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Two‐level analysis of covariance structures for unbalanced designs with small level‐one samples
Author(s) -
Lee SikYum,
Poon WaiYin
Publication year - 1992
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1992.tb00980.x
Subject(s) - covariance , estimator , statistic , goodness of fit , mathematics , lisrel , statistical inference , statistics , analysis of covariance , statistical hypothesis testing , test statistic , econometrics , structural equation modeling
The main purpose of this paper is to develop basic statistical theory for two‐level analysis of covariance structures. Major asymptotic results for statistical inference, such as the asymptotic distributions of the estimator and the goodness‐of‐fit test statistic are derived, based on an unbalanced design with only small numbers of level‐one units. Computationally, it is shown that the solution can be obtained via standard programs, such as LISREL, EQS and COSAN. The behaviour of the estimates is illustrated by an artificial example and a real‐life example. Some possibilities of extending the results to a more general two‐level model, and to situations with arbitrary distributions and elliptical distributions are also investigated.