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Showing papers on "Random effects model published in 1990"


Journal ArticleDOI
TL;DR: In this paper, three small-area models, of Battese, Harter, and Fuller (1988), Dempster, Rubin, and Tsutakawa (1981), and Fay and Herriot (1979), are investigated.
Abstract: Small-area estimation has received considerable attention in recent years because of a growing demand for reliable small-area statistics. The direct-survey estimators, based only on the data from a given small area (or small domain), are likely to yield unacceptably large standard errors because of small sample size in the domain. Therefore, alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency. These estimators use models, either implicitly or explicitly, that connect the small areas through supplementary (e.g., census and administrative) data. For example, simple synthetic estimators are based on implicit modeling. In this article, three small-area models, of Battese, Harter, and Fuller (1988), Dempster, Rubin, and Tsutakawa (1981), and Fay and Herriot (1979), are investigated. These models are all special cases of a general mixed linear model involving fixed and random effects, and a small-area mean can be expr...

690 citations


ReportDOI
TL;DR: This article developed a general multi-period multinomial probit model for panel data to estimate the living arrangements of the elderly, which has the following features: (a) in each period choices do not necessarily obey the assumption of independence of irrelevant alternatives.
Abstract: This paper develops a general multiperiod-multinomial probit model for panel data to estimate the living arrangements of the elderly. The model has the following features: (a) In each period choices do not necessarily obey the assumption of independence of irrelevant alternatives. (b) Unobserved person-specific attributes are treated as random effects. These random effects may also be correlated across alternatives. (c) In addition, unobserved choice-specific utility components may persist over some time, creating an autoregressive and/or heteroscedastic error structure. The model is estimated by simulating the choice probabilities in the likelihood function. We examine several variants of the specification of the correlation structure and investigate the extent the biases created by ignoring intertemporal correlations.

157 citations


Journal ArticleDOI
TL;DR: In this paper, a method based on maximizing the marginal likelihood for analyzing binary data with random effects is presented, which uses local independence models as well as those that incorporate additional dependence among the responses.
Abstract: SUMMARY This paper presents a method based on maximizing the marginal likelihood for analyzing binary data with random effects. With the assumption of a parametric family that allows for a wide variety of shapes for the distribution of the random effects, the marginal likelihood can be computed without numerical integrations. The method uses local independence models as well as those that incorporate additional dependence among the responses. Two examples, a panel study with binary responses and an analysis of item-response data, will be used to illustrate the method.

137 citations


Journal ArticleDOI
TL;DR: In this paper, the Breusch and Pagan (1980) lagrange multiplier test is extended to the incomplete panel data case, and it is shown that this test retains the simple additive structure observed in the complete panel data.
Abstract: This Paper extends the Breusch and Pagan(1980) lagrange Multiplier test for the random effects model to the incomplete panel data case. It is shown that this test retains the simple additive structure observed in the complete panel data case. It should prove useful for practitioners facing incomplete panel data applications.

131 citations


Journal ArticleDOI
TL;DR: In this article, two approaches for calculating the exact likelihood for a model when the errors are Gaussian are presented for calculating covariance matrices for each subject for assumed values of the unknown parameters and estimates the fixed parameters by weighted least squares.
Abstract: SUMMARY Serial correlation in the within subject error structure in longitudinal data with unequally spaced observations is modelled using continuous time autoregressive moving averages. The models considered have both fixed and random effects in addition to serially correlated within subject errors. Two approaches are presented for calculating the exact likelihood for a model when the errors are Gaussian. The first calculates the covariance matrices for each subject for assumed values of the unknown parameters and estimates the fixed parameters by weighted least squares. The second uses a state space model and the Kalman filter to calculate the exact likelihood. Both methods involve the use of complex arithmetic. Nonlinear optimization is used to obtain maximum likelihood estimates of the parameters.

