Showing papers on "Mixed model published in 1982"

Analysis of covariance in the mixed model: higher-level, nonhomogeneous, and random regressions.

Abstract: The model generally considered in analysis of covariance has all levels of classification factors and interactions fixed, and also covariate regression coefficients fixed. Mixed models are more appropriate in most applications. A summary of estimation and hypothesis testing for analysis of covariance in the mixed model, including the case of random regression coefficients, is presented. Higher-level covariate regressions (i.e., regressions in which, for all levels of a factor or interaction, all observations on the same level have a common covariate value) are discussed. Nonestimability problems that result from defining such covariates at the levels of fixed effects are illustrated. The case of nonhomogeneous covariate regressions in the mixed model is considered in the context of interpreting predicted future differences among levels of a given factor or interaction. Nonhomogeneous regressions complicate interpretations only when they are associated with the contrast(s) of interest among fixed effects in the model. The question of whether the regressions are homogeneous is itself often of substantive interest. Different random regression coefficients associated with the levels of a random effect are also examined.

Mixed models and reduced/selective integration displacement models for nonlinear shell analysis

Abstract: Simple mixed models are developed for the geometrically nonlinear analysis of shells. A total Lagrangian description of the shell deformation is used, and the analytical formulation is based on a form of the nonlinear shallow shell theory with the effects of transverse shear deformation and bending-extensional coupling included. The fundamental unknowns consist of eight stress resultants and five generalized displacements of the shell, and the element characteristic arrays are obtained by using the Hellinger-Reissner mixed variational principle. The polynomial interpolation (or shape) functions used in approximating the stress resultants are, in general, of different degree than those used for approximating the generalized displacements. The stress resultants are discontinuous at the element boundaries and are eliminated on the element level. The equivalence and ‘near-equivalence’ between the mixed models developed herein and displacement models based on reduced/selective integration of both transverse shear and extensional energy terms is discussed. The use of reduction methods in conjunction with the mixed models is outlined and the advantages of mixed models over displacement models are delineated. Analytic expressions are derived for the rigid-body and spurious (or zero energy) models for the various mixed models and their equivalent displacement models. Also, the advantages of mixed models over equivalent displacement models are outlined. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed, and to compare their performance with other mixed models reported in the literature.

Computation of variance components using the em algorithm

Abstract: In their paper on maximum likelihood will) Incomplete data. Dempster. Laird, and Rubin (1977) noted that both maximum likelihood (ML) and restricted ML (REML) estimators of variance components in the mixed model analysis oi variance can be computed via the LM algorithm. Thi-follows from treating the random effects as missing data and using the incomplete data framework outlined in Dempster, et al. (1977). We elaborate on this idea, introducing a class of generalized ML estimates, indexed by a parameter τ, which contain REML and ordinary ML estimates as special limiting cases. This device enables us to derive a single set of iterative EM equations which yields either ML or REML estimates of the variance components, depending upon the value specified for τ.

Estimation of Mixed Weibull Parameters in Life Testing

Abstract: This paper deals with estimating parameters from a mixture of two Weibull distributions. The weighted least-squares method is used to estimate the parameters of the mixed model when data are grouped and censored. Simulation study of the variations of the weighted least-squares estimator has been carried out. A few examples have also been provided. Based on the simulation study, the weighted least-squares estimators are robust with respect to the number of intervals for the grouped data. The estimators of the scale parameters are quite sensitive to the censoring time, but those of the shape parameters are not as sensitive. This method provides a good alternative to the commonly used maximum likelihood estimators which are difficult to obtain and are frequently intractable. The techniques could easily be extended to a mixed model of more than two Weibull distributions and ungrouped and/or uncensored samples.

Canonical forms and tests of hypotheses: Part I: The general univariate mixed model

Abstract: A class of linear models is defined which contains many of the usual mixed and random models and allows the construction of tests for a wide class of hypotheses in a general manner. Characterizations are given for this class of models denoted as “regular linear models”. Problems of estimation are briefly touched and some aids to practical applications are given, followed by two examples.

Canonical forms and tests of hypotheses Part II: Multivariate mixed linear models

Abstract: In the literature on multivariate analysis of variance, exact test procedures are restricted to linear models with fixed effects only. In this paper tests are presented for multivarite linear hypotheses with respect to mixed models, which constitude a generalization of (univariate) regular models described by Roebruck (1982). Furthermore it is shown, that the matrices, which are used to compute the test statistics, can be derived from the univariate “sums of squares” in the same manner as in the case of fixed models. The applicability of this theory is demonstrated by two examples.

Extension of some models for positive-valued time series.

Abstract: : Time series models with autoregressive, moving average and mixed autoregressive-moving average correlation structure and with positive-valued non-normal marginal distribution are considered. First, a flexible mixed model GLARMA(p,q) with Gamma marginals is investigated. The correlation structure for several special cases is derived. For the first-order autoregressive case, GLAR(1), the conditional density of X sub n given X sub n-1 is derived. This leads to the formation of a likelihood function and a numerical approximation to and a simulation study of the maximum likelihood method of parameter estimation. Multivariate extensions of the model are considered briefly. Second, three methods for generating first-order moving average sequences with Exponential marginals are examined. These generalize the EMA (1) Exponential model. Negative correlation using antithetic variables is investigated in the moving average models. A preliminary analysis of wind speed data obtained over a 15-year period in the Gulf of Alaska is presented. A model with four harmonic deterministic mean multiplying random innovative factors modeled by a GLAR (1) process is developed. Correlograms and periodograms are used to determine the model for the mean and the structure of the innovation process. (Author)

Likelihood Under the Mixed Model for Quantitative Traits

Abstract: Mathematical details of obtaining the likelihood functions for testing hypotheses under the mixed model for quantitative traits are given. Since families are assumed to be chosen by the value of the trait of a particular family member, conditional distributions are required. Algorithms for efficient computation of the likelihood are given.