| The mixed effects linear model contains two types of parameters: one is thefixed effect parameters, and the other is the random effects part of the variancecomponent parameters. Many papers discussed the linear mixed model, randomeffects part of the general requirements of which are subject to the standard statedistribution, in this condition the parameters of which make various estimates.In this paper, on this basis, the main research discussed in the linear mixedmodel, random effects is not only the case of the standard normal distribution,respectively, for these two types of parameter estimation and testing.For the fixed effects model parameter estimation, this paper first proposed away to bring different linear mixed model is transformed into a linear model to meetthe assumptions, on this basis, according to different circumstances, of which thefixed effects parameters are least-squares estimation; when the model in a strongmulti-collinearity, the corresponding ridge estimate of their doing, and compare theleast-squares estimation and the pros and cons between the ridge estimation; whenone is not independent random variables When, through the transformation of themodel, find the generalized least squares parameter estimation.The QR decomposition of the design matrix can be made in the estimation ofvariance components to simplify operations, save memory and other effects, thispaper models to a certain transformation to the design matrix for QR decomposition.In the estimation of variance components, using the results to further simplify thecalculation.For the model of the random effects variance component estimates, manypapers have proposed many alternatives, this article on this basis, this article on therandom effects model in different parts of the distribution of cases, the study anddiscussion of the ANOVA estimates of variance components, MINQUE estimates,maximum likelihood estimation to restrict the maximum likelihood estimation, aswell as the spectral decomposition estimate. |
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