Structural Model
The next step in SEM is construction of a structural model that fits the data as well
as the final measurement model with fewer estimated parameters. The structural model is
that component of the general model that prescribes relations between latent variables
and observed variables that are not indicators of latent variables. In general, the multiple
regression model is a structural model without latent variables and limited to a single
outcome. However, SEM that includes the combinations of the measurements and
structural components allows a comprehensive statistical model that can be used to
evaluate relations among variables that are free of measurement error (Hoyle, 1995). The
chi-square statistic included in Table 4-11 provides a test of the null hypothesis that the
reproduced variance matrix has the specified model structure (i.e., that the model fit the
data). First, the chi-square test for the model was statistically significant, X2 (66)=
1708.237, p< .05, indicating a good fit between the model and data. However, several
researchers (Bollen, 1989; Bollen & Long, 1993; Joreskog & Sorbom, 1996) noted that
the chi-square statistic is influenced by a large sample size (for this data set N= 210). In
fact, Joreskog and Sorgom (1996) proposed that X2 be used as badness rather than a
goodness-of-fit measure in the sense that a small X2 value (relative to its degrees of
freedom) is indicative of good fit, whereas a large X2 value reflects bad fit in SEM
(Byrne, 1998). Therefore, four additional goodness of fit indices were considered for
testing a goodness of fit of SEM model. The criteria for four other indices are listed: CFI
shows a good fit at .95 or higher; RMSEA should be between .08 or lower to indicate
good model fit (Hu & Bentler, 1999); NFI and NNFI should be close to 1.0 and show a
good fit at .90 or higher. These indices except RMSEA range from 0.00 to 1.00, with