Mean Comparison: Manifest Variable Versus Latent Variable |
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Authors: | Ke-Hai Yuan Peter M Bentler |
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Institution: | (1) University of Notre Dame, USA;(2) University of California, Los Angeles;(3) Department of Psychology, University of Notre Dame, Notre Dame, IN 46556, USA |
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Abstract: | Mean comparisons are of great importance in the application of statistics. Procedures for mean comparison with manifest variables
have been well studied. However, few rigorous studies have been conducted on mean comparisons with latent variables, although
the methodology has been widely used and documented. This paper studies the commonly used statistics in latent variable mean
modeling and compares them with parallel manifest variable statistics. Our results indicate that, under certain conditions,
the likelihood ratio and Wald statistics used for latent mean comparisons do not always have greater power than the Hotelling
T2 statistics used for manifest mean comparisons. The noncentrality parameter corresponding to the T2 statistic can be much greater than those corresponding to the likelihood ratio and Wald statistics, which we find to be different
from those provided in the literature. Under a fixed alternative hypothesis, our results also indicate that the likelihood
ratio statistic can be stochastically much greater than the corresponding Wald statistic. The robustness property of each
statistic is also explored when the model is misspecified or when data are nonnormally distributed. Recommendations and advice
are provided for the use of each statistic.
The research was supported by NSF grant DMS-0437167 and Grant DA01070 from the National Institute on Drug Abuse.
We would like to thank three referees for suggestions that helped in improving the paper. |
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Keywords: | noncentrality parameter likelihood ratio statistic Wald statistic empirical power parameter bias asymptotic robustness |
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