A Dimension Reduction Method for Approximating Integrals in Latent Variable Models for Binary Data Silvia Bianconcini and Silvia Cagnone and Dimitris Rizopoulos Abstract Latent variable models for binary data 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. One problem related to these models is that the integrals involved in the maximiza- tion of the likelihood function are not solvable analytically. In the literature, one of the most common way to solve this problem is represented by techniques based on numerical integration. However, generally they present computational burden that increases as the number of latent variable increases. The aim of this study is to propose an alternative approach based on a reduction in the dimensionality of the integrals involved in the computations with significant computational savings. This approach is based on a fundamental theorem by [3] and consists of reducing the dimensionality of the integrals involved in the compu- tations. Key words: latent variables, Gauss Hermite quadrature, Laplace approximation, maximum likelihood estimation 1 The problem Latent variable models (LVM) occupy a prominent place in the social sciences where the analyzed constructs are often not directly observable and hence not di- rectly measurable. Usually, a set of indicators assumed to be related to each unob- served variable can be measured. If these indicators are discrete, problems related Silvia Bianconcini, Department of Statistics, University of Bologna e-mail: sil- via.bianconcini@unibo.it Silvia Cagnone, Department of Statistics, University of Bologna e-mail: silvia.cagnone @unibo.it Dimitris Rizopoulos, Department of Biostatistics, Erasmus University Rotterdam e-mail: d.rizopoulos@erasmusmc.nl 1