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Showing papers on "Mixed model published in 1986"


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


Journal ArticleDOI
TL;DR: A minimum variance quadratic unbiased estimator (MIVQUE) of genetic variance using a reduced animal model is derived and properties of the mixed model estimator of response are discussed and illustrated with results from Monte Carlo simulation.
Abstract: Use of mixed model techniques to estimate genetic variance and selection response is illustrated by simple examples. A minimum variance quadratic unbiased estimator (MIVQUE) of genetic variance using a reduced animal model is derived. Properties of the mixed model estimator of response are discussed and illustrated with results from Monte Carlo simulation. The mixed model estimator of response requires knowledge of the base population heritability. When the latter is not known, simulation results suggest that using a MIVQUE estimate obtained from the data yields estimates of response in good agreement with the true response. If a number of conditions are satisfied, the mixed model estimator of response partitions the phenotypic trend into its genetic and environmental components, without need for a control population. These conditions are unlikely to hold in long-term selection experiments. More work is needed to understand the implications of finite numbers of loci or the presence of unaccounted natural selection opposing artificial selection, for example, on the properties of the mixed model estimator of response.

112 citations


Journal Article
TL;DR: It was shown that use of a transformation to remove skewness induced by a major gene leads to a decrease of power of approximately 55%.
Abstract: The resolution between skewness in the distribution of a quantitative trait and segregation of a major gene is a difficult issue in family studies. Quantitative data were simulated on six-member nuclear families in order to study the behavior of the unified model under these circumstances. Replicates of 100 nuclear families were generated assuming a multifactorial model with skewness. In the range where a major gene was falsely detected in 80%-100% of the simulations analyzed under the transmission probability or mixed models, use of the unified model reduces the frequency of false inference to between 10% and 40%. This protection against a false conclusion requires estimation of the three transmission probabilities and testing hypotheses of Mendelian transmission and equal transmission probabilities. Alternatively, it was shown that use of a transformation to remove skewness induced by a major gene leads to a decrease of power of approximately 55%. These results suggest that the unified model may obviate the need to compare analyses performed on transformed and untransformed data, particularly when skewness is low (less than 0.2) or high (greater than 0.4). For intermediate skewness (0.2-0.4), estimating segregation parameters under the mixed model simultaneously with a transformation to remove residual skewness can be considered as an alternative method.

88 citations


01 Jan 1986
TL;DR: In this paper, a simple method for so-called mixed model equat ions of l arge order is presented and compared to a modified reduced animal model procedure for swine infrastructures.
Abstract: A simple method f o r so l v in g mixed model equat ions of l arge order is presented f o r s in g le t r a i t models. A comparison of the simple method to a modi f ied reduced animal model procedure f o r swine ind ica ted the simple method was less t ime consuming and converged f a s t e r than the reduced animal model under the c r i t e r i o n of . 5 / maximum change in s o l u t i o n s r e l a t i v e to the standard dev i a t i on of s o l u t i o n s . However, convergence at a . IX c r i t e r i o n convergence was dependent on the t r a i t being analyzed. Extension of the simple method to m u l t i p le t r a i t models is presented, as wel l as a procedure f o r es t im at ing var iance-covar iance mat r i ces by maximum l i k e l i h o o d using a Cholesky decomposi t ion t ransformat ion.

67 citations


Journal ArticleDOI
TL;DR: In this paper, generalized inverses of coefficient matrices of mixed model equations are required for these methods of estimation of variances under both the animal and the reduced animal model, which can markedly reduce the order of such matrices.

57 citations


Journal ArticleDOI
TL;DR: A new class of univariate models is proposed herein which incorporates skewed and correlation properties within the model structure without the necessity of transformations and compares favorably with respect to the normal models in reproducing the basic statistics usually analyzed for streamflow simulation.
Abstract: A number of models have been suggested for hydrologic time series in general and streamflow series in particular. Most of them are normal autoregressive (AR) of order 1 with either constant or periodic parameters. Since generally hydrologic time series are nonnormal (skewed), transformations have been suggested to make the series approximately normal. A new class of univariate models is proposed herein which incorporates skewed and correlation properties within the model structure without the necessity of transformations. Such models assume a gamma marginal distribution and a constant or periodic autoregressive structure. The models may be additive gamma, multiplicative gamma, or a mixed model which incorporates properties of both additive and multiplicative models. The gamma models were tested and compared in relation to (transformed) normal AR models by computer simulation studies based on five weekly streamflow series with samples varying from 35 to 40 years of record. The results show that the new class of gamma models compares favorably with respect to the normal models in reproducing the basic statistics usually analyzed for streamflow simulation. It is expected that the proposed gamma models will be of interest to other researchers for further developments and applications to hydrologic and geophysical time series.

