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Constructing Common Factors from Continuous and Categorical Data

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  • Serena Ng

Abstract

The method of principal components is widely used to estimate common factors in large panels of continuous data. This article first reviews alternative methods that obtain the common factors by solving a Procrustes problem. While these matrix decomposition methods do not specify the probabilistic structure of the data and hence do not permit statistical evaluations of the estimates, they can be extended to analyze categorical data. This involves the additional step of quantifying the ordinal and nominal variables. The article then reviews and explores the numerical properties of these methods. An interesting finding is that the factor space can be quite precisely estimated directly from categorical data without quantification. This may require using a larger number of estimated factors to compensate for the information loss in categorical variables. Separate treatment of categorical and continuous variables may not be necessary if structural interpretation of the factors is not required, such as in forecasting exercises.

Suggested Citation

  • Serena Ng, 2015. "Constructing Common Factors from Continuous and Categorical Data," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1141-1171, December.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:1141-1171
    DOI: 10.1080/07474938.2014.956625
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    1. Almlund, Mathilde & Duckworth, Angela Lee & Heckman, James & Kautz, Tim, 2011. "Personality Psychology and Economics," Handbook of the Economics of Education, in: Erik Hanushek & Stephen Machin & Ludger Woessmann (ed.), Handbook of the Economics of Education, edition 1, volume 4, chapter 0, pages 1-181, Elsevier.
    2. Filmer, Deon & Pritchett, Lant, 1998. "Estimating wealth effects without expenditure data - or tears : with an application to educational enrollments in states of India," Policy Research Working Paper Series 1994, The World Bank.
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    Cited by:

    1. Benjamin Williams, 2018. "Identification of the Linear Factor Model," Working Papers 2018-002, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    2. Wang, Fa, 2017. "Maximum likelihood estimation and inference for high dimensional nonlinear factor models with application to factor-augmented regressions," MPRA Paper 93484, University Library of Munich, Germany, revised 19 May 2019.
    3. Evan Munro & Serena Ng, 2022. "Latent Dirichlet Analysis of Categorical Survey Responses," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 256-271, January.
    4. Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
    5. Wang, Fa, 2022. "Maximum likelihood estimation and inference for high dimensional generalized factor models with application to factor-augmented regressions," Journal of Econometrics, Elsevier, vol. 229(1), pages 180-200.
    6. Evan M. Munro & Serena Ng, 2020. "Latent Dirichlet Analysis of Categorical Survey Expectations," NBER Working Papers 27182, National Bureau of Economic Research, Inc.

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