95 citations


Journal ArticleDOI
TL;DR: In this paper, statistical inference for fixed effects, random effects, and components of variance in an unbalanced linear model with variance components was discussed, and Fisher scoring and the EM-algorithm were described.
Abstract: Statistical inference for fixed effects, random effects and components of variance in an unbalanced linear model with variance components will be discussed. Variance components will be estimated by Restricted Maximum Likelihood. Iterative procedures for computing the estimates, such as Fisher scoring and the EM-algorithm, are described.

65 citations


Journal ArticleDOI
TL;DR: It is proposed that generally available program packages performing estimation of the pharmacokinetic parameters from observational data should contain the necessary software to evaluate the reliability of the parameter estimates on a second data set.
Abstract: The application of population pharmacokinetic analysis has received increasing attention in the last few years. The main goal of this report is to make investigators aware of the necessity of independent evaluation of the results obtained from a population analysis based on observational studies. We also describe with the help of a specific example (a new synthetic opiate Alfentanil) how such evaluation can be performed for parameter estimates obtained with the software system NONMEM. The method differs depending on the type of serum concentration data that are used for the evaluation. A general method is described, based on the regression model used in NONMEM, that can test for bias in the estimates af fixed and random effects independent of the number of observations per patient and dosing. Since the procedure for testing for statistically significant bias in the prediction of the average concentration and its variability can be relatively complex, we propose that generally available program packages performing estimation of the pharmacokinetic parameters from observational data should contain the necessary software to evaluate the reliability of the parameter estimates on a second data set.

61 citations


Book ChapterDOI
01 Jan 1990
TL;DR: In this paper, iterative algorithms for computing restricted maximum likelihood estimates of variance components are discussed in the context of a possibly unbalanced, mixed linear model that contains a single set of m random effects.
Abstract: In this paper, iterative algorithms for computing restricted maximum likelihood (REML) estimates of variance components are discussed in the context of a possibly unbalanced, mixed linear model that contains a single set of m random effects. The coverage includes the Newton-Raphson algorithm, the method of scoring, the EM algorithm, and the method of successive approximations.

50 citations


Book ChapterDOI
01 Jan 1990
TL;DR: In this article, the authors considered the problem of predicting the value of an unobservable random variable w from the values of an observable random vector y under each of four states of knowledge about the joint distribution of w and y, ranging from complete knowledge to "no" knowledge.
Abstract: The problem considered is that of predicting the value of an unobservable random variable w from the value of an observable random vector y. This problem is considered under each of four states of knowledge about the joint distribution of w and y, ranging from complete knowledge to “no” knowledge. Point predictors, estimators of the mean squared error of prediction, and interval predictors are presented for each case. Both frequentist and Bayesian approaches are discussed and relationships between the two are pointed out. Specifics are given for the prediction of a linear combination of the fixed and random effects in a mixed linear model. The results are illustrated by applying them to some animal breeding data.

47 citations


Journal ArticleDOI
TL;DR: In this paper, the transitions between states defined in terms of work and welfare status are modeled as a discrete-time competing-risk model with unobserved heterogeneity, and the most striking result is that welfare recipients were substantially less likely to start working while remaining on welfare afterthe 1981 changes in program rules.

42 citations


Posted Content
TL;DR: This paper developed a general multi-period multinomial probit model for panel data to estimate the living arrangements of the elderly, which has the following features: (a) in each period choices do not necessarily obey the assumption of independence of irrelevant alternatives.
Abstract: This paper develops a general multiperiod-multinomial probit model for panel data to estimate the living arrangements of the elderly. The model has the following features: (a) In each period choices do not necessarily obey the assumption of independence of irrelevant alternatives. (b) Unobserved person-specific attributes are treated as random effects. These random effects may also be correlated across alternatives. (c) In addition, unobserved choice-specific utility components may persist over some time, creating an autoregressive and/or heteroscedastic error structure. The model is estimated by simulating the choice probabilities in the likelihood function. We examine several variants of the specification of the correlation structure and investigate the extent the biases created by ignoring intertemporal correlations.

