arXiv subjects

Helen Ogden

Publications and source records attributed to Helen Ogden.

5 recordsLinked to original sources

arXiv2024

Adaptively-structured mixed models for simple clustered data

We propose adaptively-structured mixed models for simple clustered data. Like classical mixed-effects models, they share information between clusters through random effects, but they estimate the associated design functions from the data rather than requiring them to be specified in advance. This retains the mixed-effects mechanism for information sharing while allowing the structure to adapt flexibly to the data. We establish consistency and asymptotic normality for population-level estimation and show that cluster-specific predictions are asymptotically as accurate as predictions based on the true population structure. In simulations, adaptively-structured mixed models substantially improve the quality of inference relative to existing general-purpose methods while remaining computationally efficient. An application to body-fat data from adolescent girls illustrates how the method captures both the average pattern over time and variation between individuals.

stat.ME↗

arXiv2018

On the error in Laplace approximations of high-dimensional integrals

Laplace approximations are commonly used to approximate high-dimensional integrals in statistical applications, but the quality of such approximations as the dimension of the integral grows is not well understood. In this paper, we prove a new result on the size of the error in first- and higher-order Laplace approximations, and apply this result to investigate the quality of Laplace approximations to the likelihood in some generalized linear mixed models.

math.ST↗

arXiv2016

On asymptotic validity of naive inference with an approximate likelihood

Many statistical models have likelihoods which are intractable: it is impossible or too expensive to compute the likelihood exactly. In such settings, a common approach is to replace the likelihood with an approximation, and proceed with inference as if the approximate likelihood were the exact likelihood. In this paper, we describe conditions on the approximate likelihood which guarantee that this naive inference with an approximate likelihood has the same first-order asymptotic properties as inference with the exact likelihood. We investigate the implications of these results for inference using a Laplace approximation to the likelihood in a simple two-level latent variable model, and using reduced dependence approximations to the likelihood in an Ising model on a lattice.

math.ST↗

arXiv2014

A sequential reduction method for inference in generalized linear mixed models

The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when the model is sparse, in that there is only a small amount of information available on each random effect. The sequential reduction method described in this paper exploits the dependence structure of the posterior distribution of the random effects to reduce substantially the cost of finding an accurate approximation to the likelihood in models with sparse structure.

stat.CO↗

arXiv2014

Robustness properties of marginal composite likelihood estimators

Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full distribution of the response, which means that in some situations the resulting estimator will be more robust to model misspecification than the maximum likelihood estimator. The purpose of this note is to show that such increased robustness is not guaranteed. An example is given in which various marginal composite likelihood estimators are inconsistent under model misspecification, even though the maximum likelihood estimator is consistent.

math.ST↗