Statistics Project Review Of Methods Of Estimating Parameters In Nonlinear Mixed-Effects (Nlme) Models

Abstract.

This study is a critical review of theoretical issues that underline the linear mixed effects

(LME) and nonlinear mixed effects (NLME) models. These two areas are revisited under

maximum likelihood and restricted maximum likelihood 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.

Keywords: repeated-measures data, multilevel data, longitudinal data, LME, NLME, “pseudodata”

and b-splines.

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