Journal ArticleDOI
TL;DR: A mixed effects Poisson regression model is proposed for analysing potential risk factors associated with peritonitis, a bacterial infection of the peritoneum which is common among individuals on continuous ambulatory peritoneal dialysis (CAPD).
Abstract: A mixed effects Poisson regression model is proposed for analysing potential risk factors associated with peritonitis, a bacterial infection of the peritoneum which is common among individuals on continuous ambulatory peritoneal dialysis (CAPD). The model incorporates a set of fixed effects corresponding to concomitant information collected across individuals as well as a random effect due to individuals. The method of maximum likelihood is used to estimate the unknown parameters. When applied to clinical data obtained on 81 CAPD patients from four centres, the mixed effects model demonstrated a much better fit than the corresponding fixed effects Poisson regression model.

Journal ArticleDOI
TL;DR: An algorithm for transforming a multitrait into a unitrait analysis was presented for a mixed model that has equal design matrices for t traits and contains more than one random classification.

Book ChapterDOI
01 Jan 1990
TL;DR: Linear and non-linear models for the analysis of categorical data in animal breeding are reviewed and discussed and how Bayesian methodology is particularly well suited for estimating location and dispersion parameters in the underlying scale under mixed sources of variation is shown.
Abstract: Linear and non-linear models for the analysis of categorical data in animal breeding are reviewed and discussed on account of recent research made in this area. Only non-linear methods based on the threshold-liability concept introduced by Wright are described. Emphasis is on describing statistical techniques for estimating genetic merit and parameters of genetic and phenotypic variation. For each kind of methodology, the simple case of dichotomous responses is discussed in more detail as it serves as a basis for the presentation. Special consideration also is given to mixed model structures of data involving genetic effects and nuisance environmental parameters as fixed effects, as well as sire transmitting abilities, breeding values or producing abilities as random effects. A linear mixed model approach developed recently is examined in detail and extended to more general situations. For the nonlinear threshold model, it is shown how Bayesian methodology is particularly well suited for estimating location and dispersion parameters in the underlying scale under mixed sources of variation. The generality of the approach is illustrated through a discussion of extensions of the procedure.

Journal ArticleDOI
TL;DR: Extensions of the proportional hazards model to multivariate frailty distributions, modifications for application to pedigree and case-control studies, some simulation results, and applications to studies of breast cancer in twins and of lung cancer in relation to family smoking habits are described.
Abstract: It has recently been shown that the relative risks of the order of 2 to 4 that are frequently found for cancer among relatives of affected cases are unlikely to be explainable by shared environmental risk factors. Classical methods of epidemiological analysis are not well suited to such analysis because they assume that the outcomes of each individual are independent. Classical methods of genetic analysis, on the other hand, are limited in their handling of environmental factors and variable ages of onset. The recent development of random effects models for survival analysis, however, appears to bridge this gap. Specifically, a proportional hazards model is postulated for the effects of measured covariates and of one or more components of frailty that are unmeasured but assumed to have some common distribution and known covariance structure within each family. From these assumptions, the posterior expectation of the hazard for each individual can be derived, given the covariate value and the observed and expected disease history of the family. These are then treated as known in a standard partial likelihood analysis; this is essentially a form of expectation-maximization algorithm. However, this does not provide a valid estimate of the covariance matrix because it fails to take account of the variability in the estimates of the frailties; an alternative approach using the imputation-posterior algorithm is suggested. This paper describes extensions of this approach to multivariate frailty distributions, modifications for application to pedigree and case-control studies, some simulation results, and applications to studies of breast cancer in twins and of lung cancer in relation to family smoking habits.

Journal ArticleDOI
TL;DR: The results indicate that cross-sectional models for total tripmaking, transit and car usage may lead to seriously misleading results if used to assess the effects of changes in the travel environment.
Abstract: The objective of this paper is to examine whether the use of conventional trip generation models based on cross-sectional data will produce biased results. Panel data are used to control for omitted time invariant household effects. The methodology is based upon fixed and random effects models. The results indicate that cross-sectional models for total tripmaking, transit and car usage may lead to seriously misleading results if used to assess the effects of changes in the travel environment. The methodology seems to provide a proper way of taking unobserved heterogeneity into account. The difference in the results between fixed and random effects models may be the result of correlation between the omitted and included explanatory variables. A test for measurement error in the explanatory variables suggests that the results will not be significantly affected by this problem.

