This example is taken from Lehtonen and Pahkinen’s Practical Methods for Design and Analysis of Complex Surveys.
page 107 Table 3.14 Model-assisted estimation results for the population total of ue91 from an SRS sample of eight elements drawn from the Province’91 population.
data page106; input id str clu wt ue91 meanz hou85 diffhou85 smplrat; fpc = 32; datalines; 1 1 1 4 4123 2867 26881 -24014 .25 2 1 4 4 760 2867 4896 -2029 .25 3 1 5 4 721 2867 3730 -863 .25 4 1 15 4 142 2867 556 2311 .25 5 1 18 4 187 2867 1463 1404 .25 6 1 26 4 331 2867 1946 921 .25 7 1 30 4 127 2867 834 2033 .25 8 1 31 4 219 2867 932 1935 .25 ; run;
strategy: design-based estimator with srs
proc descript data = page106 filetype = sas design = wor totals deft; weight wt; nest _one_; totcnt fpc; var ue91; run;
Number of observations read : 8 Weighted count : 32 Denominator degrees of freedom : 7 Variance Estimation Method: Taylor Series (WOR) by: Variable, One. ----------------------------------------------------- | | | | Variable | | One | | | 1 | ----------------------------------------------------- | | | | | UE91 | Sample Size | 8 | | | Weighted Size | 32.00 | | | Total | 26440.00 | | | SE Total | 13282.26 | | | Mean | 826.25 | | | SE Mean | 415.07 | | | DEFF Mean #4 | 0.75 | | | DEFF Total #4 | 0.75 | -----------------------------------------------------
strategy: poststratified estimator with srs*pos
proc descript data = page106 filetype = sas design = wor totals; weight wt; nest _one_; totcnt fpc; var ue91 hou85; subgroup str; levels 1; postvar str; postwgt 8; run;
Number of observations read : 8 Weighted count : 32 Denominator degrees of freedom : 7 Variance Estimation Method: Taylor Series (WOR) Post-stratified estimates by: Variable, STR. -------------------------------------------------------------------- | | | | Variable | | STR | | | Total | 1 | -------------------------------------------------------------------- | | | | | | UE91 | Sample Size | 8 | 8 | | | Weighted Size | 8.00 | 8.00 | | | Total | 6610.00 | 6610.00 | | | SE Total | 3320.56 | 3320.56 | | | Mean | 826.25 | 826.25 | | | SE Mean | 415.07 | 415.07 | -------------------------------------------------------------------- | | | | | | HOU85 | Sample Size | 8 | 8 | | | Weighted Size | 8.00 | 8.00 | | | Total | 41238.00 | 41238.00 | | | SE Total | 21824.64 | 21824.64 | | | Mean | 5154.75 | 5154.75 | | | SE Mean | 2728.08 | 2728.08 | --------------------------------------------------------------------
strategy: ratio estimator with srs*rat
This code is shown above for page 102. strategy: regression estimator with srs*reg
The code below produces the estimate of b-hat, 0.152, shown in the middle of page 106.
proc regress data = page106 filetype = sas design = wor; weight wt; nest _one_; totcnt fpc; model ue91 = hou85; setenv decwidth = 3; run;
Number of observations read : 8 Weighted count: 32
Observations used in the analysis : 8 Weighted count: 32
Denominator degrees of freedom : 7
Maximum number of estimable parameters for the model is 2
File PAGE106 contains 8 Clusters
8 clusters were used to fit the model
Maximum cluster size is 1 records
Minimum cluster size is 1 records
Weighted mean response is 826.250000
Multiple R-Square for the dependent variable UE91: 0.998249
Variance Estimation Method: Taylor Series (WOR)
SE Method: Robust (Binder, 1983)
Working Correlations: Independent
Link Function: Identity
Response variable UE91: UE91
----------------------------------------------------------------------
Independent P-value
Variables and Beta T-Test
Effects Coeff. SE Beta T-Test B=0 B=0
----------------------------------------------------------------------
Intercept 42.655 20.540 2.077 0.076
HOU85 0.152 0.001 212.012 0.000
----------------------------------------------------------------------
-------------------------------------------------------
Contrast Degrees
of P-value
Freedom Wald F Wald F
-------------------------------------------------------
OVERALL MODEL 2.000 102820.497 0.000
MODEL MINUS
INTERCEPT 1.000 44949.184 0.000
INTERCEPT 1.000 4.312 0.076
HOU85 1.000 44949.184 0.000
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This gives the estimate of the total of hou85, 164952, which is needed for the equation. Note that 32*2867 = 91753.
proc descript data = page106 filetype = sas design = wor totals; weight wt; nest _one_; totcnt fpc; var hou85; run;
Number of observations read : 8 Weighted count : 32 Denominator degrees of freedom : 7 Variance Estimation Method: Taylor Series (WOR) by: Variable, One. ----------------------------------------------------- | | | | Variable | | One | | | 1 | ----------------------------------------------------- | | | | | HOU85 | Sample Size | 8 | | | Weighted Size | 32.00 | | | Total | 164952.00 | | | SE Total | 87298.57 | | | Mean | 5154.75 | | | SE Mean | 2728.08 | -----------------------------------------------------