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Testing multivariate normality for two-level structural equation models
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DOI：10.1016/j.jmva.2025.105562.png)
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Abstract
En 中文
Multivariate normality is a common assumption in the maximum likelihood analysis of two-level structural equation models. Under the normal assumption, the independence condition on level-1 observations is no longer satisfied. As a result, existing statistics for testing multivariate normality based independent observations cannot be directly used for the same purpose in two-level structural equation models. In this paper we tackle this problem by employing the theory of spherical matrix distributions and some properties of invariant statistics. A series of necessary tests are constructed from some existing invariant statistics with a balanced level-1 sample design. These necessary tests are applicable without requiring a large level-1 or level-2 sample size. A Monte Carlo study is carried out to demonstrate the performance of the proposed tests in the aspects of controlling type I error rates, the power against a departure from multivariate normality for level-1 variables, and the power against a departure from multivariate normality for level-2 variables. An application of the necessary tests to a practical data set is illustrated.
Keywords:
Invariant statistics
Left-spherical matrix distribution
Multivariate normality
Necessary test
Two-level structural equation model
Journal
J
IF:
1.7
Papers:
97
Citations:
5.8K
