Estimation in Generalized Mixed Models

Abstract

Regression models containing fixed and random effects may have a response variable which is not normally distributed. The generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model. Best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures. Applications in modelling discrete response variables and in survival analysis are discussed.

Restricted likelihood inference for generalized linear mixed models

“…Our approach should not be confused with other proposals, for instance McGilchrist (1994) or Noh and Lee (2007), which consider different types of estimators and do not share the invariance to reparameterization property of the modified profile likelihood. We conjecture that, in many instances, our solution may yield results similar to those obtained from the most accurate proposals in Noh and Lee (2007).…”

“…This first simulation study is based on the same setting adopted in McGilchrist (1994). The simulated data refer to a logistic regression model with a random intercept, and are generated according to a two-step procedure.…”

Modelling heterogeneity for bivariate survival data by the log-normal distribution

“…A further advantage is that a power transformation of the frailty still gives a log-normal distribution. In most cases, the frailty term is assumed to have log-normal distribution (See McGilchrist and Aisbett (1991), McGilchrist (1993, 1994, Yau andMcGilchrist (1998), andNoh et al (2006). ).…”

“…The first part is maximized to obtain ML estimates of the fixed effects and second part is free of the fixed effects. Maximizing the second component yields MHL and restricted maximum hierarchical likelihood (RMHL) estimators of σ 2 given bŷ Schall (1991) and McGilchrist (1993McGilchrist ( , 1994.…”

Matched Case Control Studies with Random Exposure Effects

“…This is further extended in Schall (1991), Breslow and Clayton (1993), Wolfinger (1993), McGilchrist andAisbett (1991), andMcGilchrist (1994) to generalised linear mixed models. This line of development is essentially based on the penalised quasi-likelihood (PQL) approach.…”