In principle there are three criteria according to which one may judge the signi…-cance or goodness of the model. The …rst and the obvious one is the magnitude and the direction of the parameter estimates and whether they are in accordance with underlying theory. The second, also related to the …rst one, is the statistical sig-ni…cance of individual parameter estimates, measured typically by the t-test. The third criteria are the global …t measures.
There are several …t criteria available for the SEM users, although they seem to be closely related to each other. 2 -test compares two models; the saturated, theoretical model, which includes all paths and the hypothesized model we impose.
Since the idea is to …nd an optimal parsimonious presentation on the true structures
in the data, the simplest model that conveys the information in the data would be ideal. A low and statistically insigni…cant 2-value suggests that our model resembles that of the saturated model. However, the 2 -test statistic is a¤ected by several factors, such as the sample and the model sizes, i.e., bigger the model the better the …t. Hence we also report other …t indices, albeit to some extent they su¤er from the same problems as they are derived from 2-tests.20
The normed …t index (NFI) is computed by comparing the 2-value of the null model (i.e. independence model, where the covariances are assumed to be zero in the model) and the hypothesized model, whereby N F I = ( 2null 2model)= 2null. The idea is to test how much better our hypothesized model performs compared with the null model. Conventionally a test value close to 0.95 indicates a good …t. The relative …t index is similar to NFI, but it accounts for the di¤erent decrees of freedom these two models have, whereby RF I = 1 [( 2model=dfmodel)=( 2null=dfnull)]. We also report Bentler’s comparative …t index (CFI), and Tucker-Lewis Index (TLI) which are written as to test the same hypothesis, i.e. they test the null of no latent variable against the alternative of latent variables existing, the former is a¤ected by the sample size as well as non-normality of the data (Bollen, 1990). TLI, in the other hand, has proven to be least a¤ected by the biasing factors (non-normality, small sample size, model complexity etc.).
Lastly to avoid the problems documented with the …t criteria related to 2 -test we report standardized root mean square residual (SRMR). The test re‡ects the closeness of the empirical covariance-variance matrix (S) and the model implied covariance matrix ( ). Comparing these two matrices reveals whether all the con-nections present in the data are presented in the model. The better the model
20AMOS 17 reports long list of …t indices. Since some of them are just new representations of the older …t indices, we report only those that seem to o¤er some new insights to the analysis.
re‡ects the data smaller the SRMR statistics. While there is no rule of thumb for the cut-o¤ value, values smaller than 0.05 are acceptable.
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