Showing papers on "Mixed model published in 1990"

Nonlinear Mixed Effects Models for Repeated Measures Data

Abstract: We propose a general, nonlinear mixed effects model for repeated measures data and define estimators for its parameters. The proposed estimators are a natural combination of least squares estimators for nonlinear fixed effects models and maximum likelihood (or restricted maximum likelihood) estimators for linear mixed effects models. We implement Newton-Raphson estimation using previously developed computational methods for nonlinear fixed effects models and for linear mixed effects models. Two examples are presented and the connections between this work and recent work on generalized linear mixed effects models are discussed.

Bayesian Inference With Geodetic Applications

Abstract: Basic concepts.- Bayes' Theorem.- Prior density functions.- Point estimation.- Confidence regions.- Hypothesis testing.- Predictive analysis.- Numerical techniques.- Models and special applications.- Linear models.- Nonlinear models.- Mixed models.- Linear models with unknown variance and covariance components.- Classification.- Posterior analysis based on distributions for robust maximum likelihood type estimates.- Reconstruction of digital images.

Use of Mixed Model Methodology in Analysis of Designed Experiments

Abstract: Applications of mixed model methods in the analysis of designed experiments are illustrated and discussed for purposes of: (1) increasing rate of selection response to create genetically diverse lines rapidly or to demonstrate feasibility of selection, (2) estimation of genetic parameters free of bias from selection and inbreeding, (3) estimation of response to selection with or without controls, and (4) verification of experimental design prior to the experiment. For traits controlled by a large number of additive loci, use of the numerator relationship matrix in the mixed model equations accounts for changes in additive genetic variance due to inbreeding, assortative mating and gametic disequilibrium resulting from selection. If the number of loci is small, non-normality of the genotypic distribution and changes in variance due to gene frequency changes (including fixation) are not accounted for but these seem to be of small consequence, at least for short-term selection. Use of mixed model methods do not require prior knowledge of base population heritability which can be estimated from the data unaltered by selection. If dominance effects are important, properties of the dominance relationship matrix and use of mixed model methods are not yet well understood in inbred and selected populations. Simulation results indicate that use of mixed model methods can be effective in randomly mated populations, even if the number of loci is small. There is evidence of bias in selected populations, however, particularly when gene frequencies are extreme. Properties of mixed model methods under dominance and other non-additive genetic models need more study.

Statistical Inferences in Populations Undergoing Selection or Non-Random Mating

Abstract: Data available to animal breeders often come from populations undergoing selection and non-random mating (SNRM). Unless this is taken into consideration, inferences based on such data may be misleading. Using a Bayesian setting, it is shown that when the information used to make breeding decisions is available, posterior densities constructed taking into consideration SNRM are identical to those constructed ignoring SNRM. Thus, methods of inference based on posterior densities including all information used to make breeding decisions, can be used ignoring complications due to SNRM. Properties of methods such as maximum likelihood (ML) and best linear unbiased prediction (BLUP) are examined under the assumption of multivariate normality in data from populations undergoing SNRM. Although expressions for ML estimators are identical with or without SNRM, their sampling properties are affected by SNRM. In the presence of SNRM, the matrices appearing in the mixed model equations cannot be considered fixed. However, it is shown under multivariate normality, that the usual expressions lead to BLUP, provided that SNRM decisions are based on translation invariant functions of the data available for calculation of BLUP.

Genetic evaluation for discrete polygenic traits in animal breeding.

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.

Mixed Model Methodology and the Box-Cox Theory of Transformations: A Bayesian Approach

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.

