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Showing papers on "Random effects model published in 1986"


Journal ArticleDOI
TL;DR: The authors analyzes several empirical examples to investigate the applicability of random effects models and the consequences of inappropriately using ordinary least squares (OLS) estimation in the presence of random group effects.

1,789 citations


Journal ArticleDOI
TL;DR: The authors surveys economic choice theory, stressing developments that permit use of data from psychometric and conjoint experiments to produce market demand forecasts, and a new method for estimating multinomial probits is described.
Abstract: This paper surveys economic choice theory, stressing developments that permit use of data from psychometric and conjoint experiments to produce market demand forecasts. Alternatives to the widely used multinomial logit model are summarized, and a new method for estimating multinomial probits is described. An integration of choice models with attitudinal scaling and perceptual mapping, within a latent variable system, is described. Estimation of such systems under either “random effects” or “fixed effects” descriptions of heterogeneity across individuals is discussed. Issues in the use of choice models to describe responses from conjoint experiments are presented. New regression diagnostic tests for the consistency of multinomial logit representations are discussed.

1,223 citations


Book
01 Jan 1986
TL;DR: One Sample Normal Theory Nonnormality Effect Dependence Exercises Two Samples Normal Theory nonnormality Unequal Variances Dependence Expercises One-Way Classification Fixed Effects Normal Theory NOMA Nonnormal UNEQV Dependence as mentioned in this paper.
Abstract: One Sample Normal Theory Nonnormality Effect Dependence Exercises Two Samples Normal Theory Nonnormality Unequal Variances Dependence Exercises One-Way Classification Fixed Effects Normal Theory Nonnormality Unequal Variances Dependence Random Effects Normal Theory Nonnormality Unequal Variances Dependence Exercises Two-Way Classification Fixed Effects Normal Theory Nonnormality Unequal Variances Dependence Mixed Effects Normal Theory Departures from assumptions Random Effects Normal Theory Departures from Assumptions Exercises Regression Regression Model Normal Linear Model Nonlinearity Nonnormality Unequal Variances Dependence Errors-in-Variables Model Normal Theory Departures from Assumptions Exercises Ratios Normal Theory Departures from Assumptions Exercises Variances Normal Theory Nonnormality Dependence Exercises

604 citations


Journal ArticleDOI
TL;DR: In this paper, a review of recent theory and methodology for inferences concerning the intraclass correlation coefficient are reviewed, under the assumption of an underlying random effects model, including point and interval estimation, significance-testing for nonzero values of the intra-class correlation, and inference procedures in multiple samples.
Abstract: Summary Recent theory and methodology for inferences concerning the intraclass correlation coefficient are reviewed, under the assumption of an underlying random effects model. Topics discussed include point and interval estimation, significance-testing for nonzero values of the intraclass correlation, and inference procedures in multiple samples.

275 citations


Journal ArticleDOI
TL;DR: In this article, an efficient algorithm for computing restricted maximum likelihood estimates of variance components in a class of models is described, characterized by effects to be absorbed, which are nested within herds, other fixed effects, random sire effects, and a random residual.

250 citations


ReportDOI
TL;DR: In this paper, a structural limited dependent variable model with which the health and retirement status of the elderly were studied was proposed and the full information maximum likelihood estimator for such a model was implemented in empirical analysis.
Abstract: in this paper we specify and estimate a structural limited dependent variable model with which we study both the health and retirement status of the elderly. Standard linear estimators, which assume that these variable sare continuous, are not appropriate and categorical estimation techniques are preferred. Our model differs from previous work in that we have longitudinal data and random effects that are correlated over time for different individuals. The problem is made more complicated because there is sample truncation, which could potentially bias coefficient estimates, since approximately twenty percent of the individuals in our sample die. We outline the full information maximum likelihood estimator for such a model and implement it in our empirical analysis. With our structural estimates we analyze, among other things, the degree to which endogeneously determined health status affects the probability of retirement and how changes in social security benefits and eligibility for transfer payments modify both healthiness and the demand for leisure.

186 citations


Journal ArticleDOI
TL;DR: In this paper, a procedure for limiting the influence of these outliers on the estimates of the model parameters is described, where the model effects are estimated by augmenting the original observations with auxiliary observations that contain the prior information represented by the variances.
Abstract: Outliers may occur with respect to any of the random components in the mixed linear model. A procedure for limiting the influence of these outliers on the estimates of the model parameters is described. Given the variances or estimates of them, the model effects are estimated by augmenting the original observations with auxiliary observations that contain the prior information represented by the variances. Large residuals among either the original or the auxiliary observations are interpreted as outlying random errors or outlying random effects, as appropriate, and Winsorized. The robust estimation of the variances is obtained by modifying the defining equations for the restricted maximum likelihood estimates under normality along the lines of Huber's proposal 2. A numerical example illustrates the use of the methodology, both as a diagnostic and as an estimation tool.

