Ratio estimation

Ratio estimation and estimates of totals based on ratios for complex survey samples. Estimating domain (subpopulation) means can be done more easily with svymean.

# S3 method for survey.design2
svyratio(numerator=formula, denominator,
   design,separate=FALSE, na.rm=FALSE,formula, covmat=FALSE,
   deff=FALSE,influence=FALSE,...)
# S3 method for svyrep.design
svyratio(numerator=formula, denominator, design,
   na.rm=FALSE,formula, covmat=FALSE,return.replicates=FALSE,deff=FALSE, ...)
# S3 method for twophase
svyratio(numerator=formula, denominator, design,
    separate=FALSE, na.rm=FALSE,formula,...)
# S3 method for svyratio
predict(object, total, se=TRUE,...)
# S3 method for svyratio_separate
predict(object, total, se=TRUE,...)
# S3 method for svyratio
SE(object,...,drop=TRUE)
# S3 method for svyratio
coef(object,...,drop=TRUE)
# S3 method for svyratio
confint(object,  parm, level = 0.95,df =Inf,...)

Arguments

numerator,formula: formula, expression, or data frame giving numerator variable(s)
denominator: formula, expression, or data frame giving denominator variable(s)
design: survey design object
object: result of svyratio
total: vector of population totals for the denominator variables in object, or list of vectors of population stratum totals if separate=TRUE
se: Return standard errors?
separate: Estimate ratio separately for strata
na.rm: Remove missing values?
covmat: Compute the full variance-covariance matrix of the ratios
deff: Compute design effects
return.replicates: Return replicate estimates of ratios
influence: Return influence functions
drop: Return a vector rather than a matrix
parm: a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
level: the confidence level required.
df: degrees of freedom for t-distribution in confidence interval, use degf(design) for number of PSUs minus number of strata
...: Other unused arguments for other methods

Details

The separate ratio estimate of a total is the sum of ratio estimates in each stratum. If the stratum totals supplied in the total argument and the strata in the design object both have names these names will be matched. If they do not have names it is important that the sample totals are supplied in the correct order, the same order as shown in the output of summary(design).

When design is a two-phase design, stratification will be on the second phase.

Value

svyratio returns an object of class svyratio. The predict method returns a matrix of population totals and optionally a matrix of standard errors.

References

Levy and Lemeshow. "Sampling of Populations" (3rd edition). Wiley

Author

Thomas Lumley

Examples

data(scd)

## survey design objects
scddes<-svydesign(data=scd, prob=~1, id=~ambulance, strata=~ESA,
nest=TRUE, fpc=rep(5,6))
scdnofpc<-svydesign(data=scd, prob=~1, id=~ambulance, strata=~ESA,
nest=TRUE)

# convert to BRR replicate weights
scd2brr <- as.svrepdesign(scdnofpc, type="BRR")

# use BRR replicate weights from Levy and Lemeshow
repweights<-2*cbind(c(1,0,1,0,1,0), c(1,0,0,1,0,1), c(0,1,1,0,0,1),
c(0,1,0,1,1,0))
scdrep<-svrepdesign(data=scd, type="BRR", repweights=repweights)
#> Warning: No sampling weights provided: equal probability assumed

# ratio estimates
svyratio(~alive, ~arrests, design=scddes)
#> Ratio estimator: svyratio.survey.design2(~alive, ~arrests, design = scddes)
#> Ratios=
#>         arrests
#> alive 0.1535064
#> SEs=
#>           arrests
#> alive 0.007596705
svyratio(~alive, ~arrests, design=scdnofpc)
#> Ratio estimator: svyratio.survey.design2(~alive, ~arrests, design = scdnofpc)
#> Ratios=
#>         arrests
#> alive 0.1535064
#> SEs=
#>           arrests
#> alive 0.009807304
svyratio(~alive, ~arrests, design=scd2brr)
#> Ratio estimator: svyratio.svyrep.design(~alive, ~arrests, design = scd2brr)
#> Ratios=
#>         arrests
#> alive 0.1535064
#> SEs=
#>             [,1]
#> [1,] 0.009418401
svyratio(~alive, ~arrests, design=scdrep)
#> Ratio estimator: svyratio.svyrep.design(~alive, ~arrests, design = scdrep)
#> Ratios=
#>         arrests
#> alive 0.1535064
#> SEs=
#>             [,1]
#> [1,] 0.009418401


data(api)
dstrat<-svydesign(id=~1,strata=~stype, weights=~pw, data=apistrat, fpc=~fpc)

## domain means are ratio estimates, but available directly
svyratio(~I(api.stu*(comp.imp=="Yes")), ~as.numeric(comp.imp=="Yes"), dstrat)
#> Ratio estimator: svyratio.survey.design2(~I(api.stu * (comp.imp == "Yes")), ~as.numeric(comp.imp == 
#>     "Yes"), dstrat)
#> Ratios=
#>                                  as.numeric(comp.imp == "Yes")
#> I(api.stu * (comp.imp == "Yes"))                      439.9305
#> SEs=
#>                                  as.numeric(comp.imp == "Yes")
#> I(api.stu * (comp.imp == "Yes"))                      19.24367
svymean(~api.stu, subset(dstrat, comp.imp=="Yes"))
#>           mean     SE
#> api.stu 439.93 19.244

## separate and combined ratio estimates of total
(sep<-svyratio(~api.stu,~enroll, dstrat,separate=TRUE))
#> Stratified ratio estimate: svyratio.survey.design2(~api.stu, ~enroll, dstrat, separate = TRUE)
#> Ratio estimator: Stratum == 1L
#> Ratios=
#>            enroll
#> api.stu 0.8518163
#> SEs=
#>             enroll
#> api.stu 0.00703236
#> Ratio estimator: Stratum == 2L
#> Ratios=
#>            enroll
#> api.stu 0.8105702
#> SEs=
#>             enroll
#> api.stu 0.02047726
#> Ratio estimator: Stratum == 3L
#> Ratios=
#>            enroll
#> api.stu 0.8356958
#> SEs=
#>             enroll
#> api.stu 0.01818744
(com<-svyratio(~api.stu, ~enroll, dstrat))
#> Ratio estimator: svyratio.survey.design2(~api.stu, ~enroll, dstrat)
#> Ratios=
#>            enroll
#> api.stu 0.8369569
#> SEs=
#>              enroll
#> api.stu 0.007757103

stratum.totals<-list(E=1877350, H=1013824, M=920298)

predict(sep, total=stratum.totals)
#> $total
#>          enroll
#> api.stu 3190022
#> 
#> $se
#>           enroll
#> api.stu 29756.44
#> 
predict(com, total=sum(unlist(stratum.totals)))
#> $total
#>          enroll
#> api.stu 3190038
#> 
#> $se
#>           enroll
#> api.stu 29565.98
#> 

SE(com)
#> api.stu/enroll 
#>    0.007757103 
coef(com)
#> api.stu/enroll 
#>      0.8369569 
coef(com, drop=FALSE)
#>            enroll
#> api.stu 0.8369569
confint(com)
#>                    2.5 %    97.5 %
#> api.stu/enroll 0.8217532 0.8521605