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the more likely the rejection of the model and the more likely a Type II error. Thus,
as the case here, with large samples, even small differences between the observed
model and the perfect-fit model may be found significant. One fit index that is less
sensitive to sample size is the chi-square/
df
statistic (Bryant & Yarnold, 2001). In
the factor analysis reported above, the value of
2
/
df
was 2.77, within acceptable
χ
limits.
Multiple-group CFA
. For this aspect of the analysis, we selected the two ethnic
groups focused on in the study, including White (
n
=
1,156, 32.8%) and Latino
=
(
n
1,125, 31.9%). Our confirmatory factor analysis next dealt with the question
of whether the nine measures were equivalent across the White and Latino/a sub-
groups. The assumption of structural equivalence was tested using a multi-group
CFA that allows factorial invariance across groups. Testing for factorial invariance
involves comparing a set of models in which factor structure and factor loadings are
held equal across groups and assessing fit indices when elements of these structures
are constrained (Marsh et al., 2006). Thus, we developed an initial baseline model
(Model 1), which is totally non-invariant in that there were no assumptions being
made about group invariance across groups. Then we imposed invariance constraints
for factor loadings and factor means (Model 2), and factor variances (Model 3).
Model 1 examined whether the items in each of the nine factors were grouped
in accordance with theoretical expectations (
2
χ
=
3,199.21,
df
=
1,792,
p
=
0.000,
2
/df
χ
0.04). Model 2 tested whether
factor loadings and factor means were the same across groups. This model is impor-
tant because a minimal criterion for structural equivalence is that the factor loadings
relating each indicator to its hypothesized factor are the same across all groups.
(
=
2.14, CFI
=
0.95, TLI
=
0.95, RMSEA
=
2
2
/df
χ
=
3,360.47,
df
=
1,837,
p
=
0.000,
χ
=
1.83, CFI
=
0.947, TLI
=
0.943,
RMSEA
0.039). The difference in chi-square between the constrained and uncon-
strained models was significant (
=
2
45,
p<
0.000); however, the
differences in RMSEA and other fit indices were very small.
We then tested the assumption that factor variances as well as factor loadings
and factor means were equal across groups (Model 3). The most restrictive model
provided a good fit to the data (
Δχ
=
161.26,
Δ
df
=
2
2
/df
χ
=
=
=
χ
=
3,397.08,
df
1,855,
p
0.000,
1.83, CFI
0.039), and the Bayesian Information
Criteria (BIC) showed that this model best fit to the data. Although all three models
showed good fit, Model 3 is most parsimonious in terms of number of parameters
to be estimated. In summary, there was good support for the invariance of factor
loadings, factor means, and factor variances across White and Latino/a groups.
=
0.946, TLI
=
0.943, RMSEA
=
Structural Equation Model Analysis
SEM MIMIC model for Latino and White students
. An approach based on a
multiple-indicator-multiple-indicator cause model (MIMIC; Kaplan, 2000, Jöreskog
& Sörbom, 1993) was used for evaluating relations between motivational and
learning strategy factors and background variables. This extended SEM MIMIC