Journal ArticleDOI
TL;DR: In this article, a number of models are presented and estimated describing the correlation of trip making over time, and unobserved heterogeneity is taken into account using random effects using the generalized methods of moments procedure.
Abstract: A number of models are presented and estimated describing the correlation of trip making over time. Unobserved heterogeneity is taken into account using random effects. The basic models considered are the serial correlation and the state-dependence model. Trip making in total and by transit was best described using state-dependence models; trip making by car by a model with lagged exogenous variables. The generalized methods of moments procedure is used for estimation of the models: it is asymptotically efficient and does not require assumptions about the initial conditions.

Book ChapterDOI
01 Jan 1990
TL;DR: In this article, an extension of the Box-Cox theory of transformations to univariate mixed linear models is presented, including estimation of the transformation and of the required variance components, including computing algorithms.
Abstract: It is often assumed in animal breeding theory that models used for data analysis are “correct” with respect to functional form and distributional assumptions. However, a transformation may be needed to achieve this. An extension of the Box-Cox theory of transformations to univariate mixed linear models is presented. The discussion includes estimation of the transformation and of the required variance components, including computing algorithms. An analysis of fixed effects and breeding values after the transformation involves the following steps: (1) estimate ratios of variance components and the transformation parameter from their joint posterior distribution; (2) conditionally on these values, integrate out the residual variance (σ e 2 ) from the joint posterior distribution of fixed, random effects and σ e 2 , and (3) complete inferences using a multivariate-t distribution.

Book ChapterDOI
01 Jan 1990
TL;DR: This chapter describes the dynamic models for panel data and provides the treatment of initial observations in dynamic random effects models.
Abstract: Publisher Summary This chapter describes the dynamic models for panel data. It also discusses the consequences of estimating a static panel model using data on individuals who are involved in a dynamic adjustment process. Whenever a static model is used to explain economic behavior, it is implicitly assumed that individuals adjust immediately to changes in the exogenous variables or to random shocks, or that any adjustment is completed between waves. One of the advantages of panel data is that it can model the adjustment process. The chapter further discusses the fixed effect and random effect estimators in dynamic models. It also provides the treatment of initial observations in dynamic random effects models.

Journal ArticleDOI
TL;DR: In this article, a more general pooling model is proposed, which views storm parameters as being random and independent samples from a random effect probability model; the random effects may be because of parameter bias arising from errors in catchment rainfall, or model simplification.

Journal ArticleDOI
TL;DR: In this article, the authors present exact tests concerning the variance components of the random effects and estimable linear functions of the fixed effects in an unbalanced mixed two-way cross-classification with interaction model.
Abstract: The testing of both variance components and fixed effects in an unbalanced mixed model has relied on approximate techniques, particularly, Satterthwaite's approximation of the test statistics. The derived tests have unknown distributions, both under the null and alternative hypotheses, due to the lack of independence and chi-squaredness of the mean squares involved. Hence, the appeal for exact testing techniques is understandable. This article presents exact tests concerning the variance components of the random effects and estimable linear functions of the fixed effects in an unbalanced mixed two-way cross-classification with interaction model. The derivations are based on techniques similar to those applied by Khuri and Littell (1987, Biometrics 43, 545-560) to the same model, but with all random effects. The proposed methodology requires that the data under consideration contain no empty cells.

