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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1510801791

Digital Object Identifier
doi:10.1214/17-EJS1360

Mathematical Reviews number (MathSciNet)
MR3724224

Zentralblatt MATH identifier
06816620

Subjects
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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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