process involving a step function relating the p-value to the probability of selection is introduced in the context of a random effects model for meta-analysis.
Abstract: Publication selection effects arise in meta-analysis when the effect magnitude estimates are observed in (available from) only a subset of the studies that were actually conducted and the probability that an estimate is observed is related to the size of that estimate. Such selection effects can lead to substantial bias in estimates of effect magnitude. Research on the selection process suggests that much of the selection occurs because researchers, reviewers and editors view the results of studies as more conclusive when they are more highly statistically significant. This suggests a model of the selection process that depends on effect magnitude via the p-value or significance level. A model of the selection process involving a step function relating the p-value to the probability of selection is introduced in the context of a random effects model for meta-analysis. The model permits estimation of a weight function representing selection along the mean and variance of effects. Some ideas for graphical procedures and a test for publication selection are also introduced. The method is then applied to a meta-analysis of test validity studies.

304 citations


Journal ArticleDOI
TL;DR: In this article, a log-normal survival model was proposed to estimate the probability of early termination in longitudinal studies. But the model is not suitable for the case where the data are missing in a non-ignorably way.
Abstract: This paper describes the problem of informative censoring in longitudinal studies where the primary outcome is rate of change in a continuous variable. Standard approaches based on the linear random effects model are valid only when the data are missing in a non-ignorable fashion. Informative censoring, which is a special type of non-ignorably missing data, occurs when the probability of early termination is related to an individual subject's true rate of change. When present, informative censoring causes bias in standard likelihood-based analyses, as well as in weighted averages of individual least-squares slopes. This paper reviews several methods proposed by others for analysis of informatively censored longitudinal data, and outlines a new approach based on a log-normal survival model. Maximum likelihood estimates may be obtained via the EM algorithm. Advantages of this approach are that it allows general unbalanced data caused by staggered entry and unequally-timed visits, it utilizes all available data, including data from patients with only a single measurement, and it provides a unified method for estimating all model parameters. Issues related to study design when informative censoring may occur are also discussed.

294 citations


Journal ArticleDOI
TL;DR: In this article, the Gibbs sampler is used to compute the Gibbs sampling and the Gibbs sample is compared with the Kaplan-Meier and Berliner-Hill estimators for left-censored data.
Abstract: Life Testing and Reliability Estimation Under Asymmetric Loss.- Bayesian Computations In Survival Models Via the Gibbs Sampler.- Bayesian Nonparametric Survival Analysis: A Comparison of the Kaplan-Meier and Berliner-Hill Estimators.- Modelling Time-Varying Hazards and Covariate Effects.- Analysis of Trials with Treatment - Individual Interactions.- Assessment of Dependence In the Life Times of Twins.- Estimating Random Effects In the Framingham Heart Study.- Survival Analysis in Genetics: Danish Twin Data Applied To a Gerontological Question.- Some Issues in the Collection and Analysis of Field Reliability Data.- Bayesian Modelling For Fatigue Crack Curves.- Statistical Analysis Of a Weibull Process With Left- Censored Data.- Kernel Density Estimation from Record-Breaking Data.- Semiparametric Estimation Of Parametric Hazard Rates.- Cox-Type Regression Analysis for Large Numbers of Small Groups of Correlated Failure Time Observations.- Information Bounds For the Additive and Multiplicative Intensity Models.- Survival Analysis For Left Censored Data.- Regression Analysis for Discrete and Continuous Truncated and Eventually Censored Data.- Independent Delayed Entry.- Periodic Inspections in a Longitudinal Study: Viewing Occult Tumors Through a Filter.- Survival Under Multiple Time Scales in Dynamic Environments.- Nonparametric Identifiability of Marginal Survival Distributions in the Presence of Dependent Competing Risks and a Prognostic Covariate.- Frailty Models For Multiple Event Times.- A Nonparametric Approach To Dependence For Bivariate Censored Data.- Marginal and Conditional Models for the Analysis of Multivariate Failure Time Data.- Multivariate Failure Time Analysis: Discussion of Papes by Oakes Pons, Kaddour and De Turckheim and Prentice and Cai.- Survivor Functions as Dependent Variables In Demographic Analysis.- Relation Between The Rate Of Return To Tenure, Earnings Growth and Job Switching.- List of Contributors.

