Showing papers on "Mixed model published in 1988"
TL;DR: In this article, the first and second moments of a random vector of breeding values are derived from simple genetic assumptions and matrix expressions are derived for the first two moments of the vector.
255 citations
TL;DR: In this article, an iterative algorithm was developed that combines contributions due to production records (if any) and due to relationships to approximate the reciprocal of prediction error variance for sire models.
110 citations
TL;DR: A mixed model using a gamma-Poisson distribution with a random scale parameter having an inverse gamma prior and an empirical Bayes approach is used to estimate relative risks for geographic regions and annual rates for demographic groups within each region.
Abstract: A mixed model is proposed for the analysis of geographic variability in mortality rates. In addition to demographic parameters and random geographic parameters, the model includes additional random-effects parameters to adjust for extra-Poisson variability. The model uses a gamma-Poisson distribution with a random scale parameter having an inverse gamma prior. An empirical Bayes approach is used to estimate relative risks for geographic regions and annual rates for demographic groups within each region. Lung cancer in Missouri is used to motivate and illustrate the procedure. Observed disease-specific death rates of specific age/sex groups, within regional units such as counties or cities, are generally quite unreliable for all but the largest units. The amount of information available from any one unit is generally limited. But modeling the variability between and within units can improve estimates, as demonstrated frequently in empirical Bayes examples. A numerical comparison with the fixed eff...
102 citations
TL;DR: In this article, the simplex method was used as an alternative to the EM algorithm in computing maximum likelihood estimates in mixed probit and logit models with binomial data, which was used to estimate heritability and to predict sire effects when analysing a lamb mortality data set.
Abstract: SUMMARY The simplex method, a derivative-free function maximisation algorithm, is used as an alternative to the EM algorithm in computing maximum likelihood estimates in mixed probit and logit models with binomial data The models are used to estimate heritability and to predict sire effects when analysing a lamb mortality data set
57 citations
TL;DR: In this article, the authors derived the locally best invariant unbiased test for the random effects model corresponding to an equiblock and equireplicate design, and a locally best unbiased test with mixed treatment effects corresponding to a balanced incomplete block design for the mixed effects model with random treatment effects.
Abstract: It is an open problem in the literature to derive optimum tests for the equality of treatment effects in an unbalanced two-way classification model. For such models without interaction, optimum tests are derived in the following cases: (i) the locally best invariant unbiased test for the random effects model corresponding to an equiblock and equireplicate design, (ii) the locally best invariant unbiased test for the mixed effects model with mixed treatment effects corresponding to a balanced incomplete block design and (iii) the uniformly most powerful invariant test or the locally best invariant test for the mixed effects model with random treatment effects. Robustness of the optimum invariant tests against suitable deviations from normality is also indicated.
40 citations
TL;DR: A graphical technique and a procedure for discriminating among genetic hypotheses based on a mixed model accounting for all these factors are proposed and illustrated by using simulated data.
Abstract: Statistical techniques for detection of major loci and for making inferences about major locus parameters such as genotypic frequencies, effects and gene action from field-collected data are presented. In field data, major genotypic effects are likely to be masked by a large number of environmental differences in addition to additive and nonadditive polygenic effects. A graphical technique and a procedure for discriminating among genetic hypotheses based on a mixed model accounting for all these factors are proposed. The methods are illustrated by using simulated data.
22 citations
TL;DR: The idea of treating the random effects as fixed for constructing a test for a linear hypothesis (of fixed effects) in a mixed linear model is considered in this article, where the authors examine when such a test statistic can be computed and what are its distributional properties with respect to the actual mixed model.
Abstract: The Idea of treating the random effects as fixed for constructing a test for a linear hypothesis (of fixed effects) in a mixed linear model is considered in this paper. The paper examines when such a test statistic can be computed and what are its distributional properties with respect to the actual mixed model.
17 citations
TL;DR: The present paper presents a much simpler method that employs regular mixed model equations modified for selection of base animals that can be used for dealing with grouping in sire evaluation or animal model evaluation.
15 citations
TL;DR: In this paper, the design matrix is partitioned into singly manageable strips and recursively called a regression routine with low-dimensional subproblems, which can be implicitly and transparently done for a wide class of growth-curve problems.
