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A Structural Equation Model of Support for English-only Policies and Social Limitation of Immigrants and Minorities
Unformatted Document Text:  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

Authors: Barker, Valerie. and Giles, Howard.
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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


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