View Submission - COMPSTAT2022

A0634
**Title: **A stochastic optimization algorithm for pairwise likelihood estimation of factor models with ordinal data
**Authors: **Giuseppe Alfonzetti - University of Padova (Italy) **[presenting]**

**Abstract: **The typical computational challenge of maximum likelihood estimation for non-linear latent variable models is the integration of the latent variables from their joint likelihood with the observed data. When tackled with a quadrature approach, the integration implies an exponential complexity in the dimension of the latent space. Moving to a pairwise likelihood estimator allows replacing this integral with the sum of many bidimensional problems. Unfortunately, their amount grows with the square of the number of items, which prevents the estimation to be feasible on large datasets. To solve this problem in the common case of ordinal data, a stochastic optimization algorithm is proposed in order to scale the estimation on large factor models. At each iteration, a cheap approximation to the gradient of the pairwise likelihood is computed by sampling a small subset from the complete pool of pairs. The complexity per iteration achieved does not depend on the sample size, grows only quadratically with the dimension of the latent space and potentially only linearly with the number of items.