Title
Matrix--free Likelihood Method for Exploratory Factor Analysis with High-dimensional Gaussian Data
Degree Type
Creative Component
Semester of Graduation
Spring 2019
Department
Statistics
First Major Professor
Somak Dutta
Degree(s)
Master of Science (MS)
Major(s)
Statistics
Abstract
This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis (EFA) with high-dimensional Gaussian data. By implementing a Lanczos algorithm and a limited-memory quasi-Newton method, we develop a matrix free algorithm (HDFA) which does partial singular value decomposition (partial SVD) for data matrix where number of observations $n$ is typically less than the dimension $p$ and it only requires limited amount of memory during likelihood maximization. We perform simulation study with both the randomly generated models and the data-driven models. Results indicate that HDFA substantially outperforms the EM algorithm in all cases. Furthermore, Our algorithm is applied to fit factor models for a fMRI dataset with suicidal attempters, suicidal nonattempters and a control group.
Copyright Owner
Dai, Fan
Copyright Year
2019
File Format
Recommended Citation
Dai, Fan, "Matrix--free Likelihood Method for Exploratory Factor Analysis with High-dimensional Gaussian Data" (2019). Creative Components. 452.
https://lib.dr.iastate.edu/creativecomponents/452
