A note on distributional properties of the Jöreskog-Sörbom fit indices

Abstract

Jöreskog-Sörbom fit indices, central and noncentral chi-square variables, structured covariance matrix, biasedness of GFI and AGFI, fit index for GLS estimate,

Developing and testing a measure for the ethical culture of organizations: the corporate ethical virtues model

“…As the GFI is sensitive to the number of estimated parameters, alternatives have been proposed such as the adjusted GFI (AGFI) and the parsimonious GFI (PGFI) by James, Mulaik, and Brett (1982), which correct the GFI by taking into account the number of parameters estimated and degrees of freedom. Other measures of fit, which are used by Hu and Bentler (1999) and Maiti and Mukherjee (1990), are the root of the mean of the squared residuals (differences between the observed and estimated correlations; RMSR), and the root mean square error of approximation (a measure of the discrepancy per degree of freedom; RMSEA), which should have values no larger than 0.06. Bentler's (1990) comparative fit index (CFI), which relates the (lack of) fit of the estimated model to that of a null model (the same model, but with covariances set equal to zero), is sometimes preferred to indicate goodness-of-fit (cf.…”

A test of the quasi-circumplex structure of human values

“…Additional free parameters did not improve the model Wt. Consistent with common practice (Byrne, 2001;Hu & Bentler, 1999), multiple indices were used to estimate model Wt, including (1) 2 likelihood ratio; (2) F 0 , the maximum likelihood discrepancy function, a measure of absolute Wt; (3) GFI (Jöreskog & Sörbom, 1986), which is analogous to a squared multiple correlation; (4) AGFI (Jöreskog & Sörbom, 1986), a parsimony weighted measure of model Wt (both GFI and AGFI were computed from formulas presented in Maiti & Mukherjee, 1990); and (5) RMSEA (Browne & Cudeck, 1992;Steiger & Lind, 1980), also a parsimony weighted measure of model Wt. Results are consistent with those of Tsai and Böckenholt (2002), who tested the SVS circumplex structure using Guttman's (1954) additive model, which is comparable to the Fourier series correlation functions used by CIRCUM (Browne, 1992).…”

Interpersonal Personality Measures Show Circumplex Structure Based on New Psychometric Criteria

“…We began by constraining the model to equal communality (i.e., constant radius) and equal spacing, then relaxed one constraint, then the other, then both. The indexes used to assess model fit were (a) the maximum-likelihood discrepancy function, (b) the chi-square likelihood ratio, (c) the root mean square error of approximation (RMSEA; Brown & Cudeck, 1992), (d) the goodness-of-fit index (GFI; Jöreskog & Sörbom, 1986), and (e) the adjusted GFI (AGFI; Jöreskog & Sörbom, 1986;Maiti & Mukherjee, 1990). Unlike the other measures of model fit, RMSEA and AGFI are parsimony-weighted indexes, which therefore take into account model complexity (i.e., the number of parameters estimated).…”