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本文研究既含有固定效应又含有随机效应的线性混合模型，在随机效应的方差不同即异方差情况下，即考虑方差受外界因素的影响，如温度、湿度等，我们称之为协变量，在有协变量情况下对方差建立对数线性模型，运用最大似然估计讨论了固定效应的估计和随机效应的预测，并且用约束最大似然（REML）方法研究对数线性模型中参数和随机误差中参数（离差参数）的估计，并讨论估计量的性质及离差参数估计量的渐近正态性。“,”In this paper we study linear mixed model with fixed effects and random effects. Under the heteroscedasticity, we consider the variance is affected by environment, for example, temperature or humidity, we call them covariates. We study the log-linear models of variance with covariates. We discuss the estimation of fixed effects and prediction of random effects using the maximum likelihood estimation, and study the estimation of dispersion parameter with restricted maximum likelihood（REML） method. The properties of estimators and the asymptotic properties of dispersion estimators is presented, is proposed.