Social Limitation Structural Equation Model 16

vitality from the respective indicator of Anglo group vitality and by summing these to

form a composite score (alpha = .84).

The language group identity index, with one item removed for a total of three

items, posted a score of .63. And the Spanish mass media index (6 items) posted a

score of .89. The indices and items are summarized in Table 2.

TABLE 2 ABOUT HERE

**Results **

To test the model in Figure 2, we used structural equation modeling. This is a

procedure whereby the predicted covariance matrix is compared with the obtained

covariance matrix. The match between the two is assessed by means of a chi-square

test. A nonsignificant chi-square indicates that the model fits the data well. However,

this is not a reliable indicator. "With small samples, the computed

2

actually may not be

distributed as

2

, leading to inaccurate probability levels" (Tabachnick & Fidell, 1996, p.

748). A good fit may be indicated by a ratio of

2

to the degrees of freedom in the range

of 2 to 1 or 3 to 1 (Carmines & McIver, 1981). There are also a variety of measures of

model fit. One of the most widely used is the root mean square approximation

(RMSEA). A RMSEA of about .05 or less indicates a close fit of the model in relation to

the degrees of freedom (Browne & Cudeck, 1993). And also, the comparative fit index

(CFI) is a statistic that falls between 0 and 1. CFI values close to 1 indicate a very good

model fit to data (Arbuckle & Wothke, 1999). A similar interpretation is made when

using the Tucker Lewis Index (TLI).

The hypothesized model illustrated in Figure 1 is nonrecursive. This means that

it contains two structural equation models where the dependent variable of one equation