Abstract:
This study is a critical review of theoreticalissues that underline the linear mixed effects
(LME) and nonlinear mixed effects (NLME) models. These two areas are revisited under
maximum likelihood and restricted maximumlikelihood estimation frameworks. We also
review methods of estimating parameters in both linear and nonlinear mixed effects models.
In the case of LME, we consider different ways of developing the likelihood estimators, key
among these methods are the “pseudo-data” approach, orthogonal triangular decomposition
method and the use of penalized least squares problem.
For NLME, we intended to investigate the computational efficiency and accuracy of computational methods, like the b-splines, that could be used to approximate the log-likelihood
function in non-linear mixed effects models. This was not achieved in this study but can
be an interesting area for further research work. We critically review the four methods of
estimating parameters by Pinheiro and Bates (1995) through proving a number of lemmas.
Our proves led us to same stated results by different researchers in different papers. This is a
key issue in the investigation of other expansion methods and comparing their computational
efficiency and accuracy with these existing ones.
We conclude by giving an insight into linear mixed effects models by analyzing a data set
from livestock where we examine incorporation of random effects to study variations among
rams (sires) and ewes (dams) and their influences on lamb weaning weight. Factors like year
of birth of the lamb, sex of lamb, age at weaning, age of dam, ewe breed and ram breed are
found to influence the weaning weight differently. With the random terms (ewes and rams)
specified in the model the estimate of the residual among lamb variance is found to reduce
due to taking into account the variations among rams and ewes within breeds. It was our
intention to obtain heritability estimates which determine the proportion of the variation
among offspring that have been handed down from parents out of these random estimates.
