Linear Mixed Model Framework Research Articles

The Use of Linear Mixed Models to Estimate Variance Components from Data on Twin Pairs by Maximum Likelihood

It is shown that maximum likelihood estimation of variance components from twin data can be parameterized in the framework of linear mixed models. Standard statistical packages can be used to analyze univariate or multivariate data for simple models such as the ACE and CE models. Furthermore, specialized variance component estimation software that can handle pedigree data and user-defined covariance structures can be used to analyze multivariate data for simple and complex models, including those where dominance and/or QTL effects are fitted. The linear mixed model framework is particularly useful for analyzing multiple traits in extended (twin) families with a large number of random effects.

The Use of Linear Mixed Models to Estimate Variance Components from Data on Twin Pairs by Maximum Likelihood

It is shown that maximum likelihood estimation of variance components from twin data can be parameterized in the framework of linear mixed models. Standard statistical packages can be used to analyze univariate or multivariate data for simple models such as the ACE and CE models. Furthermore, specialized variance component estimation software that can handle pedigree data and user-defined covariance structures can be used to analyze multivariate data for simple and complex models, including those where dominance and/or QTL effects are fitted. The linear mixed model framework is particularly useful for analyzing multiple traits in extended (twin) families with a large number of random effects.

A Monte Carlo EM algorithm for generalized linear mixed models with flexible random effects distribution.

A popular way to represent clustered binary, count, or other data is via the generalized linear mixed model framework, which accommodates correlation through incorporation of random effects. A standard assumption is that the random effects follow a parametric family such as the normal distribution; however, this may be unrealistic or too restrictive to represent the data. We relax this assumption and require only that the distribution of random effects belong to a class of 'smooth' densities and approximate the density by the seminonparametric (SNP) approach of Gallant and Nychka (1987). This representation allows the density to be skewed, multi-modal, fat- or thin-tailed relative to the normal and includes the normal as a special case. Because an efficient algorithm to sample from an SNP density is available, we propose a Monte Carlo EM algorithm using a rejection sampling scheme to estimate the fixed parameters of the linear predictor, variance components and the SNP density. The approach is illustrated by application to a data set and via simulation.

Association and linkage for age at onset of a common oligogenic disease using genetic variance component models.

The aims of our analysis were: (1) to investigate association of single nucleotide polymorphisms (SNPs) and other covariates with age at onset in the simulated Genetic Analysis Workshop (GAW) 12 general population data, and (2) to use the polygenic random effects estimated during model fitting (sigma squared A random effects) as input to a Haseman-Elston linkage analysis. The association analyses used genetic variance component models in a generalized linear mixed models framework and were fitted using Gibbs sampling. This method successfully detected the only three sequenced genes that were also major genes. The single-point linkage analysis used all markers provided. Regions of linkage were found close to all four of the sites of major genes that explained a non-trivial component of the variance of age at onset. In all four cases the linkage peak fell within 5 cM of the true location. In three cases the peak significance was p < 0.01.

Linear and threshold model genetic parameters for disease, fertility and milk production in dairy cattle

AbstractThis study provides estimates of genetic parameters for various diseases, fertility and 305-day milk production traits in dairy cattle using data from a UK national milk recording scheme. The data set consisted of 63891 multiple lactation records on diseases (mastitis, lameness, milk fever, ketosis and tetany), fertility traits (calving interval, conception to first service, number of services for a conception, and number of days to first service), dystocia and 305-day milk, fat and protein yield. All traits were analysed by multi-trait repeatability linear animal models (LM). Binary diseases and fertility traits were further analysed by threshold sire models (TM). Both LM and TM analyses were based on the generalized linear mixed model framework. The LM included herd-year-season of calving (HYS), age at calving and parity as fixed effects and genetic, permanent environmental and residual effects as random. The TM analyses included the same effects as for LM, but HYS effects were treated as random to avoid convergence problems when HYS sub-classes had 0 or 100% incidence. Because HYS effects were treated as random, herd effects were fitted as fixed effects to account for effect of herds in the data. The LM estimates of heritability ranged from 0•389 to 0•399 for 305-day milk production traits, 0•010 to 0•029 for fertility traits and 0•004 to 0•038 for diseases. The LM estimates of repeatability ranged from 0•556 to 0•586 for 305-day milk production traits, 0•029 to 0•086 for fertility traits and 0•004 to 0•100 for diseases. The TM estimates of heritabilities and repeatabilities were greater than LM estimates for binary traits and were in the range 0•012 to 0•126 and 0•013 to 0•168, respectively. Genetic correlations between milk production traits and fertility and diseases were all unfavorable: they ranged from 0•07 to 0•37 for milk production and diseases, 0•31 to 0•54 for milk production and poor fertility and 0•06 to 0•41 for diseases and poor fertility. These results show that future selection programmes should include disease and fertility for genetic improvement of health and reproduction and for sustained economic growth in the dairy cattle industry.

The Effect of Drop-Out on the Efficiency of Longitudinal Experiments

SUMMARY It is shown that drop-out often reduces the efficiency of longitudinal experiments considerably. In the framework of linear mixed models, a general, computationally simple method is provided, for designing longitudinal studies when drop-out is to be expected, such that there is little risk of large losses of efficiency due to the missing data. All the results are extensively illustrated using data from a randomized experiment with rats.

Using a Generalized Linear Mixed Model to Analyze Dichotomous Choice Contingent Valuation Data

Willingness-to-pay (WTP) responses from dichotomous choice contingent valuation studies are often modeled using logistic regression, from which estimates of mean or median WTP are calculated. However, a great many factors influence an individual's WTP, some of which may be unobserved. Hence, the regression model may have inadequate explanatory power, and parameter estimates may be biased and their significance overestimated. The effects of this overdispersion are examined within a generalized linear mixed modeling framework, and an example given using published data from Cooper and Loomis (1992).