Abstract
Generalized structured component analysis has been proposed as an alternative to partial least squares for path analysis with latent variables. In practice, observed and latent variables may often be hierarchically structured in that their individual-level scores are grouped within higher-level units. The observed and latent variable scores nested within the same higher-level group are likely to be more similar than those in different groups, thereby giving rise to the interdependence of the scores within the same group. Unless this interdependence is taken into account, obtained solutions are likely to be biased. In this paper, generalized structured component analysis is extended so as to account for the nested structures of both observed and latent variables. An alternating least-squares procedure is developed for parameter estimation. An empirical application concerning the measurements of customer-level customer satisfaction nested within different companies is presented to illustrate the usefulness of the proposed method.
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The work reported in this paper was supported by Grant 290439 and Grant 10630 from the Natural Sciences and Engineering Research Council of Canada to the first and second authors, respectively. We wish to thank Claes Fornell for generously providing us with the ACSI data.
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Hwang, H., Takane, Y. & Malhotra, N. Multilevel Generalized Structured Component Analysis. Behaviormetrika 34, 95–109 (2007). https://doi.org/10.2333/bhmk.34.95
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DOI: https://doi.org/10.2333/bhmk.34.95