If you specify the WLLCHISQ option in the TABLES statement, PROC SURVEYFREQ computes a Wald test for independence based on the log odds ratios. See the section Wald Chi-Square Test for more information about Wald tests.
For a two-way table of rows and
columns, the Wald log-linear test is based on the
array of elements
,
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where is the estimated total for table cell
. The null hypothesis of independence between the row and column variables can be expressed as
for all
and
. This null hypothesis can be stated equivalently in terms of cell proportions.
The generalized Wald log-linear chi-square statistic is computed as
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where is the
array of the
, and
estimates the variance of
,
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where is the covariance matrix of the estimates
, which is computed as described in the section Covariance of Totals.
is a diagonal matrix with the estimated totals
on the diagonal, and
is the
by
linear contrast matrix.
Under the null hypothesis of independence, the statistic approximately follows a chi-square distribution with
degrees of freedom for large samples.
PROC SURVEYFREQ computes the Wald log-linear statistic as
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Under the null hypothesis of independence, approximately follows an
distribution with
numerator degrees of freedom. PROC SURVEYFREQ computes the denominator degrees of freedom as described in the section Degrees of Freedom. Alternatively, you can specify the denominator degrees of freedom with the DF= option in the TABLES statement.
For tables larger than , PROC SURVEYFREQ also computes the adjusted Wald log-linear
statistic as
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where , and
is the denominator degrees of freedom computed as described in the section Degrees of Freedom. Alternatively, you can specify the value of
with the DF= option in the TABLES statement. Note that for
tables,
, so the adjusted Wald
statistic equals the (unadjusted) Wald
statistic, with the same numerator and denominator degrees of freedom.
Under the null hypothesis, approximately follows an
distribution with
numerator degrees of freedom and
denominator degrees of freedom.