Retransformation bias: A look at the box-cox transformation to linear balanced mixed ANOVA models

Abstract: After a Box-Cox transformation to data following a linear balanced mixed ANOVA model, final results may be presented after retransformation to the original scale of measurement Consequently, estimation of means which may be unbiased in the transformed scale will not be so after retransformation In this article, the bias introduced together with the corresponding variance is assessed It is found that whereas bias may not be a serious problem, the variances are inflated for positive transformation parameter the closer it is to zero

Accounting for Selection and Mating Biases in Genetic Evaluations

Abstract: When selection has occurred, the means and variances of random variables are different from those under the usual assumptions of mixed linear models. Consequently, the solution to regular mixed model equations sometimes gives biased estimators and predictors. Given multivariate normal distributions and a vector variable used to make selection and mating decisions, the mixed model equations can be modified to yield unbiased estimators and predictors. This modification is described and several examples are given of its application, including cow culling, selection on records not available for analysis, estimation of genetic and environmental trends, association between sire and herd values, genetic groups, differential treatment, and assortative mating with and without selection.

Exact tests for the random and fixed effects in an unbalanced mixed two-way cross-classification 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.

Parameter estimation in variance component models for binary response data.

Abstract: Mixed model analysis of categorical response data is an important but difficult analytical problem. This paper first reviews mixed model analysis from a Bayesian perspective in the linear model setting, and then shows how the general Bayes approach can be extended to categorical data. Some limitations of the Bayes approach in this setting are discussed. Both maximum and quasi-likelihood approaches in the categorical data case are also described.

Extension of the Stein Estimating Procedure through the Use of Estimating Functions

Abstract: This article extends the Stein method through the use of estimating functions (Godambe 1960) to address the simultaneous estimation of k population parameters, θ1, …, θ k , in a mixed model setting. The procedure generalizes the Stein method by (a) allowing us to deal effectively with complications, such as inequality of population variances, that may arise in non-Gaussian mixed models; (b) being appropriate for estimating θ i in populations of varying sizes and, in particular, populations of small sizes; and (c) applying to situations where it cannot be assumed that the θ i 's have unbiased estimators or even estimators of finite moment. The focus of the article is on the quadratic variance function exponential family (Morris 1983b). Estimators for the parameters of the mixed model are developed in a regression model setting in which the θ i 's are allowed to vary with a vector of covariates. An application to incidence rates for the Iceland Breast Cancer Incidence Data is presented for illustra...

Extension of the Stein estimating procedure through the use of estimating functions

Abstract: This article extends the Stein method through the use of estimating functions (Godambe 1960) to address the simultaneous estimation of k population parameters, θ1, …, θ k , in a mixed model setting. The procedure generalizes the Stein method by (a) allowing us to deal effectively with complications, such as inequality of population variances, that may arise in non-Gaussian mixed models; (b) being appropriate for estimating θ i in populations of varying sizes and, in particular, populations of small sizes; and (c) applying to situations where it cannot be assumed that the θ i 's have unbiased estimators or even estimators of finite moment. The focus of the article is on the quadratic variance function exponential family (Morris 1983b). Estimators for the parameters of the mixed model are developed in a regression model setting in which the θ i 's are allowed to vary with a vector of covariates. An application to incidence rates for the Iceland Breast Cancer Incidence Data is presented for illustra...

Two methods for parameter estimation using multiple-trait models and beef cattle field data.

Abstract: Two methods are presented for estimating variances and covariances from beef cattle field data using multiple-trait sire models. Both methods require that the first trait have no missing records and that the contemporary groups for the second trait be subsets of the contemporary groups for the first trait; however, the second trait may have missing records. One method uses pseudo expectations involving quadratics composed of the solutions and the right-hand sides of the mixed model equations. The other method is an extension of Henderson's Simple Method to the multiple trait case. Neither of these methods requires any inversions of large matrices in the computation of the parameters; therefore, both methods can handle very large sets of data. Four simulated data sets were generated to evaluate the methods. In general, both methods estimated genetic correlations and heritabilities that were close to the Restricted Maximum Likelihood estimates and the true data set values, even when selection within contemporary groups was practiced. The estimates of residual correlations by both methods, however, were biased by selection. These two methods can be useful in estimating variances and covariances from multiple-trait models in large populations that have undergone a minimal amount of selection within contemporary groups.

Analytic statistical models

Abstract: Analytic statistical models , Analytic statistical models , کتابخانه دیجیتال جندی شاپور اهواز

A Bayesian analysis of the mixed linear model

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.

