Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects

By Sophia Rabe-Hesketh, A. Skrondal, Andrew Pickles. 2005

760 citations recorded by the source corpus.

Abstract Gauss–Hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models. Unfortunately, the estimates are biased for large cluster sizes and/or intraclass correlations. We show that adaptive quadrature largely overcomes these problems. We then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables. The models can include several nested random effects (intercepts and coefficients) representing unobserved heterogeneity at different levels of a hierarchical dataset. The required multivariate integrals are evaluated efficiently using spherical quadrature rules. Simulations show that adaptive quadrature performs well in a wide range of situations.

Subfields: Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9fb5356ffcf9f820c10feab4e33b77e2d2fc4649

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In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Handbook of multilevel analysis (2008, methodology): “For example, the standard estimation method for generalized linear models is IRLS [82] and it can be used to compute estimators based on “robust” loss functions, which are less sensitive to outliers [48].”
High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature (2005, background): “Similar considerations apply in other multilevel treatments of binary and polytomous data (see Hedeker and Gibbons, 1994), a fact confirmed by a number of recent papers on generalized linear mixed models (Lesaffre and Spiessens, 2001; Rabe-Hesketh, Skrondal, and Pickles 2002, 2005b ).”
Bayesian Multilevel Analysis and MCMC (2008, background): “[56] for the original, and larger, data set).”
Correlation and studies of habitat selection: problem, red herring or opportunity? (2010, background): “distance as a covariate) Hjermann (2000); Rhodes et al. (2005), Johnson et al.”
Human capital in social and commercial entrepreneurship (2016, positive): “In this case, the independence assumption does not hold, and a multi-level, random effects model should be employed (Peterson et al., 2012; Rabe-Hesketh et al., 2005).”
Modeling Ordered Choices: A Primer and Recent Developments (2008, neutral): “[See, also, Sanko et al. (2004) who looked at ownership of cars and motorcycles.”
Modelling wildlife–human relationships for social species with mixed‐effects resource selection models (2007, methodology): “We derived maximum-likelihood estimates (MLEs) in GLLAMM using adaptive quadrature ( Rabe-Hesketh, Skrondal & Pickles 2005 ) with 12 integration points.”