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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ahj.2004.09.031 Byline: Sidney C. Port (a)(b), Mark O. Goodarzi (c), Noel G. Boyle (d), Robert I. Jennrich (a) Abstract: The prognostic significance of blood glucose (BG) for nondiabetic patients in a stable chronic phase of cardiovascular disease (CVD) has been sparsely investigated, especially for glucose within the normal range. In particular, it is unknown if for these patients there is a graded relation of mortality to glucose or if there is a lower threshold. Author Affiliation: (a) Department of Statistics, University of California Los Angeles, Calif (b) Department of Mathematics, University of California Los Angeles, Calif (c) Division of Endocrinology, Diabetes, and Metabolism, Cedars-Sinai Medical Center and Department of Medicine, David Geffen School of Medicine at University of California Los Angeles, Calif (d) Division of Cardiology, Department of Medicine, David Geffen School of Medicine at University of California Los Angeles, Calif Article History: Received 5 May 2004; Accepted 20 September 2004

Likelihood profiles for arbitrary functions of the model parameters are useful for constructing likelihood ratio confidence intervals, diagnosing linear approximation intervals, suggesting linearizing transforms, and many other purposes. This article [...]

An extension of the profile t plot proposed by D.M. Bates and D.G. Watts, the signed root deviance profile (SRDP), that constructs likelihood ratio (LR) confidence intervals for a parametric function g(theta) in a maximum likelihood analysis is considered. Specifically, the SRDP's applications are demonstrated. These include the transformation of parametric functions whose linear approximation intervals approximate their LR intervals when inverted., We investigate a natural extension of the profile t plot of Bates and Watts to a general parametric function g([Theta]) of the parameters [Theta] in a general maximum likelihood analysis. [...]

Gradient direction plots, profile T plots and bias indices can be used to indicate transformations of parameter functions that have enhanced linear approximation interval coverage probabilities. The three have slight differences, therefore leading to ease of application as the main factor for selection. The BR bias index is the least effective for applications due to difficulties it poses in computing., We investigate linear approximation (LA) confidence intervals for functions g([theta]) of the parameters [theta] in a nonlinear regression model. These intervals are almost universally used and generally perform well, but [...]

Linear approximation confidence intervals in a nonlinear regression model are investigated to determine why they sometimes exhibit poor coverage probabilities. The results show that the linear approximation interval is invariant under reparameterization conditions. The use of profile t plots and asymmetry and bias indices for diagnosing linear approximation intervals is also investigated., 1. INTRODUCTION Linear approximation (LA) confidence intervals are very popular in statistical applications. They appear most often as an estimate and standard error obtained by linear approximation methods. Their use [...]

The evolutionary success of individuals must ultimately be evaluated in terms of their lifetime contribution of mature young to the breeding population. The greater lifetime breeding success of the more dominant hens in an unconfined flock of Red Junglefowl (Gallus gallus) gave crucial evidence why female dominance hierarchies have evolved in this species. The number of chicks reared to independence by 28 hens of one flock from 1982 to 1988 was significantly associated with a hen's dominance, life-span, and year of hatching. Of these, dominance was by far the most important factor. It, by itself, could explain differences in the number of chicks reared as shown by log-linear analysis. This suggests that the associations with life-span and year of hatching may result from the fact that these are correlated with dominance. The top 3 hens in the peck order added more offspring of breeding age to the population than did the remaining 25 adult hens of the flock. Eleven of the 28 hens reared no young successfully.

The popularity of the EM algorithm in the computation of maximum likelihood estimates is due to its simplistic applications. However, it often exhibits slow convergence. An alternative method for conjugate gradient acceleration of the EM algorithm is proposed. The technique treats an EM step as a generalized gradient while a generalized conjugate gradient algorithm will be an EM accelerator. This method is relatively simple and is applicable to problems having a large number of parameters.

The EM algorithm is a very popular and widely applicable algorithm for the computation of maximum likelihood estimates. Although its implementation is generally simple, the EM algorithm often exhibits slow convergence and is costly in some areas of application. Past attempts to accelerate the EM algorithm have most commonly been based on some form of Aitken acceleration. Here we propose an alternative method based on conjugate gradients. The key, as we show, is that the EM step can be viewed (approximately at least) as a generalized gradient, making it natural to apply generalized conjugate gradient methods in an attempt to accelerate the EM algorithm. The proposed method is relatively simple to implement and can handle problems with a large number of parameters, an important feature of most EM algorithms. To demonstrate the effectiveness of the proposed acceleration method, we consider its application to several problems in each of the following areas: estimation of a covariance matrix from incomplete multivariate normal data, confirmatory factor analysis, and repeated measures analysis. The examples in these areas demonstrate promise for the new acceleration method. In terms of operation counts, for all of the examples considered the accelerated EM algorithm increases the speed of the EM algorithm, in some cases by a factor of 10 or more. In the context of repeated measures analysis, we give a new EM algorithm that, compared to earlier algorithms, can have a considerably smaller cost per iteration. We have not, however, attempted to evaluate the performance of this latter algorithm here. KEY WORDS: Factor analysis; Incomplete data; Repeated measures., 1. INTRODUCTION The EM algorithm is a general approach to the computation of maximum likelihood estimates (Dempster, Laird, and Rubin 1977). An attractive feature of EM algorithms is their simplicity [...]