Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation techniques are rarely covered in introductory statistical texts. Because of the wide...

Generalized linear mixed models (GLMM) form a very general class of random effects models for discrete and continuous responses in the exponential family. They are useful in a variety of applications. The traditional likelihood approach for GLMM usually involves high dimensional integrations which are computationally intensive. In this work, we investigate the case of binary outcomes analyzed u...

Bijma et al. (2007a,b) presented a quantitative genetic theory of multilevel selection and showed how to estimate the relevant parameters using standard restricted maximum-likelihood (REML) methodology. Extending their results we develop a wider class of models that provide a more realistic framework for capturing the effects of interacting individuals. These models also make use of standard RE...

ABSTRACT The SAS ® procedure MIXED provides a single tool for analyzing a large array of models used in statistics, especially experimental design, through the use of REML estimation. A strategy for identifying mixed models is followed by a description of REML estimation along with a simple example that illustrates its advantages. A comparison of some of the available tests for variance compone...

AIM Intravascular ultrasound (IVUS) is a useful modality for visualizing atherosclerotic lesions in coronary arteries, not only for the degree of arterial luminal stenosis but also for the plaque composition within the vessel walls. We aimed to determine the relationship between the clinical parameters and coronary plaque characteristics evaluated by IVUS in patients with stable angina under me...

Residual maximum likelihood estimation (REML) is often preferred to maximum likelihood estimation as a method of estimating covariance parameters in linear models because it takes account of the loss of degrees of freedom in estimating the mean and produces unbiased estimating equations for the variance parameters. In this note it is shown that REML has an exact conditional likelihood interpret...

A unified frequency domain cross-validation (FDCV) method is proposed to obtain a heteroskedasticity and autocorrelation consistent (HAC) standard error. This enables model/tuning parameter selection across both parametric nonparametric spectral estimators simultaneously. The candidate class for this approach consists of restricted maximum likelihood-based (REML) autoregressive lag-weights with...

This paper considers double generalized linear models, which allow the mean and dispersion to be modelled simultaneously in a generalized linear model context. Estimation of the dispersion parameters is based on a χ1 approximation to the unit deviances, and the accuracy of the saddle-point approximation which underlies this is discussed. Approximate REML methods are developed for estimation of ...

Plant breeders traditionally have estimated genotypic and phenotypic correlations between traits using the method of moments on the basis of a multivariate analysis of variance (MANOVA). Drawbacks of using the method of moments to estimate variance and covariance components include the possibility of obtaining estimates outside of parameter bounds, reduced estimation efficiency, and ignorance o...

95 Estimating heritability, the proportion of variation in phenotypic values due to (additive) genetic effects, is an important subject matter to plant and animal breeders alike. In most applications there is not an analytic expression for the restricted maximum likelihood (REML) estimator of heritability since it is obtained via an iterative procedure. The focus of this paper is to find a clos...