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Dimension Reduction in Hierarchical Linear Models

In: Measurement and Multivariate Analysis

Author

Listed:
  • Yoshio Takane

    (McGill University)

  • Michael A. Hunter

    (University of Victoria)

Abstract

Summary In many disciplines of social sciences, data are often hierarchically structured. Academic performance may be measured of students who are nested in classes which are in turn nested within schools. Multi-level analysis based on the hierarchical linear model (HLM) has been effectively used to capture the hierarchical nature of such data. Most of the existing studies that employ HLM, however, use only a few predictor variables at all levels, because interpretation of parameters in HLM will become increasingly more difficult as the number of parameters increases. To alleviate the difficulty, we propose a method of reducing the dimensionality of the parameter space in HLM in a manner similar to reduced-rank regression models. We describe the two-level HLM, present a parameter estimation procedure and suggest where the rank-reduction may be applied. An example is given to illustrate the proposed method.

Suggested Citation

  • Yoshio Takane & Michael A. Hunter, 2002. "Dimension Reduction in Hierarchical Linear Models," Springer Books, in: Shizuhiko Nishisato & Yasumasa Baba & Hamparsum Bozdogan & Koji Kanefuji (ed.), Measurement and Multivariate Analysis, pages 145-154, Springer.
    • Handle: RePEc:spr:sprchp:978-4-431-65955-6_15
    DOI: 10.1007/978-4-431-65955-6_15
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