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The SEM statistic root mean square error of approximation (RMSEA) expresses the
lack of fit due to reliability and model specification or misspecification. The RMSEA
expresses fit per degree of freedom of the model and should be less than 0.10 for
acceptable fit, with .05 or lower indicating a very good-fitting model. The goodness-offit
index (GFI) and adjusted goodness-of-fit index (AGFI), which adjust for the number
of parameters estimated, range from 0 to 1, with values of 0.9 or greater indicating a
good-fitting model (Joreskog and Sorbom, 2003).) These two indexes are analogous to
R 2 in multiple regression analysis, which is the estimated relationship between a
dependent variable and more than one explanatory variable. GFI and AGFI are affected
by sample size and can be large for models that are poorly specified. The current
consensus is not to use these measures (Klein, 2004).
RMSEA, the discrepancy per degree of freedom, is included in most discussions of
SEM as a good estimate of goodness of fit (Chen, et al., 2008; Garson, n.d.;
Schumacker and Lomax, 2004: 82). RMSEA has a range from 0 to 1; some say values
of 0.08 or less are desired, others, other values (Hu and Bentler, 1999). A perfectly
fitting model would yield a RMSEA of 0.0; some researchers say a good model fit is
generally accepted if RMSEA is less than or equal to 0.05. However, Chen, Curran,
Bollen, Kirby, and Paxton (2008) evaluated the choice of fixed cut-off points in
assessing the RMSEA test statistic as a measure of goodness-of-fit. The results of their
study indicate that there is little empirical support for the use of 0.05 or any other values
as universal cut-off values to determine adequate model fit, regardless of whether the
point estimate is used alone or jointly with the confidence interval. Chen et al.’s
analyses suggested that to achieve a certain level of power or Type I error rate (finding a
difference in a sample when there is none in the population), the choice of cut-off values
depends on model specifications, degrees of freedom, and sample size. The results of
their analyses indicate that an appropriate value for RMSEA for a correctly specified
model is about 0.078 for rejection of the null hypothesis of lack of fit with a confidence
level of p=0.05
RMSEA is a popular measure of fit, partly because it does not require comparison with
a null model and thus does not require the researcher posit as plausible a model in which
there is complete independence of the latent variables (note that Schwartz’ SSA-derived
cultural values model yield correlated, non-orthogonal SEM models). Also, RMSEA
has a known distribution, related to the non-central chi-square distribution, and thus
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