In this example we use the dclus2 two-stage cluster sample from the California Academic Performance Index, which was created in an earlier example. The syntax and options for svyglm are the same for designs with and without replicate weights.
The outcome variable is 2000 API, predicted by the proportions of students learning English (ell), receiving subsidized means (means) and having moved to the school within the past year (mobility). This is a linear regression model, so no family argument to svyglm is needed.
> summary(svyglm(api00 ~ ell + meals + mobility, design = dclus2))
Call:
svyglm.survey.design(formula = api00 ~ ell + meals + mobility,
design = dclus2)
Survey design:
svydesign(id = ~dnum + snum, weights = ~pw, data = apiclus2)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 811.4907 30.8795 26.279 <2e-16 ***
ell -2.0592 1.4075 -1.463 0.146
meals -1.7772 1.1053 -1.608 0.110
mobility 0.3253 0.5305 0.613 0.541
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 8296.727)
Number of Fisher Scoring iterations: 2
A useful property of regression models is that they provide another way to get domain estimates. Suppose we want the mean of api00 for each school type:
> summary(svyglm(api00~stype-1, dclus2))
Call:
svyglm.survey.design(formula = api00 ~ stype - 1, design = dclus2)
Survey design:
svydesign(id = ~dnum + snum, weights = ~pw, data = apiclus2)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
stypeE 692.81 30.28 22.88 <2e-16 ***
stypeH 598.34 16.96 35.27 <2e-16 ***
stypeM 642.35 45.34 14.17 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 17389.33)
Number of Fisher Scoring iterations: 2
> svyby(~api00,~stype,dclus2,svymean, keep.var=TRUE)
stype statistic.api00 SE
E E 692.8104 30.28244
H H 598.3407 16.96500
M M 642.3520 45.34363
This equivalence helps in thinking about domain estimators and how they handle more complex designs.