160 citations


Journal ArticleDOI
TL;DR: In this article, a random coefficient regression model with multi-stage nested classification is considered, and linear Bayes estimators are obtained for random effects at all stages, and estimators of the structural parameters are proposed.
Abstract: A random coefficient regression model with multi-stage nested classification is considered. Linear Bayes estimators are obtained for random effects at all stages, and estimators of the structural parameters are proposed.

81 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the estimation of the parameters when some of the observations are right-censored, where the response is a waiting time and the variability in log times is modelled by a normal distribution.
Abstract: SUMMARY Maximum likelihood estimation of a vector regression parameter and variance com- ponents is considered for the mixed effects model when observations are right censored. A general scheme of estimation is given using the EM algorithm and detailed results found for the model with between and within block variation. This model is applied to the logarithms of survival times from a repeated measures design. In this paper we consider the estimation of the parameters when some of the observa- tions are right-censored. This can occur with repeated measurements on subjects where the response is a waiting time and the variability in log times is modelled by a normal distribution. Alternative models for this situation are given by Clayton & Cuzick (1985) and their methods involve partially parametric techniques using ranks and are based on models involving extreme value, log gamma and logistic distributions. We are concerned with use of the EM algorithm (Dempster, Laird & Rubin, 1977) to estimate the parameters of the mixed model. For uncensored data, Hartley & Rao (1967) have considered this solution. The analysis leads to a method which is straightforward to implement for the repeated measures model. Dempster et al. (1984) give an account of the method with uncensored observations. In ? 2 we consider a general implementation of the EM algorithm for the pure random effects model with censored data and then, in ? 3, we give explicit results for the simple random effects model. Section 4 uses these results for the analysis of repeated measures and ? 5 discusses some miscellaneous points arising. Finally, in ? 6, we give an example involving skin graft data, where there has been extensive analysis using matched pairs techniques.

35 citations


Journal ArticleDOI
TL;DR: Quadratic forms utilizing solutions to best linear unbiased prediction equations after absorbing all fixed effects into the equations for random effects were computed and pseudo expectations derived as mentioned in this paper, where pseudo expectations are taken as if a priori values are equal to true values rather than being taken as constants.

35 citations


Journal ArticleDOI
TL;DR: In this paper, the Cox regression model is used to solve large systems of equations corresponding to certain Cox regression models, and a procedure analogous to Gauss-Seidel iteration is proposed.

Journal ArticleDOI
TL;DR: In this paper, a restricted maximum likelihood procedure is described to estimate variance and covariance components in a multivariate mixed model when records are missing for some traits, which is computationally less demanding per round of iteration than the method of scoring, although the number of iterations required to reach convergence is increased.

Journal ArticleDOI
TL;DR: In this article, the authors compared two-stage predictors on the basis of their conditional (on the random effects) and unconditional bias and mean squared errors, and found that the least squares predictor and the positive part James-Stein predictor were the best linear unbiased predictor.
Abstract: Prediction of an arbitrary linear combination of the random effects of a balanced one-way random model is investigated. Alternative two-stage predictors are compared on the basis of their conditional (on the random effects) and unconditional bias and mean squared errors. When the true value of the ratio of expected mean squares is known, there exists a best linear unbiased predictor (BLUP). When the true value is unknown, a two-stage predictor, obtained from the BLUP by replacing the true value with an estimated value, can be used. When the ratio of expected mean squares is estimated by maximum likelihood, Bayesian methods, or various related methods, a two-stage predictor is obtained whose properties compare favorably with, for example, those of the least squares predictor and the positive-part James—Stein predictor.

Journal ArticleDOI
TL;DR: In this paper, a conservative approximation of the exact procedure developed by Wald (1940) can be used for hand calculations, when the exact solution is desired, a solution procedure is recommended that is computationally convenient and allows the investigator to determine the precision of the estimate.
Abstract: Several methods are compared for constructing confidence intervals on the intraclass correlation coefficient in the unbalanced one-way classification. The results suggest that a conservative approximation of the exact procedure developed by Wald (1940) can be used for hand calculations, When the exact solution is desired, a solution procedure is recommended that is computationally convenient and allows the investigator to determine the precision of the estimate. In cases where a prior estimate of the correlation is available, researchers may select intervals based on either the analysis of variance or unweighted sums of squares estimator.

