Sweden: The MU284 Population of Sweden Municipalities from Sarndal et...

Description Usage Format Details Source References Examples

Description

This data set comes from Sarndal et al.'s book (1992), Appendix B. It contains different variables that describe 284 municipalities in Sweden.

Usage

1

Format

A data frame with 284 observations on the following 11 variables.

id

Identifier running from 1 to 284

P85

1985 population (in thousands)

P75

1975 population (in thousands)

RMT85

Revenues from the 1985 municipal taxation (in millions of kronor)

CS82

Number of Conservative seats in municipal council

SS82

Number of Social-Democratic seats in municipal council

S82

Total number of seats in municipal council

ME84

Number of municipal employees in 1984

REV84

Real estate values according to 1984 assessment (in millions of kronor)

REG

Geographic region indicator

CL

Cluster indicator (a cluster consists of a set of neighboring municipalities)

Details

In this package, REV84 is used as a stratification variable and RMT85 as a survey variable.

Source

Sarndal, C. E., Swensson, B. and Wretman, J. (1992). Model Assisted Survey Sampling. Springer Verlag, New York.

References

Rivest, L.-P. (2002). A generalization of the Lavallee and Hidiroglou algorithm for stratification in business surveys. Survey Methodology, 28(2), 191-198.

Examples

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X <- Sweden$REV84
Y <- Sweden$RMT85

# Study of the relationship between X and Y
plot(log(X), log(Y))
# Extreme values are omitted for a more robust estimation
keep <- X/Y>quantile(X/Y,0.03)&X/Y<quantile(X/Y,0.97)
plot(log(X)[keep], log(Y)[keep])
reg<-lm( log(Y)[keep]~log(X)[keep] )
summary(reg)

# Stratification assuming X=Y
nomodel <- strata.LH(x=X, CV=0.05, Ls=3, alloc=c(0.5,0,0.5), takeall=1, model="none")
nomodel
var.strata(nomodel, y=Y) # The target CV is not reached

# Stratification taking into account a loglinear model between X and Y, 
# using the estimated parameters values
model <- strata.LH(x=X, CV=0.05, Ls=3, alloc=c(0.5,0,0.5), takeall=1, model="loglinear",
        model.control=list(beta=reg$coef[2], sig2=summary(reg)$sigma^2, ph=1))
model
var.strata(model, y=Y) # The target CV is reached

Example output

Call:
lm(formula = log(Y)[keep] ~ log(X)[keep])

Residuals:
     Min       1Q   Median       3Q      Max 
-0.84984 -0.10637  0.04057  0.16796  0.48769 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  -3.15302    0.15698  -20.09   <2e-16 ***
log(X)[keep]  1.05836    0.02067   51.20   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2568 on 264 degrees of freedom
Multiple R-squared:  0.9085,	Adjusted R-squared:  0.9082 
F-statistic:  2622 on 1 and 264 DF,  p-value: < 2.2e-16

Given arguments:
x = X
CV = 0.05, Ls = 3, takenone = 0, takeall = 1
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none
algo = Kozak: minsol = 1000, idopti = nh, minNh = 2, maxiter = 10000, 
              maxstep = 28, maxstill = 280, rep = 5, trymany = TRUE

Strata information:
          |      type rh |    bh     E(Y)      Var(Y)  Nh nh   fh
stratum 1 | take-some  1 |  3004  1502.83    468029.9 202 15 0.07
stratum 2 | take-some  1 |  8375  4937.00   2023832.4  67 11 0.16
stratum 3 |  take-all  1 | 59878 16177.80 189197136.0  15 15 1.00
Total                                                 284 41 0.14

Total sample size: 41 
Anticipated population mean: 3088.088 
Anticipated CV: 0.04929343 
Note: CV=RRMSE (Relative Root Mean Squared Error) because takenone=0.
Given arguments:
strata = nomodel
y = Y
rh.postcorr = FALSE

Strata information:
          |      type rh  Nh nh   fh |    E(Y)     Var(Y)
stratum 1 | take-some  1 202 15 0.07 |  100.69    3187.04
stratum 2 | take-some  1  67 11 0.16 |  348.75   26797.29
stratum 3 |  take-all  1  15 15 1.00 | 1726.67 4022741.42
Total                    284 41 0.14                     

Total sample size: 41 
Anticipated population mean: 245.088 
Anticipated CV: 0.05952448 
Note: CV=RRMSE (Relative Root Mean Squared Error) because takenone=0.
Given arguments:
x = X
CV = 0.05, Ls = 3, takenone = 0, takeall = 1
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = loglinear: beta = 1.058355, sig2 = 0.06593083, ph = 1 1 1
algo = Kozak: minsol = 1000, idopti = nh, minNh = 2, maxiter = 10000, 
              maxstep = 28, maxstill = 280, rep = 5, trymany = TRUE

Strata information:
          |      type ph rh |    bh     E(Y)    Var(Y)  Nh nh   fh
stratum 1 | take-some  1  1 |  2763  2187.25   1388449 191 17 0.09
stratum 2 | take-some  1  1 |  7850  7553.66  10766246  77 20 0.26
stratum 3 |  take-all  1  1 | 59878 27963.55 773675582  16 16 1.00
Total                                                  284 53 0.19

Total sample size: 53 
Anticipated population mean: 5094.417 
Anticipated CV: 0.0492482 
Note: CV=RRMSE (Relative Root Mean Squared Error) because takenone=0.
Given arguments:
strata = model
y = Y
rh.postcorr = FALSE

Strata information:
          |      type rh  Nh nh   fh |    E(Y)     Var(Y)
stratum 1 | take-some  1 191 17 0.09 |   95.27    2701.16
stratum 2 | take-some  1  77 20 0.26 |  327.52   26528.41
stratum 3 |  take-all  1  16 16 1.00 | 1636.88 3892258.23
Total                    284 53 0.19                     

Total sample size: 53 
Anticipated population mean: 245.088 
Anticipated CV: 0.04787021 
Note: CV=RRMSE (Relative Root Mean Squared Error) because takenone=0.

stratification documentation built on May 1, 2019, 9:13 p.m.