Generalizability theory and common factor analysis are based upon the random effects model of the analy sis of variance, and both are subject to the factor inde terminacy problem: The unobserved random variables (common factor scores or universe scores) are indeter minate. In the one-facet (repeated measures) design, the extent to which true or universe scores and com mon factor scores are not uniquely defined is shown to be a function of the dependability (reliability) of the data. The minimum possible correlation between equivalent common factor scores is a lower bound es timate of reliability.
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References
1.
Bock, R.D. (1960). Components of variance analysis as a structural and discriminal analysis for psychological tests. British Journal of Statistical Psychology, 13, 151-163.
2.
Burt, C. (1947). A comparison of factor analysis and analysis of variance. British Journal of Psychology, Statistical Section , 1, 3-26.
3.
Cattell, R.B. (1973). Personality and mood by questionnaire: A handbook of interpretive theory, psycho-metrics, and practical procedures. San Francisco: Jossey-Bass.
4.
Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysisfor the behavioral sciences (2nd ed.). Hillsdale NJ: Lawrence Erlbaum.
5.
Cohen, J., & Nee, J.C.M. (1984). Estimators for two measures of association for set correlation. Educational and Psychological Measurement , 44, 907-917.
6.
Comrey, A.L. (1973). A first course in factor analysis. New York: Academic Press.
7.
Creasy, M.A. (1957). Analysis of variance as an altemative to factor analysis, Journal of the Royal Statistical Society, Series B (Methodological), 19, 318-325.
8.
Cronbach, L.J., Gleser, G.C., Nanda, H., & Rajaratnam, N. (1972). The dependability of behavioral measurements. New York: Wiley.
9.
Guttman, L. (1955). The indeterminacy of factor score matrices with implications for five other basic problems of common-factor theory. British Journal of Statistical Psychology, 8, 65-82.
10.
Heermann, E.F. (1966). The algebra of factorial indeterminacy. Psychometrika, 31, 539-543.
11.
Jensen, A.R. (1983). The definition of intelligence and factor-score indeterminacy. The Behavioral and Brain Sciences, 6, 313-315.
12.
Lord, F., & Novick, M. (1968). Statistical theories of mental test scores. Reading MA: Addison-Wesley.
13.
McDonald, R.P. (1974). The measurement of factor indeterminacy. Psychometrika, 39, 203-222.
14.
McDonald, R.P. (1977). The indeterminacy of components and the definition of common factors. British Journal of Statistical Psychology , 30, 165-176.
15.
McKeon, F.M. (1969). Relations among canonical reliability, canonical factor analysis, and multivariate association. Psychometrika Monograph Supplement, 34 (No. 15).
16.
Mulaik, S.A. (1972). The foundations of factor analysis. New York: McGraw-Hill.
17.
Mulaik, S.A., & McDonald, R.P. (1978). The effect of additional variables on factor indeterminacy in models with a single common factor. Psychometrika, 43, 177-192.
18.
Schönemann, P.H. (1971). The minimum average correlation between equivalent sets of uncorrelated factors. Psychometrika, 36, 21-30.
19.
Schönemann, P.H. (1983). Do IQ tests really measure intelligence?The Behavioral and Brain Sciences, 6, 311-313.
20.
Schönemann, P.H., & Wang, M.M. (1972). Some new results on factor indeterminacy. Psychometrika, 37, 61-91.
21.
Steiger, J.H., & Schönemann, P.H. (1978). A history of factor indeterminacy . In S. Shye (Ed.), Theory construction and data analysis in the social sciences (pp. 136-178). San Francisco: Jossey-Bass.
22.
Winer, B.J. (1971). Statistical principles in experimental design . New York: McGraw-Hill.
