Boosting originated as a machine learning procedure developed for classification purposes. In the statistical approach to boosting, it was then viewed as a method for fitting a statistical model by sequentially minimizing an objective loss function. Early stopping criteria are fundamental to obtain regularized estimates and to prevent overfitting. The component-wise version of the algorithm also performs variable selection since, at each step, only the coefficients of the covariate that most improves the fit are updated. However, the non-convexity of the likelihood function of latent variable models poses new challenges. Focusing on factor analysis models for binary data, we propose a new algorithm that exploits the directions of negative curvature. To reduce the computational burden, a pairwise likelihood was chosen as an objective function, and a group lasso penalty was included in order to automatically select the number of latent variables in the procedure. Starting with a model that includes only the thresholds, at each step only two coefficients are updated after selecting either a Newton-type direction or a negative curvature direction. The solution attained tends to be sparse, thus facilitating interpretation without requiring a posterior rotation of the factor loadings.
about the speaker
Michela Battauz is an associate professor of statistics at the University of Udine (Italy). She received her PhD in statistics from the University of Padua. Her research interest include latent variable models, item response theory, equating, mixed effects models, measurement error models and statistical learning. Her research has been published in international journals such as Psychometrika, Journal of Educational and Behavioral Statistics, Journal of Statistical Software, Multivariate Behavioral Research, British Journal of Mathematical and Statistical Psychology, Computational Statistics & Data Analysis.