Approximate Likelihood Inference via Dimension Reduction in Latent Variable Models

• Activity Number: 168
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Silvia Cagnone*+ and Silvia Bianconcini and Dimitris Rizopoulos
• Companies: University of Bologna and University of Bologna and Erasmus University Medical Center
• Keywords: latent variable models ; Laplace approximation ; binary data ; dimension reduction method ; adaptive quadrature

Abstract

Latent variable models represent a useful tool in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In these cases, problems related to the integration of the likelihood function of the model can arise since analytical solutions do not exist. Usually, numerical quadrature based methods like Gauss Hermite or adaptive Gauss-Hermite are used to overcome this problem. They work quite well in several situations, but become unfeasible in presence of many latent variables and/or random effects. We propose an alternative approach based on a reduction in the dimensionality of the integrals involved in the computations that allows for significant computational savings. This approach is based on a fundamental theorem by Rahaman and Xu (2004) who provide a convenient way to represent the Taylor series expansion of the integrand up to a specific order without involving any partial derivative. We discuss the application of the method in latent variable models for multidimensional binary data.