272 citations


Journal ArticleDOI
TL;DR: This study examines the relative strengths of two different methodologies - stochastic frontier models (SF) and data envelopment analysis (DEA) in estimating firm-specific technical efficiency and indicates that for simple underlying technologies the relative performance of the stochastics frontier models vis-a-vis DEA relies on the choice of functional forms.

268 citations


Book ChapterDOI
TL;DR: The aim of this article is first to review how the standard econometric methods for panel data may be adapted to the problem of estimating frontier models and (in)efficiencies, and to clarify the difference between the fixed and random effect model.
Abstract: The aim of this article is first to review how the standard econometric methods for panel data may be adapted to the problem of estimating frontier models and (in)efficiencies. The aim is to clarify the difference between the fixed and random effect model and to stress the advantages of the latter. Then a semi-parametric method is proposed (using a non-parametric method as a first step), the message being that in order to estimate frontier models and (in)efficiences with panel data, it is an appealing method. Since analytic sampling distributions of efficiencies are not available, a bootstrap method is presented in this framework. This provides a tool allowing to assess the statistical significance of the obtained estimators. All the methods are illustrated in the problem of estimating the inefficiencies of 19 railway companies observed over a period of 14 years (1970–1983).

260 citations


Journal ArticleDOI
TL;DR: In this article, the authors use the concept of a latent variable to derive the joint distribution of a continuous and a discrete outcome, and then extend the model to allow for clustered data.
Abstract: We use the concept of a latent variable to derive the joint distribution of a continuous and a discrete outcome, and then extend the model to allow for clustered data. The model can be parameterized in a way that allows one to write the joint distribution as a product of a standard random effects model for the continuous variable and a correlated probit model for the discrete variable. This factorization suggests a convenient approach to parameter estimation using quasi-likelihood techniques. Our approach is motivated by the analysis of developmental toxicity experiments for which a number of discrete and continuous outcomes are measured on offspring clustered within litters. Fetal weight and malformation data illustrate the results.

244 citations


Journal ArticleDOI
TL;DR: A random-effects model for the analysis of clustered survival times, such as those reflecting the mortality experience of children in the same family, is discussed, and two specifications of the model are fit to child survival data from Guatemala.
Abstract: This article discusses a random-effects model for the analysis of clustered survival times, such as those reflecting the mortality experience of children in the same family. We describe parametric and nonparametric approaches to the specification of the random effect and show how the model may be fitted using an accelerated EM algorithm. We then fit two specifications of the model to child survival data from Guatemala. These data had been analyzed before using standard hazard models that ignore cluster effects.

182 citations


Journal ArticleDOI
TL;DR: In this article, the problem of predicting a linear combination of the fixed and random effects of a mixed-effects linear model is considered, where the best linear-unbiased predictor depends on parameters which generally are unknown.
Abstract: The problem considered is that of predicting a linear combination of the fixed and random effects of a mixed-effects linear model. More generally, the problem considered is that of predicting an unobservable random variable from a set of observable random variables. The best linear-unbiased predictor depends on parameters which generally are unknown. Various exact or approximate expressions are given for the mean squared error (MSE) of the predictor obtained by replacing the unknown parameters with estimates. Several estimators of the MSE are investigated.

Journal ArticleDOI
TL;DR: This paper develops and implements a fully Bayesian approach to meta-analysis, in which uncertainty about effects in distinct but comparable studies is represented by an exchangeable prior distribution, along with a parametrization that allows a unified approach to deal easily with both clinical trial and case-control study data.
Abstract: This paper develops and implements a fully Bayesian approach to meta-analysis, in which uncertainty about effects in distinct but comparable studies is represented by an exchangeable prior distribution. Specifically, hierarchical normal models are used, along with a parametrization that allows a unified approach to deal easily with both clinical trial and case-control study data. Monte Carlo methods are used to obtain posterior distributions for parameters of interest, integrating out the unknown parameters of the exchangeable prior or ‘random effects’ distribution. The approach is illustrated with two examples, the first involving a data set on the effect of beta-blockers after myocardial infarction, and the second based on a classic data set comprising 14 case-control studies on the effects of smoking on lung cancer. In both examples, rather different conclusions from those previously published are obtained. In particular, it is claimed that widely used methods for meta-analysis, which involve complete pooling of ‘O-E’ values, lead to understatement of uncertainty in the estimation of overall or typical effect size.

Journal ArticleDOI
TL;DR: In this paper, the authors considered a simultaneous equations model with panel data and unobservable individual effects in each structural equation, and provided efficient GMM estimators along the lines of two-stage and three-stage least squares.

