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Statistics Thursday Colloquium
(Seminar/Conference)
Host: Department of Statistics
Time: October 4, 2012, 3:30pm
Location: 300 Seitz Hall
Reception: Following the seminar, please join us for refreshments at Top of the Stairs (217 College Ave.)
Speaker: Netsanet T. Imam, Department of Biostatistics, State University of New York at Buffalo
Title: Factor Analysis Regression for Predictive Modeling with High-Dimensional Data
Abstract: We present factor-model based method to predict a univariate response, y, as a linear function of explanatory variables, x = (x1; x2; : : : ; xp), where the sample size, n, is less than p. We estimate the coefficient parameters of the model using bivariate common factor analysis. We compare the performance of the factor analysis (FA) regression with partial least squares (PLS) regression and principal component regression (PCR) under three underlying correlation structures: arbitrary correlation, factor model correlation structure, and when y is independent of x. Under each structure, we generated Monte Carlo training samples of sizes n < p from a multivariate normal distribution with parameters defining each of three underlying structures: arbitrary co-
variance matrix, FA covariance structure, and independence structure. Parameters were fixed at estimates obtained from analysis of a real datasets, assuming the parameter restrictions of the respective structures. Given the independence structure, we observe severe overfitting by PLS regression compared to FA regression and PCR. Under
the two dependent structures, FA regression has comparable average mean square error of prediction than PCR and PLS regression.
More information...
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231-5630