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Showing papers on "Random effects model published in 1980"


Journal ArticleDOI
Bjørn Sundt1
TL;DR: In this paper, a hierarchical credibility regression model with random parameters on two levels was proposed. But this model was later extended to a model with n levels of random parameters, and the model was shown to be more robust than the one with two levels.
Abstract: In a recent paper the author developed a hierarchical credibility regression model with random parameters on two levels. In the present paper this approach is extended to a model with random parameters on n levels.

32 citations


Journal ArticleDOI
TL;DR: It is proved that the method yields consistent estimators and predictors of response probabilities for any desired linear function of the model, provided that the linear combination involving the fixed effects is estimable.
Abstract: Summary A method of genetic evaluation of polychotomies based on the logistic distribution is presented. Logarithmic transformations of counts are expressed as linear combinations of fixed effects and random variables. Realized values of random elements in the model are predicted by the solution of equations similar to Henderson's multi-trait best linear unbiased prediction, but with a variance-covariance matrix of the residuals estimated from the data. It is proved that the method yields consistent estimators and predictors of response probabilities for any desired linear function of the model, provided that the linear combination involving the fixed effects is estimable. The method appears to have properties similar to those of minimum logit chi-square estimators. An example is pre

27 citations


Journal ArticleDOI
TL;DR: In this paper, two more models are proposed for the analysis of matched pairs in factorial experiments with binary data, which are applied to two-period crossover designs and compared with previous methods of analysis and between the models proposed.
Abstract: Two more models are proposed for the analysis of matched pairs in factorial experiments with binary data. They are applied to two-period crossover designs. Estimation and test procedures are derived both approximately and by maximizing likelihoods. Comparisons are made with previous methods of analysis and between the models proposed.

12 citations


Journal ArticleDOI
TL;DR: In this paper, an approximation to the joint distribution of the mean squares (and hence the F ratio) by using Laguerre polynomials is derived, and these results are then used to examine the effects of departure from normality on the traditional F-ratio distribution.
Abstract: In this article we consider the unbalanced random-effects model as given in (1.1) with random variables from nonormal universes. Assuming that the αi 's are independently distributed of the eij 's, an approximation to the joint distribution of the mean squares (and hence the F ratio) by using Laguerre polynomials is derived. These results are then used to examine the effects of departure from normality on the traditional F-ratio distribution.

7 citations


Journal ArticleDOI
TL;DR: In this article, the authors present methods for the development of exact confidence intervals for ratios of linear functions of fixed effects in mixed models, which are used in animal breeding experiments from which estimates of ratios are desired.
Abstract: Summary Mixed linear models are widely used in animal breeding experiments from which estimates of ratios are desired. This paper presents methods for the development of exact confidence intervals for ratios of linear functions of fixed effects in mixed models. Approximate confidence intervals for ratios involving random effects can also be obtained by these methods. Additional problems considered include pooled ratio estimation from multiple data sets with constant variance and the case of unequal error variance with two sources of heterogeneity. Confidence intervals obtained here are expected to be larger than those based on approximations of the variance of a ratio through Taylor's series, since the latter underestimate the true variance under certain conditions.

2 citations


Book ChapterDOI
Stanley Sawyer1
TL;DR: In this article, the authors discuss isotropic random walks on a set of graphs called infinite homogeneous trees, and describe a population genetics model on these graphs such that migration between generations is represented by an isotropical random walk.
Abstract: The purpose here is to discuss isotropic random walks on a set of graphs called infinite homogeneous trees, and to describe a population genetics model on these graphs such that migration between generations is represented by an isotropic random walk. The population model is of “Stepping Stone” type, which are used in Biology to model selectively neutral gene flow in a stationary interbreeding population. Here the main influences are local migration and the consolidative effects of random finite offspring distributions. In one or two dimensions, these random effects cause expanding waves which can mimic the “waves of advance” of epidemiological models or genetic models with selection. In three or more dimensions, or in infinite trees, there are still waves of advance but they do not exclude other types behind the “wave” (see §3 below).

1 citations