Electronic Journal of Statistics

Approximate likelihood inference in generalized linear latent variable models based on the dimension-wise quadrature

Silvia Bianconcini, Silvia Cagnone, and Dimitris Rizopoulos

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We propose a new method to perform approximate likelihood inference in latent variable models. Our approach provides an approximation of the integrals involved in the likelihood function through a reduction of their dimension that makes the computation feasible in situations in which classical and adaptive quadrature based methods are not applicable. We derive new theoretical results on the accuracy of the obtained estimators. We show that the proposed approximation outperforms several existing methods in simulations, and it can be successfully applied in presence of multidimensional longitudinal data when standard techniques are not applicable or feasible.

Article information

Electron. J. Statist., Volume 11, Number 2 (2017), 4404-4423.

Received: September 2017
First available in Project Euclid: 16 November 2017

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Primary: 62H25: Factor analysis and principal components; correspondence analysis 62F12: Asymptotic properties of estimators 62P10: Applications to biology and medical sciences 62P25: Applications to social sciences

Binary variables Laplace approximation longitudinal data $M$-estimators numerical integration random effects

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Bianconcini, Silvia; Cagnone, Silvia; Rizopoulos, Dimitris. Approximate likelihood inference in generalized linear latent variable models based on the dimension-wise quadrature. Electron. J. Statist. 11 (2017), no. 2, 4404--4423. doi:10.1214/17-EJS1360. https://projecteuclid.org/euclid.ejs/1510801791

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