Journal ArticleDOI
TL;DR: In this article, the multiple observations model has been used for classification in a variety of fields, such as medicine, where individuals from two populations differ in the variability of these measurements over time, and this model can exploit that difference as an aid to classification.
Abstract: In this paper the multiple observations, or two factor mixed hierarchical, model for the classification problem has been studied. Under this model the Bayes classification statistic and some of its properties are discussed. It will be seen that the multiple observations model inclueds the fixed effects model as a special case and bears an interesting relationship to the random effects model. The multiple observations model has a potentialk application in a variety of fields. In medicine, for example, a patient to be classified as “healthy” versus “non—healthy” might be observed on several attributes at multiple points in time. If individuals from the two populations differ in the variability of these measurements over time, this model can exploit that difference as an aid to classification. Multivariate normality is assumed throughout this paper.

Journal ArticleDOI
TL;DR: In this paper, the exact posterior distribution for the fixed effect vector and the error variance of a Bayesian estimator for the variances of random effects is derived. And the mixed model is defined.
Abstract: The mixed model is defined. The exact posterior distribution for the fixed effect vector is obtained. The exact posterior distribution for the error variance is obtained. The exact posterior mean and variance of a Bayesian estimator for the variances of random effects is also derived. All computations are non-iterative and avoid numerical integrations.

Posted Content
TL;DR: In this paper, a framework for efficient IV estimators of random effects models with information in levels which can accommodate predetermined variables is developed, which clarifies the relationship between the existing estimators and the role of transformation in panel data models.
Abstract: This article develops a framework for efficient IV estimators of random effects models with information in levels which can accommodate predetermined variables. Our formulation clarifies the relationship between the existing estimators and the role of transformation in panel data models. We characterise the valid transformations for relevant models and show the optimal estimators are invariant to the transformation used to remove individual effects. We present an alternative transformation for models with predetermined instruments which preserves the orthogonality among the errors. Finally, we consider models with predetermined variables that have constant correlation with effects and illustrate their importance with simulations.

Journal ArticleDOI
TL;DR: In this paper, the estimation of the components of variance of the one-way random effects model is considered when the assumption of normality is removed, and the asymptotic relative efficiency of the estimators, derived by minimizing the mean squared error, is evaluated.

Journal ArticleDOI
TL;DR: In this paper, the empirical and predicted error variances of sire effects were estimated from 10 random subsets of the data of proven sires in Switzerland where average herd-year subclass size for first lactation records is less than 4.

Journal ArticleDOI
TL;DR: In this article, the properties of the locally most powerful nonparametric criterion against logistic alternatives developed by Govindarajulu (1975) for testing one-way random effects modcls are investigated.
Abstract: We investigate the properties of the locally most powerful nonparametric criterion against logistic alternatives developed by Govindarajulu (1975) for testing one-way random effects modcls We deduce the appropriate computational forms for the test criterion T and tabulate the critical values of T for α = 01, 05 and 010, and various sample sizes Certain features of the computational methods are discussed In the tables we retain only those sample sizes beyond which the asymptotic theory is meaningful We also study the power comparison of the test for two populations with the classical F-test under a range of normal alternatives


Journal ArticleDOI
TL;DR: In this article, the problem of simultaneously estimating p normal variances is investigated when the parameters are believed a priori to be similar in size. A hierarchical Bayes approach is employed and the resulting estimator is compared to common estimators used including one proposed by Box and Tiao (1973) using a Bayesian approach with a noninformative prior.
Abstract: The problem of simultaneously estimating p normal variances is investigated when the parameters are believed a priori to be similar in size. A hierarchical Bayes approach is employed and the resulting estimator is compared to common estimators used including one proposed by Box and Tiao (1973) using a Bayesian approach with a noninformative prior. The technique is then applied to estimate components of variance in the one way layout random effect model of the analysis of variance.

Journal ArticleDOI
TL;DR: In this article, a framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure.
Abstract: Summary A framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure The approach has two major uses; firstly, as a pedagogical tool in the derivation of formulae, and secondly, as a practical tool for developing computational strategies without needing complicated matrix formulae that are often unwieldy in complex hierarchical models The proposed technique is based upon symbolic application of the sweep operator SWP to an appropriate tableau of means and covariances The method is illustrated with standard linear model specifications, including the so-called mixed model, with both fixed and random effects