Abstract/Details

BEHAVIOR OF SOME ELLIPTICAL THEORY ESTIMATORS WITH NONNORMAL DATA IN A COVARIANCE STRUCTURES FRAMEWORK: A MONTE CARLO STUDY (ROBUSTNESS, MAXIMUM LIKELIHOOD, ASYMPTOTICALLY DISTRIBUTION FREE)

HARLOW, LISA LAVOIE.   University of California, Los Angeles ProQuest Dissertations Publishing,  1985. 8519103.

Abstract (summary)

A large Monte Carlo study was conducted to study the behavior of elliptical estimators in a covariance structures framework. For comparison purposes, the normal theory estimator, ML, and the more general estimator, ADF, were also utilized. The behavior of the estimators was examined under multivariate normality as well as twelve different conditions of nonnormality. The nonnormality conditions differed with regard to the values for univariate skewness and kurtosis that were assigned to the variables. Over the thirteen conditions, skewness ranged from -2.0 to +2.0, with kurtosis ranging from -1.0 to +8.0.

Two sample sizes of 400 and 200 were utilized in each of the 13 conditions, as were two versions of a small confirmatory factor analysis model. The first version, labelled Model A, was an example of a small model that was invariant under a constant scaling factor (ICSF). The second version, labelled Model B, was an example of a non-ICSF model where the six factor loadings were fixed apriori at specified values.

The widely used normal theory estimator, ML, appeared to behave rather well over the 13 conditions in terms of parameter estimates and chi-square statistics when analyzing Model A with 200 or 400 subjects. The standard errors for ML, however, appeared to be biased when using nonnormal data.

The more general ADF estimator performed as well or better than ML under the same conditions of nonnormality with one exception. ADF appears to require more subjects than ML and it is recommended that at least 400 or more subjects are utilized.

The elliptical estimators that utilize the Mardia-based kappa (i.e., E(,1) and CML1) may provide adequate results when examining non-ICSF models or when the degrees of freedom and the number of subjects are fairly large. The elliptical estimators, however, seem to have a tendency to over-correct for positive kurtoses and under-correct for negative kurtoses. Although the parameter estimates appear to be relatively unbiased under nonnormality, the chi-square statistic and the standard errors are more sensitive to kurtosis in the data.

Indexing (details)


Subject
Psychological tests;
Quantitative psychology
Classification
0632: Quantitative psychology
Identifier / keyword
Psychology
Title
BEHAVIOR OF SOME ELLIPTICAL THEORY ESTIMATORS WITH NONNORMAL DATA IN A COVARIANCE STRUCTURES FRAMEWORK: A MONTE CARLO STUDY (ROBUSTNESS, MAXIMUM LIKELIHOOD, ASYMPTOTICALLY DISTRIBUTION FREE)
Author
HARLOW, LISA LAVOIE
Number of pages
221
Degree date
1985
School code
0031
Source
DAI-B 46/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-204-24058-2
University/institution
University of California, Los Angeles
University location
United States -- California
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8519103
ProQuest document ID
303360947
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303360947/A880C451A61A4D6EPQ