Abstract
It is common to encounter latent variables with ordinal data in social or behavioral research. Although a mediated effect of latent variables (latent mediated effect, or LME) with ordinal data may appear to be a straightforward combination of LME with continuous data and latent variables with ordinal data, the methodological challenges to combine the two are not trivial. This research covers model structures as complex as LME and formulates both point and interval estimates of LME for ordinal data using the Bayesian full-information approach. We also combine weighted least squares (WLS) estimation with the bias-corrected bootstrapping (BCB; Efron Journal of the American Statistical Association, 82, 171–185, 1987) method or the traditional delta method as the limited-information approach. We evaluated the viability of these different approaches across various conditions through simulation studies, and provide an empirical example to illustrate the approaches. We found that the Bayesian approach with reasonably informative priors is preferred when both point and interval estimates are of interest and the sample size is 200 or above.
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Notes
The BCB method cannot be implemented in Mplus up to now.
The MCMC engine in Mplus was not well understood and studied, as compared with that in the more-accessible BUGS program, when we conducted the simulation study.
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Acknowledgments
This research was supported by the Humanities and Social Sciences Research Grant from the Ministry of Education in China. Grant No.: 14YJA880005.
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Appendix A: BUGS code of the Bayesian approach for LME with ordinal data
Appendix A: BUGS code of the Bayesian approach for LME with ordinal data
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Chen, J., Zhang, D. & Choi, J. Estimation of the latent mediated effect with ordinal data using the limited-information and Bayesian full-information approaches. Behav Res 47, 1260–1273 (2015). https://doi.org/10.3758/s13428-014-0526-3
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DOI: https://doi.org/10.3758/s13428-014-0526-3