Journal ArticleDOI
TL;DR: In this paper, the results of a series of studies examining intercorrelations among a set of p + 1 variables are presented, and a test of whether a common population correlation matrix underlies the set of empirical results is given.
Abstract: This article outlines analyses for the results of a series of studies examining intercorrelations among a set of p + 1 variables. A test of whether a common population correlation matrix underlies the set of empirical results is given. Methods are presented for estimating either a pooled or average correlation matrix, depending on whether the studies appear to arise from a single population. A random effects model provides the basis for estimation and testing when the series of correlation matrices may not share a common population matrix. Finally, I show how a pooled correlation matrix (or average matrix) can be used to estimate the standardized coefficients of a regression model for variables measured in the series of studies. Data from a synthesis of relationships among mathematical, verbal, and spatial ability measures illustrate the procedures.

Journal ArticleDOI
TL;DR: The seminonparametric (SNP) method, popular in the econometrics literature, is proposed for use in population pharmacokinetic analysis and a graphical modelbuilding strategy based on the SNP method is described.
Abstract: The seminonparametric (SNP) method, popular in the econometrics literature, is proposed for use in population pharmacokinetic analysis. For data that can be described by the nonlinear mixed effects model, the method produces smooth nonparametric estimates of the entire random effects density and simultaneous estimates of fixed effects by maximum likelihood. A graphical modelbuilding strategy based on the SNP method is described. The methods are illustrated by a population analysis of plasma levels in 136 patients undergoing oral quinidine therapy.

Journal ArticleDOI
TL;DR: It is found that estimated fixed effects are compatible for all approaches, but that appropriate standard errors for the NPML require adjusting the likelihood-based standard errors.
Abstract: We discuss the performance of non-parametric maximum likelihood (NPML) estimators for the distribution of a univariate random effect in the analysis of longitudinal data. For continuous data, we analyse generated and real data sets, and compare the NPML method to those that assume a Gaussian random effects distribution and to ordinary least squares. For binary outcomes we use generated data to study the moderate and large-sample performance of the NPML compared with a method based on a Gaussian random effect distribution in logistic regression. We find that estimated fixed effects are compatible for all approaches, but that appropriate standard errors for the NPML require adjusting the likelihood-based standard errors. We conclude that the non-parametric approach provides an attractive alternative to Gaussian-based methods, though additional evaluations are necessary before it can be recommended for general use.

Book ChapterDOI
01 Jan 1992
TL;DR: A survey of models for multiple event times that are reminiscent of the classical results of Greenwood and Yule (1920) on “accident — proneness”, and methods of inference about the frailty distribution and regression parameters.
Abstract: In some clinical, epidemiologic and animal studies multiple events, possibly of different types, may occur to the same experimental unit at different times. Examples of such data include times to tumor detection, times from remission to relapse into an acute disease phase, and times to discontinuation of an experimental medication. Methods for the statistical analysis of such data need to account for heterogeneity between subjects. This can be achieved by incorporation of additional unobserved random effects into standard survival models. We concentrate on models including frailties — unobserved random proportionality factors applied to the time-dependent intensity function. In this paper we survey some such models, exhibit connections with extensions of the standard Andersen-Gill (1982) model for multiple event times that are reminiscent of the classical results of Greenwood and Yule (1920) on “accident — proneness”, and discuss methods of inference about the frailty distribution and regression parameters. The methods are illustrated by application to some animal tumor data of Gail, Santner and Brown (1980) and to data from a recently completed large multicenter clinical trial.

Journal ArticleDOI
TL;DR: In this paper, the random effect in the selectivity equation is specified as a function of the means of time varying variables, which helps to alleviate the bias caused by the correlation between the random effects and the regressors.

Journal Article
TL;DR: The authors showed that a uniformly distributed n x n orthogonal matrix has any n113 x n 1/3 block well approximated (in total variation) by independent normal random variables.
Abstract: Let Xl,-.. , Xk be a sequence of random vectors. We give symmetry conditions on the joint distribution which imply that it is well approximated by a mixture of normal distributions. Examples include linear regression models, fixed and random effect analysis of variance models, and models with structured covariance matrices. The main technical tool shows that a uniformly distributed n x n orthogonal matrix has any n113 x n1/3 block well approximated (in total variation) by independent normal random variables.

