1,721,021 research outputs found
Reliable generalized linear latent variable models estimation via simulated maximum likelihood
No full textA LAPLACE APPROXIMATION APPROACH FOR p2 NETWORK REGRESSION MODELS WITH CROSSED RANDOM EFFECTS
No full textMaximum likelihood estimation based on the Laplace approximation for p2 network regression models with crossed random effects
No full textThe class of p2 models is suitable for modelling binary relation data in social network analysis. A p2 model is essentially a regression model for multinomial responses, featuring within-dyad dependence and correlated crossed random effects to represent heterogeneity of actors. It has some desirable properties, including simple generation of networks from a given model specication, or the possibility of extension to multilevel data structures. Despite these points, this class of models is used much less frequently in empirical applications than other models for network data. A possible reason for this fact may lie in the computational difficulties existing to estimate such models. The estimation methods proposed in the literature for estimating the parameters of p2 models include joint maximization methods and Bayesian methods based on MCMC, both with some drawbacks. The aim of this paper is to investigate maximum likelihood estimation based on the Laplace approximation approach, that may be equipped with importance sampling. Practical implementation requires some attention, but it can be performed in an efficient manner, and the paper provides details on software implementation using R and ADMB. Numerical examples and simulation studies illustrate the methodology
A comparison of scalable estimation methods for large-scale logistic regression models with crossed random effects
Full text linkParameter estimation of generalized linear models with crossed random effects for large-scale settings is hampered by challenging numerical hindrances. This contribution focuses on logistic regression with crossed-random intercepts and it investigates the properties of two estimation methods for which a scalable software implementation exists, namely the all-row-column and penalized quasi- likelihood methods. The results of a simulation study for sparse settings inspired by e-commerce data, with sample sizes up to 10^6, suggest that the all-row-column method is preferable over penalized quasi-likelihood
Restricted likelihood inference for generalized linear mixed models
No full textWe aim to promote the use of the modified profile likelihood function for estimating the variance parameters of a GLMM in analogy to the REML criterion for linear mixed models. Our approach is based on both quasi-Monte Carlo integration and numerical quadrature, obtaining in either case simulation-free inferential results. We will illustrate our idea by applying it to regression models with binary responses or count data and independent clusters, covering also the case of two-part models. Two real data examples and three simulation studies support the use of the proposed solution as a natural extension of REML for GLMMs. An R package implementing the methodology is available online
A comparison of unconstrained parameterisations for additive mean and covariance matrix modelling
No full textCovariance models for multivariate normal data must ensure the positive definiteness of the covariance matrix. Computational scalability for handling large samples is further desirable. We propose flexible covariance modelling by reparameterising the covariance matrix according to two different approaches, namely the matrix logarithm and the modified Cholesky decomposition. The performances of the proposed additive covariance models (ACM) are compared on an electricity load modelling application
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