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Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested designs. We explore the modifications that are required in order to adapt an EM algorithm with first-order and fully exponential Laplace approximations to a non-nested, multiple response model. The equations in the estimation routine are expressed as functions of the first four derivatives of the conditional likelihood of an arbitrary GLMM, providing a template for future applications. We apply the method to a joint Poisson-binary model for ranking sporting teams, and discuss the estimation of a correlated random effects model designed to evaluate the sensitivity of value-added models for teacher evaluation to assumptions about the missing data process. Source code in R is provided in the online supplementary material.

The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the design of experiments for likelihood estimation of parameters in the conditional model. We provide two novel approximations that substantially reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes, or Monte Carlo approximations thereof: (i) an asymptotic approximation which is accurate when there is strong dependence between observations in the same block; (ii) an approximation via Kriging interpolators. For logistic random intercept models, we show how interpolation can be especially effective for finding pseudo-Bayesian designs that incorporate uncertainty in the values of the model parameters. The new results are used to provide the first evaluation of the efficiency, for estimating conditional models, of optimal designs from closed-form approximations to the information matrix derived from marginal models. It is found that correcting for the marginal attenuation of parameters in binary-response models yields much improved designs, typically with very high efficiencies. However, in some experiments exhibiting strong dependence, designs for marginal models may still be inefficient for conditional modelling. Our asymptotic results provide some theoretical insights into why such inefficiencies occur.

Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the variability in the data is not adequately described by the models, which often exhibit a prescribed mean--variance link, and (2) the accommodation of hierarchical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various members of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these phenomena may occur simultaneously, models combining them are uncommon. This paper proposes a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. We place particular emphasis on so-called conjugate random effects at the level of the mean for the first aspect and normal random effects embedded within the linear predictor for the second aspect, even though our family is more general. The binary, count and time-to-event cases are given particular emphasis. Apart from model formulation, we present an overview of estimation methods, and then settle for maximum likelihood estimation with analytic--numerical integration. Implications for the derivation of marginal correlations functions are discussed. The methodology is applied to data from a study in epileptic seizures, a clinical trial in toenail infection named onychomycosis and survival data in children with asthma.

LibriVox volunteers bring you 14 recordings of <em>Convention</em> by Agnes Lee. This was the weekly poetry project for December 21st, 2008.

<i>A Phantom Lover</i> is a supernatural novella by Vernon Lee (pseudonym of Violet Paget) first published in 1886. Set in a Kentish manor house, the story concerns a portrait painter commissioned by a squire, William Oke, to produce portraits of him and his wife, the eccentric Mrs. Alice Oke, who bears a striking resemblance to a woman in a mysterious, seventeenth century painting. (Summary by Anthony Leslie)

<p>An early example of the female private detective, Jennette Lee’s Millicent Newberry made her first appearance in The Green Jacket in 1917 and was also featured in two later books, The Mysterious Office in 1922 and Dead Right in 1925. Miss Newberry brings her own unique perspective to her cases, only accepting those where she has a say in what happens to the guilty party. She is rarely without her knitting, using it as a technique to put clients and suspects alike at ease, while also knitting her notes on the case into the pattern! In The Green Jacket, Millie goes undercover to solve a case involving a stolen emerald necklace that, despite the efforts of other detectives, including her former boss, Tom Corbett, has never been recovered. (Summary by J. M. Smallheer)

4Lost Art of Reading

By Gerald Stanley Lee

Gerald Stanley Lee speaks here-in of books and self in the time of factories, tall buildings and industry and big city making, the effects of modern civilization on the individual. - Summary by Joseph Tabler

5Anecdotes of the Habits and Instinct of Animals

By Mrs. Robert Lee

Stories about unusual interactions between animals and humans that reflect some attitudes to the wild in the mid-eighteen hundreds, including trophy hunting.<br><br>"Chronically ill and often in pain," the author, Mary Custis Lee, experienced "hardship with sturdy and radiant faith." Maybe that's why she did not turn away in this book, from unpleasant and often gory accounts of animal encounters. (Summary by Czandra)

6Hauntings

By Vernon Lee

"Hence, my four little tales are of no genuine ghosts in the scientific sense; they tell of no hauntings such as could be contributed by the Society for Psychical Research, of no specters that can be caught in definite places and made to dictate judicial evidence. My ghosts are what you call spurious ghosts (according to me the only genuine ones), of whom I can affirm only one thing, that they haunted certain brains, and have haunted, among others, my own and my friends'—yours, dear Arthur Lemon, along the dim twilit tracks, among the high growing bracken and the spectral pines, of the south country; and yours, amidst the mist of moonbeams and olive-branches, dear Flora Priestley, while the moonlit sea moaned and rattled against the moldering walls of the house whence Shelley set sail for eternity." (Summary by Vernon Lee from the Preface)

Muna Lee was a poet, novelist, translator and activist. This collection, first published in 1923, explores themes of love and place. - Summary by Newgatenovelist

By the age of 30, Alexander III of Macedon, commonly known as Alexander the Great, had mastered a vast empire. But the brilliant young warrior-king was unable to master his own passions or those of his generals and closest friends and advisors. Court intrigue thus threatened to undo all that Alexander had managed to do. <BR><BR> Considered one of Nathaniel Lee's best tragedies, [i]The Rival Queens, or, The Death of Alexander the Great[/i] dramatizes a story of the rivalry between Alexander the Great's two wives: Roxana, his first, and Statira, who displaced her. The play was first performed at London's Theatre Royal by the King's Company. It was influenced by Gauthier de Costes, seigneur de la Calprenède's, [i]Cassandre[/i]. - Summary by Brian Fullen