Journal ArticleDOI
TL;DR: In this paper, it is shown that it is possible to estimate the distributions of the random coefficients consistently and that this is often possible and provide practical representative estimators of these distributions.
Abstract: Random coefficient regression models are important in representing linear models with heteroscedastic errors and in unifying the study of classical fixed effects and random effects linear models. For prediction intervals and for bootstrapping in random coefficient regressions, it is necessary to estimate the distributions of the random coefficients consistently. We show that this is often possible and provide practical representative estimators of these distributions.

Journal ArticleDOI
TL;DR: A brief overview of non-linear models for the analysis of repeated measures and various estimation procedures proposed for such models are given, with particular emphasis on mixed-effects non- linear models and on various estimation procedure proposed forsuch models.
Abstract: Given the importance of longitudinal studies in biomedical research, it is not surprising that considerable attention has been given to linear and generalized linear models for the analysis of longitudinal data. A great deal of attention has also been given to non-linear models for repeated measurements, particularly in the field of pharmacokinetics. In this article, a brief overview of non-linear models for the analysis of repeated measures is given. Particular emphasis is placed on mixed-effects non-linear models and on various estimation procedures proposed for such models. Several of these estimation procedures are compared via a simulation study. In addition, simulation is used to investigate the effects of model misspecification, particularly with respect to one's choice of random-effects. A relatively straightforward measure useful in selecting an appropriate set of random effects is investigated and found to perform reasonably well.

Journal ArticleDOI
TL;DR: In this paper, a response surface model in the presence of a random block effect is considered to be a mixed-effects model and the main emphasis of the proposed analysis is on estimation and testing of the fixed effects.
Abstract: In many experimental situations, a response surface design is divided into several blocks to control an extraneous source of variation The traditional approach in most response surface applications is to treat the block effect as fixed in the assumed model There are, however, situations in which it is more appropriate to consider the block effect as random This article is concerned with inference about a response surface model in the presence of a random block effect Since this model also contains fixed polynomial effects, it is considered to be a mixed-effects model The main emphasis of the proposed analysis is on estimation and testing of the fixed effects A two-stage mixed-model procedure is developed for this purpose The variance components due to the random block effect and the experimental error are first estimated and then used to obtain the generalized least squares estimator of the fixed effects This procedure produces the so-called Yates combined intra- and inter-block estimator By cont

Journal ArticleDOI
TL;DR: The use of a random effects model for binary data in the interpretation of crossover studies is described in this article, where the model incorporates normally distributed subject effects, common to all responses from the same subject, into the linear part of the logistic regression model.
Abstract: The use of a random effects model for binary data in the interpretation of crossover studies is described. The model incorporates normally distributed subject effects, common to all responses from the same subject, into the linear part of the logistic regression model. The case of two treatments and two periods is considered, although extensions of the methodology to more general cases are possible. The paper describes how the model can be fitted and how the results can be interpreted. It is shown how data from subjects who miss the second period of treatment can be included in the analysis. Implications of the model on sample size calculations are studied, and a table to aid such calculations is provided. The methodology is illustrated with data from a recent pharmarceutical study of inhalation devices.

Journal ArticleDOI
TL;DR: This paper examined the relationship between unemployment and crime using regional data for Scotland over the period 1974 to 1988 and found a well-determined positive relationship between the regional unemployment rate and the crime rate, which is invariant to the estimator used.
Abstract: This paper attempts to examine the perennial question of the relationship between unemployment and crime using regional data for Scotland over the period 1974 to 1988. The econometric problems posed by autocorrelation, heteroscedasticity, and cross-sectional correlation are addressed within a feasible generalized least squares framework. A fixed effects and a random effects model are also estimated. A well-determined positive relationship between the regional unemployment rate and the crime rate is detected, which is invariant to the estimator used. Copyright 1992 by Scottish Economic Society.

Book ChapterDOI
01 Jan 1992
TL;DR: In this article, the authors proposed methods for fitting a broad class of models of this type, in which both the repeated measures and the survival time are modelled using random effects.
Abstract: In models for repeated observations of a measured response, the length of the response vector may be determined by a survival process related to the response. If the measurement error is large, and probability of death depends on the true, unobserved value of the response, then the survival process must be modelled. Wu and Carroll (1988) proposed a random effects model for a two-sample longitudinal data in the presence of informative censoring, in which the individual effects included only slopes and intercepts. We propose methods for fitting a broad class of models of this type, in which both the repeated measures and the survival time are modelled using random effects. These methods permit us to estimate parameters describing the relationship between measures of disease progression and survival time; and we apply them to results of AIDS clinical trials.

