Finite mixtures of simpler component models such as mixtures of normals and mixtures of generalized linear models (GLM) have proven useful for modelling data arising from a heterogeneous population, typically under an independence assumption. Mixed-effects models are often used to handle correlation as arises in longitudinal or other clustered data. In Chapter 3 of this dissertation, we present...

BACKGROUND Compared with normal subjects, depressed patients have shorter rapid eye movement sleep latency (REML), increased REM and decreased slow wave sleep as a percentage of total sleep time (REM%, SWS%), and longer sleep latency (SL). Obstructive sleep apnea (OSA) patients experience longer REML, decreased REM% and SWS%, and shorter SL. We examined the interplay of depressive symptoms, OSA...

Association-mapping methods promise to overcome the limitations of linkage-mapping methods. The main objectives of this study were to (i) evaluate various methods for association mapping in the autogamous species wheat using an empirical data set, (ii) determine a marker-based kinship matrix using a restricted maximum-likelihood (REML) estimate of the probability of two alleles at the same locu...

INTRODUCTION Estimation of covariance components by Restricted Maximum Likelihood (REML) fitting an animal model is widely carried out using a derivative-free (DF) algorithm to locate the maximum of the likelihood function. While such algorithms have proven robust and easy to use, they are generally slow to converge, often requiring many likelihood evaluations, in particular for multivariate an...

INTRODUCTION Maximising the (log) likelihood (logL) in restricted maximum likelihood (REML) estimation of variance components almost invariably represents a constrained optimisation problem. Iterative algorithms available to solve this problem differ substantially in computational resources needed, ease of implementation, sensitivity to choice of starting values and rates of convergence. One of...

Estimation of heritability is an important task in genetics. The use of linear mixed models (LMMs) to determine narrow-sense SNPheritability and related quantities has received much recent attention, due of its ability to account for variants with small effect sizes. Typically, heritability estimation under LMMs uses the restricted maximum likelihood (REML) approach. The common way to report th...