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Factor analysis parameter estimation from incomplete data

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  • Roberts, W.J.J.

Abstract

An expectation–maximization (EM) algorithm for factor analysis parameter estimation when observations are missing is developed. In contrast to existing EM algorithms for this problem, the algorithm here is developed assuming the missing observations are not part of the complete data in the EM formulation. The resulting algorithm provides increased computational efficiency through sparse matrix operations. The algorithm is demonstrated on two sparse, high-dimensional data sets that are prohibitively large for existing algorithms: the Netflix movie recommendation data set and the Yahoo! musical item data set. The resulting factor models are applied to predict missing values using conditional mean estimation, achieving root mean square errors of 0.9001 and 24.08 on the Netflix and Yahoo! data sets, respectively.

Suggested Citation

  • Roberts, W.J.J., 2014. "Factor analysis parameter estimation from incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 61-66.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:61-66
    DOI: 10.1016/j.csda.2013.08.018
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    References listed on IDEAS

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    1. Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 69-76, March.
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    1. Forzani, Liliana & García Arancibia, Rodrigo & Llop, Pamela & Tomassi, Diego, 2018. "Supervised dimension reduction for ordinal predictors," Computational Statistics & Data Analysis, Elsevier, vol. 125(C), pages 136-155.
    2. Jianhua Zhao & Changchun Shang & Shulan Li & Ling Xin & Philip L. H. Yu, 2025. "Choosing the number of factors in factor analysis with incomplete data via a novel hierarchical Bayesian information criterion," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 19(1), pages 209-235, March.
    3. Nikolaos Zirogiannis & Yorghos Tripodis, 2018. "Dynamic factor analysis for short panels: estimating performance trajectories for water utilities," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 131-150, March.

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