Journal ArticleDOI
TL;DR: In this paper, the problem of estimating a ratio of variance components in the balanced one-way random effects model is considered, and it is shown that in terms of mean squared error, the ML, REML (or truncated ANOVA), and Bayes modal estimators (using the noninformative prior) are inadmissible.
Abstract: The problem of estimating a ratio of variance components in the balanced one-way random effects model is considered. It is shown that in terms of mean squared error, the ML, REML (or truncated ANOVA), and Bayes modal estimators (using the noninformative prior) are inadmissible. An estimator that dominates all three is derived. Two other estimators that are adaptive in nature are also introduced. The new estimators are shown to possess much-improved mean squared error properties. The results easily extend to balanced higher-way random or mixed effects models.

Journal ArticleDOI
TL;DR: The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry in this paper, and it is shown that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalized spectral decomposition.
Abstract: The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.

01 Aug 1986
TL;DR: In this paper, the locally best invariant test for the equality of the treatment effects is derived for two-way random effects and mixed effects balanced models, and shown to be equivalent to the usual F-tests under fixed effects models.
Abstract: : In one-way random effects unbalanced model the locally best invariant test for the equality of the treatment effects is derived Surprisingly, this is different from the widely used familiar F-test In the balanced case, however the two tests coincide and represent the uniformly most powerful invariant tests, For two-way random effects and mixed effects balanced models, the uniformly most powerful invariant test for the equality of the treatment effects is derived both with and without interaction, and shown to be equivalent to the usual F-tests under fixed effects models The optimum invariant tests derived here are shown not to depend on the assumption of normality Different aspects of null, nonnull and optimality robustness of these tests (Kariya and Sinha, Annals of Statistics, 1985) are studied In the unbalanced two-way models however unlike in the fixed effects model providing a UMPI test, both random and mixed effects models present a difficulty which is pointed out Keywords: Multivariate analysis; Analysis of variance

Journal ArticleDOI
David G. Ward1
TL;DR: In the one-facet (repeated measures) design, the extent to which true or universe scores and com- mon factor scores are not uniquely defined is shown to be a function of the dependability (reliability) of the data as mentioned in this paper.
Abstract: Generalizability theory and common factor analysis are based upon the random effects model of the analy sis of variance, and both are subject to the factor inde terminacy problem: The unobserved random variables (common factor scores or universe scores) are indeter minate. In the one-facet (repeated measures) design, the extent to which true or universe scores and com mon factor scores are not uniquely defined is shown to be a function of the dependability (reliability) of the data. The minimum possible correlation between equivalent common factor scores is a lower bound es timate of reliability.


Journal ArticleDOI
TL;DR: In this article, the variance-covariance matrix of random effects in a mixed linear model can be singular because identical twins are used or because a base population has been selected As a consequence, the usual mixed model equations cannot be used for estimation and prediction.

Journal ArticleDOI
TL;DR: In this paper, a preliminary testing procedure for design ettecta in a ran-dom effects covariance model is compared with the usual procedure to see if the power of the latter can be improved.
Abstract: A preliminary testing procedure for design ettecta in a ran-dom effects covariance model is Compared with the usual procedure to see if the power of the latter can be improved. A procedure which ignores the random covariate effects is included for comparison and for study of misspecification effects. Methodology is based on Roebruck's (1982) results for regular linear models.

Journal ArticleDOI
TL;DR: In this paper, a method for constructing simultaneous confidence intervals for functions of expected values of mean squares obtained when analyzing a balanced design by a random effects linear model is presented, with probability of simultaneous coverage guaranteed to be greater than or equal to the specified confidence coefficient.
Abstract: This paper demonstrates a method, derived byKhuri (1981), of constructing simultaneous confidence intervals for functions of expected values of mean squares obtained when analyzing a balanced design by a random effects linear model. The method may be applied to obtain confidence intervals for the variance components and other linear functions of the expected mean squares used in generalizability theory, with probability of simultaneous coverage guaranteed to be greater than or equal to the specified confidence coefficient. The Khuri intervals are compared with the approximate intervals obtained by usingSatterthwaite’s (1941, 1946) method in conjunction with Bonferroni’s inequality.