IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v118y2023i542p1385-1401.html
   My bibliography  Save this article

Generalized Factor Model for Ultra-High Dimensional Correlated Variables with Mixed Types

Author

Listed:
  • Wei Liu
  • Huazhen Lin
  • Shurong Zheng
  • Jin Liu

Abstract

As high-dimensional data measured with mixed-type variables gradually become prevalent, it is particularly appealing to represent those mixed-type high-dimensional data using a much smaller set of so-called factors. Due to the limitation of the existing methods for factor analysis that deal with only continuous variables, in this article, we develop a generalized factor model, a corresponding algorithm and theory for ultra-high dimensional mixed types of variables where both the sample size n and variable dimension p could diverge to infinity. Specifically, to solve the computational problem arising from the non-linearity and mixed types, we develop a two-step algorithm so that each update can be carried out in parallel across variables and samples by using an existing package. Theoretically, we establish the rate of convergence for the estimators of factors and loadings in the presence of nonlinear structure accompanied with mixed-type variables when both n and p diverge to infinity. Moreover, since the correct specification of the number of factors is crucial to both the theoretical and the empirical validity of factor models, we also develop a criterion based on a penalized loss to consistently estimate the number of factors under the framework of a generalized factor model. To demonstrate the advantages of the proposed method over the existing ones, we conducted extensive simulation studies and also applied it to the analysis of the NFBC1966 dataset and a cardiac arrhythmia dataset, resulting in more predictive and interpretable estimators for loadings and factors than the existing factor model.

Suggested Citation

  • Wei Liu & Huazhen Lin & Shurong Zheng & Jin Liu, 2023. "Generalized Factor Model for Ultra-High Dimensional Correlated Variables with Mixed Types," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1385-1401, April.
  • Handle: RePEc:taf:jnlasa:v:118:y:2023:i:542:p:1385-1401
    DOI: 10.1080/01621459.2021.1999818
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2021.1999818
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01621459.2021.1999818?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:118:y:2023:i:542:p:1385-1401. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.