A strategy for analysing mixed and pooled exponentials

Abstract: It is shown that a linear plot of the mean residual life on the failure rate characterizes the mixture of two exponentials. This plot is used to estimate the two components in the mixing distribution with the two largest mixing proportions. The EM algorithm is then used with these as initial values to obtain the MLE. Gradient plots are used to see if a higher-order fit is needed. A heuristic is given on how to use the gradient plots to identify components in the higher-order fit when this is the case. Graphs of an assignment function are then used to determine if the data are from a mixed model or simply the effect of pooling.

Survival, Endurance and Censored Observations in Animal Breeding

Abstract: Longevity and other survival measures are important traits and these are usually subjected to censoring. Methods in failure time analysis, useful for the censored data encountered in animal breeding, are described. The value of the Cox model and of other rank regression models is highlighted. These methods incorporate an unknown transformation in the model, solving the scale problems frequently confronted in genetic analysis. Bayesian approaches allow models to accommodate random factors such as additive genetic values. Effects are estimated by solving, perhaps several times, a linear system of equations that resembles Henderson’s mixed model equations. Proposed numerical techniques are tested on an actual data set.

Quasi‐likelihood inference in a generalized linear mixed model for balanced data

Abstract: For modelling the effect of crossed, fixed factors on the response variable in balanced designs with nested stratifications, a generalized linear mixed model is proposed. This model is based on a set of quasi-likelihood assumptions which imply quadratic variance functions. From these variance functions, deviances are obtained to quantify the variation per stratification. The effects of the fixed factors will be tested, an dispersion components will be estimated. The practical use of the model is illustrated by reanalysing a soldering failures problem.

A new approach to variance component estimation with diagnostic implications

Abstract: Closed form expressions are developed for the estimators of functions of the variance components in balanced, mixed, linear models. These estimators are averages of sample covariances (variances) which offer diagnostic information on the data and the model. The cause of negative estimates may be revealed. Examples illustrate the basic concepts.

Analysis of Linear and Non-Linear Growth Models with Random Parameters

Abstract: This paper discusses the analysis of growth data using mixed models. Both Bayes and frequentist approaches are outlined for the linear model. The use of the EM algorithm is shown to offer a flexible and straightforward computational approach to the analysis. Extensions to non-linear models are described.

An algorithmic approach to bayesian linear model calculations

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

Nonlinear regression for split plot experiments

Abstract: Marcia L. Gumpertz and John O. Rawlings North Carolina State University 159 Split plot experimental designs are common in studies of the effects of air pollutants on crop yields. Nonlinear functions such the Weibull function have been used extensively to model the effect of ozone exposure on yield of several crop species. The usual nonlinear regression model, which assumes independent errors, is not appropriate for data from nested or split plot designs in which there is more than one source of random variation. The nonlinear model with variance components combines a nonlinear model for the mean with additive random effects to describe the covariance structure. We propose an estimated generalized least squares (EGLS) method of estimation for this model. The variance components are estimated two ways: by analysis of variance, and by an approximate MINQUE method. These methods are demonstrated and compared with results from ordinary nonlinear least squares for data from the National Crop Loss Assessment Network (NCLAN) program regarding the effects of ozone on soybeans. In this example all methods give similar point estimates of the parameters of the Weibull function. The advantage of estimated generalized least squares is that it produces proper estimates of the variances of the parameters and of estimated yields, which take the covariance structure into account. A computer program that fits the nonlinear model with variance components by the EGLS method is available from the authors.

Maximum likelihood estimators for the two way mixed model

Abstract: Maximum likelihood and restricted maximum likelihood estimators are derived for the variance and covariance parameters of Scheffe's extended mixed model two-way layout. Hadamard's inequality and matrix diagonalizing methods are used to obtain positive semidefinite covariance matrix estimates as well as a modified estimate for the error variance σ e 2 . Nonnegative estimators for σ B 2 and σ AB 2 are also given in contrast to the uniformly minimum variance unbiased estimators