The effects of subject-to-variable ratio, measurement scale, and number of factors on the stability of the factor model

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Educational Research

First Committee Member

Richard H. Williams, Committee Chair

Second Committee Member

Edward B. Applegate, Committee Member


The purpose of this study was to examine the stability of the factor model when the following characteristics of the data were changed: number of factors, measurement scales, subject-to-variable ratio (svr), and the failure to use asymptotic covariances (AC) for non-continuous data.To study the effects, congeneric measurement models were simulated in three different factor structures (2-factor, 4-factor, 6-factor) with theta-delta = 0.95, phi = 0.5, lambda = 0.9 with 12 variables using a Monte Carlo process. The stability of each factor structure was investigated when the following conditions were systematically varied: measurement characteristics--the use of continuous, ordinal, or nominal (dichotomous) data; a systematic variation in the svrs--(2:1 to 1000:1); and the inclusion or omission of an AC matrix in conjunction with either ordinal or nominal data. Confirmatory factor analysis (CFA) procedures were performed on each simulated model with the different data characteristics, svr, and use of AC using LISREL8 (Joreskog & Sorbom, 1993b) and PRELIS 2 (Joreskog & Sorbom, 1993a). Therefore, for each of the factor structures and svrs studied, the results obtained from CFA were for the following: (a) continuous, (b) ordinal without AC, (c) ordinal with AC, (d) dichotomous without AC, and (e) dichotomous with AC. The analysis was then carried out using six goodness-of-fit indices: (a) chi-square, (b) GFI, (c) AGFI, (d) RMR, (e) AIC, and (f) ECVI, with replications performed as necessary.The results indicated that when continuous data were used, factor stability was achieved in all three factor models (2-factor, 4-factor, 6-factor) with a svr of 9:1. When ordinal data were factored, stability in the three models was achieved at a svr of 10:1 when the AC was not included, and 20:1 when the AC was included. When dichotomous data were factored without the AC, none of the models estimated reached a stable level even at the 1000:1 svr. However, when the AC was included a svr of 20:1 was needed in all three factors.Thus, it was found that the stability of the factor model was not affected by the number of factors, but was affected by measurement properties, svr, and use or non-use of AC for non-continuous data.


Education, Tests and Measurements; Education, Educational Psychology; Psychology, Psychometrics

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