Journal ArticleDOI
TL;DR: In this paper, the authors estimate the home run ability of 12 great major league players by using the Gibbs sampling algorithm to detect aberrant seasons and estimate parameters of interest by inspection of various posterior distributions.
Abstract: The problem of interest is to estimate the home run ability of 12 great major league players. The usual career home run statistics are the total number of home runs hit and the overall rate at which the players hit them. The observed rate provides a point estimate for a player's “true” rate of hitting a home run. However, this point estimate is incomplete in that it ignores sampling errors, it includes seasons where the player has unusually good or poor performances, and it ignores the general pattern of performance of a player over his career. The observed rate statistic also does not distinguish between the peak and career performance of a given player. Given the random effects model of West (1985), one can detect aberrant seasons and estimate parameters of interest by the inspection of various posterior distributions. Posterior moments of interest are easily computed by the application of the Gibbs sampling algorithm (Gelfand and Smith 1990). A player's career performance is modeled using a lo...

Journal ArticleDOI
TL;DR: In this paper, the point or interval prediction of the value of a linear combination of the fixed and random effects is considered, where a common approach is "empirical BLUP" (best linear unbiased prediction), in which an estimate of the variance ratio is regarded as the true value.
Abstract: Unbalanced mixed linear models that contain a single set of random effects are frequently employed in animal breeding applications, in small-area estimation, and in the analysis of comparative experiments. The problem considered is that of the point or interval prediction of the value of a linear combination of the fixed and random effects or the value of a future data point. A common approach is "empirical BLUP (best linear unbiased prediction)," in which an estimate of the variance ratio is regarded as the true value. Empirical BLUP is satisfactory-or can be made satisfactory by introducing appropriate modifications-unless the estimate of the variance ratio is imprecise and is close to zero, in which case more sensible point and interval predictions can be obtained by adopting a Bayesian approach. Two animal breeding examples are used to illustrate the similarities and differences between the Bayesian and empirical BLUP approaches.

Journal ArticleDOI
TL;DR: The extent to which application of statistical stopping rules in clinical trials can create an artificial heterogeneity of treatment effects in overviews (meta-analyses) of related trials is explored.
Abstract: This paper explores the extent to which application of statistical stopping rules in clinical trials can create an artificial heterogeneity of treatment effects in overviews (meta-analyses) of related trials. For illustration, we concentrate on overviews of identically designed group sequential trials, using either fixed nominal or O'Brien and Fleming two-sided boundaries. Some analytic results are obtained for two-group designs and simulation studies are otherwise used, with the following overall findings. The use of stopping rules leads to biased estimates of treatment effect so that the assessment of heterogeneity of results in an overview of trials, some of which have used stopping rules, is confounded by this bias. If the true treatment effect being studied is small, as is often the case, then artificial heterogeneity is introduced, thus increasing the Type I error rate in the test of homogeneity. This could lead to erroneous use of a random effects model, producing exaggerated estimates and confidence intervals. However, if the true mean effect is large, then between-trial heterogeneity may be underestimated. When undertaking or interpreting overviews, one should ascertain whether stopping rules have been used (either formally or informally) and should consider whether their use might account for any heterogeneity found.

Journal ArticleDOI
TL;DR: In this article, a methodology is provided to account for heterogeneity in intrinsic brand preferences and intrinsic purchase propensities across households in nested logit models of purchase incidence and brand choice.

Journal ArticleDOI
TL;DR: The authors proposed two methods of estimation for the parameters of the nonlinear model for the mean: (1) estimated generalized least squares (EGLS), and (2) maximum likelihood (MLE) by the method of scoring.
Abstract: The nonlinear model with variance components, which combines a nonlinear model for the mean with additive random effects, is applicable to split-plot and nested experiments. We propose two methods of estimation for the parameters of the nonlinear model for the mean: (1) estimated generalized least squares (EGLS), and (2) maximum likelihood (MLE) by the method of scoring. Using a generalization of Klimko and Nelson's theorem on strong consistency of least squares estimators, it is possible to show that both the MLE and the EGLS estimators are strongly consistent, asymptotically normal, and asymptotically efficient.