Abstract: A fixed-effects formulation of repeated-measures and growth-curve problems usually leads to an unwieldy linear model, so mixed models are widely used for inference that the conditional linear error model could otherwise support with weaker distributional assumptions. Very high-dimensional regressions (not necessarily arising this way) can be fitted by the proposed alternating algorithm, which partitions the design matrix into singly manageable strips and recursively calls a regression routine with low-dimensional subproblems. Convergence to the full least squares solution with modest memory and time requirements is a consequence of the behavior of cyclically iterated projections of linear spaces. The partitioning can be implicitly and transparently done for a wide class of growth-curve problems. The method does not hinge on any balance or completeness properties of the design. In all cases coefficients and residuals are recoverable from standard regression output after convergence, but package-su...
10 citations
TL;DR: In this paper, asymptotic relative efficiencies are considered for a three factor mixed effects model with the assumption that the observations are realisations of a univariate normal distribution.
Abstract: A basic assumption in the analysis of variance is that the observations are realisations of a univariate normal distribution. However, if the observations are rounded, the question arises of how this affects the usual tests. Rayner, Dodds and Best (1986) considered a one factor fixed effects model with regard to simulated sizes and approximate asymptotic relative efficiencies. Here asymptotic relative efficiencies are considered for a three factor mixed effects model. The method generalises readily to other ANOVA models.
9 citations
TL;DR: In this paper, the authors presented a method for computing a g-inverse of the full coefficient matrix by a set of linear functions of a ginverse for the reduced model.
TL;DR: In this paper, the variance components for balanced designs under squared error loss were improved by using a linear combination of chi-square scale parameters, which can be expressed as linear combinations of chi square scale parameters.
Abstract: Taking Albert's (1976) formulation of a mixed model ANOVA, we consider improved estimation of the variance components for balanced designs under squared error loss. Two approaches are presented. One extends the ideas of Stein (1964), The other is developed from the fact that variance components can be expressed as linear combinations of chi-square scale parameters. Encouraging simulation results are presented.
TL;DR: In this paper, exact mean squared errors of two-stage predictors are obtained for a class of mixed models with two variance components that includes the balanced one-way random model and other analysis-of-variance models with proportional frequencies and one balanced random factor.
TL;DR: In this article, an equivalent model with fewer elements in the random vector can be used to solve this problem, some examples are presented, and algorithms for BLUE, BLUP, MIVQUE, and REML are presented.
Abstract: Some linear models have a very large number of elements in the vector representing random factors. Consequently, it Is impossible to Invert the resulting mixed model coefficient matrix. This inverse is needed for sampling variances and prediction error variances and for computation of MIVQUE and REML estimates of variances and covariances. An equivalent model with fewer elements in the random vector can be used to solve this problem, Some examples are presented, and algorithms for BLUE, BLUP, MIVQUE, and REML are presented.
TL;DR: In this article, the authors considered unbalanced mixed models under heteroscedastic variances and showed that the problems appear to be anologous to those from balanced mixed models with homoscaledastic variance.
Abstract: In this paper we consider unbalanced mixed models (Scheffe's model) under heteroscedastic variances. By using the harmonic mean approach, It is shown that the problems appear to be anologous to those problems from balanced mixed models under homoscedastic variance. Thus, by using harmonic mean approach, statistical inferences about fixed effects and variance components are derived by using those from balanced models under homoscedastic variance. Laguerre polynomial expansion is used Lo approximate sampling distributions of relevant statistics.
TL;DR: In this paper, the W-matrix is applied for the mixed analysis of variance model to compute maximum likelihood estimates of the fixed parameters and variance components and an efficient algorithm is developed in this paper for the Wmatrix in the sense of storage economy and computing time.
Abstract: W-matrix is applied for the mixed analysis of variance model to compute maximum likelihood estimates of the fixed parameters and variance components. An efficient algorithm is developed in this paper for the W-matrix in the sense of storage economy and computing time. The efficiency of the algorithm is demonstrated through examples which are given.
01 Sep 1988
TL;DR: In this article, the analysis of experiments arranged in blocks chosen at random is presented, and the power of the test for the block effect is obtained using a certain approximation by Hirotsu (1979).
Abstract: : This article is concerned with the analysis of experiments arranged in blocks chosen at random. Estimates of the polynomial parameters in the associated response surface model are obtained free of blocks. Tests concerning the polynomial and random block effects are presented. Furthermore, the power of the test for the block effect is obtained using a certain approximation by Hirotsu (1979). A numerical example is given to illustrate the implementation of the proposed analysis. Keywords: Design moments; Fixed and random effects; Mixed model; Orthogonal blocking; Polynomial and block effects; Response surface model.