Identification, parameter restrictions and equivalence in factor analysis models.
Item
-
Title
-
Identification, parameter restrictions and equivalence in factor analysis models.
-
Identifier
-
AAI9325140
-
identifier
-
9325140
-
Creator
-
Rose, Tedd.
-
Contributor
-
Adviser: David Rindskopf
-
Date
-
1993
-
Language
-
English
-
Publisher
-
City University of New York.
-
Subject
-
Education, Educational Psychology | Education, Tests and Measurements
-
Abstract
-
Factor analysis is a popular data analysis methodology that summarizes a large quantity of observed variables with a smaller number of observed variables. It is used in such fields as education, psychology, sociology, and marketing, with variables representing such areas as aptitude, intelligence, personality, values, and attitudes.;This work examines issues of identification, parameter restrictions, and equivalence among four commonly used factor analysis models: one-factor, second-order, group-factor, and bi-factor. The comparisons were conducted in two settings: one with six observed measures, the other with nine. (Identification was also examined with twelve observed measures.).;The initial issue that was examined was the identification of each of the four factor analysis models. Identification deals with the ability to solve for unknown parameters in a model in terms of the elements of the known covariance matrix. Algebraic proofs were provided for identified models; in such situations, solutions were presented for the model parameters in terms of the elements of the population variance-covariance matrix. Guidelines useful in establishing model identification were discussed. In situations where a model is not identified, efforts were made to identify it.;Parameter restrictions and relaxations were explored for the four models wherein one model was examined as being possibly more- (or less-) restricted than another. A quasi-hierarchy of models was demonstrated for models with both six and nine observed measures.;In certain special cases, parameter restrictions in a model may lead to models which are equivalent, instead of more-restricted. Two models are said to be equivalent when there is a one-to-one transformation between their respective estimated parameters. For two models to be equivalent they must estimate the same number of parameters; however, this is not a sufficient condition for equivalence to occur. Model equivalence was established by demonstrating the existence of identical restrictions between the observed variances and covariances between the models.;As a result of the equivalence, or non-discriminability, between models the choice of model acceptance would be made on the basis of theoretical plausibility or parsimony, rather than a comparison between model goodness-of-fit test statistics.
-
Type
-
dissertation
-
Source
-
PQT Legacy CUNY.xlsx
-
degree
-
Ph.D.