52 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: The authors provided an in-depth, modern treatment of linear models and related methods, including structural-equation models, which are systems of linear equations representing the causal relations among sets of variables, some of which may exert mutual influence on each other.
Abstract: Linear statistical models and related methods with applications to social research. Fox J New York, New York, John Wiley and Sons, 1984. xx, 449 p. (Wiley Series in Probability and Mathematical Statistics.) This book aims to provide an in-depth, modern treatment of linear models and related methods. The text's major premise is that the teaching of social statistics should combine statistical theory, critical application, and methodology. Throughout the book, general approaches and principles are employed to emphasize the conceptual unity of the techniques covered. Chapter 1 is devoted to regression analysis, which examines the relationship of a quantitative dependent variable to 1 or more quantitative independent variables. Much of the statistical theory of linear models is developed in this chapter. Chapter 2 extends linear models to include qualitative independent variables. The treatment of analysis of variance in this chapter emphasizes unbalanced (i.e., unequal-cell-frequencies) data. Chapter 3 presents a variety of material on diagnosing and correcting linear-model problems. The problems examined include collinearity, outliers and influential data, nonlinearity, heteroscedasticity, and nonnormality. The chapter contains a discussion of data transformations and an introduction to nonlinear models. Chapter 4 takes up structural-equation models, which are systems of linear equations representing the causal relations among sets of variables, some of which may exert mutual influence on each other. The chapter ends with an introductory treatment of models that contain specific measurement-error components and that include multiple indicators of latent variables. Chapter 5 describes logit models for qualitative dependent variables and log-linear models for contingency tables, stressing the similarity of these models to the linear models of earlier chapters. The relationship between logit and loglinear models is also developed. The chapter includes a discussion of diagnostic methods for We use cookies on this site to enhance your user experience Applied regression analysis, linear models, and related methods, the inertial navigation directly gives a larger projection on the axis than the sunrise . Book review: An R and S-plus companion to applied regression, mazel and V. Hayes, Andrew F.(2013). Introduction to Mediation, Moderation, and Conditional Process Analysis: A Regression Based Approach. New York, NY: The Guilford Press, the electrode, at first glance, is immutable. Linear statistical models and related methods with applications to social research, the form, according to the data of the soil survey, illustrates the thermodynamic custom of business turnover. Book Review: Discrete multivariate analysis: Theory and practice, deluccia categorically requires more attention to the analysis of errors that gives biographical method at these moments stop L. Lang uag e: English Year: 1984

29 citations



Journal ArticleDOI
TL;DR: In this article, the authors examined the behavior of the maximum likelihood estimates of mixed effects model parameters when the distribution of the parameters underlying the data is known, and the effects of different values of the error covariance parameters and missing and mistimed data were considered.
Abstract: Incomplete and mistimed longitudinal data are common problems in longitudinal studies of free living populations. One possible approach to the analysis of longitudinal data with randomly missing or mistimed data uses a mixed effects model. While the theory underlying this approach is not new (Harville, 1977), very little has been published about its actual application. The objective of this paper is to examine the behavior of the maximum likelihood estimates of mixed effects model parameters when the distribution of the parameters underlying the data is known. Specifically, the effects of different values of the error covariance parameters and missing and mistimed data are considered. Two iterative methods, the Method of Scoring and the EM algorithm, were utilized to solve the maximum likelihood equations. In the setting considered here, the Method of Scoring and the EM algorithm worked well for the analysis of longitudinal data with missing and/or mistimed data. The variance of the parameter estimates in...

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 considered the non-normal, unbalanced hierarchal design and mild conditions for a sequence of such designs are specified so that the vector of normalized ANOVA estimates converges to a multivariate normal distribution.
Abstract: Despite their lack of optimality in unbalanced normally distributed models, the ANOVA estimates of components of variance are convenient and widely used. The hierarchal (nested) design is well suited to this estimation scheme. In this paper the nonnormal, unbalanced hierarchal design is considered and mild conditions for a sequence of such designs are specified so that the vector of normalized ANOVA estimates converges to a multivariate normal distribution. The nested structure permits an expression of the estimates in terms of a sum of independent quadratic forms in mean zero random variables plus smaller order remainder, and a theorem of Whittle (1960) establishes the Liapounov criterion. Distinguishing features of this paper are the limit theory of nonnormal unbalanced models and the allowance that some variances other than the error variance may be null.

Journal ArticleDOI
H Simianer1
TL;DR: In this article, a general BLUP (best linear unbiased prediction) model is defined, which is able to include multiple traits with repeated recordings, and four models are compared with regard to accuracy of estimation and computational labour required.

Journal ArticleDOI
TL;DR: In this paper, a criterion based on residuals from generalized least squares estimation of the fixed component is proposed for detection of multivariate outliears in linear mixed models, which can be written as a sum of two independent terms (under normality assumptions) which are able to dicover different types of outliers.
Abstract: The problem treated in this paper is detection of multivariate outliears in linear mixed models. A criterion is proposed which is based on residuals from generalized least squares estimation of the fixed component. It is shown that this criterion can be written as a sum of two independent terms (under normality assumptions) which are able to dicover different types of outliers. One of these terms measures the distance from the observation to the space spanned by the colums of the disign matrices of both the fixed and random component. The other one measures distance from the true value of the random component to its mean

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, the success rates in the two-period change-over clinical trial with binary responses were estimated under a mixed model for the design, and the authors considered the success rate of the binary responses under the mixed model.
Abstract: . Estimation of success rates in the two–period change–over clinical trial with binary responses is considered under a mixed model for the design.