svystatTM: Estimation of Totals and Means in Subpopulations
In DiegoZardetto/ReGenesees: R Evolved Generalized Software for Sampling Estimates and Errors in Surveys
svystatTM R Documentation
Estimation of Totals and Means in Subpopulations
Description
Computes estimates, standard errors and confidence intervals for Totals and Means in subpopulations.
Usage
svystatTM(design, y, by = NULL, estimator = c("Total", "Mean"),
vartype = c("se", "cv", "cvpct", "var"),
conf.int = FALSE, conf.lev = 0.95, deff = FALSE,
na.rm = FALSE)
## S3 method for class 'svystatTM'
coef(object, ...)
## S3 method for class 'svystatTM'
SE(object, ...)
## S3 method for class 'svystatTM'
VAR(object, ...)
## S3 method for class 'svystatTM'
cv(object, ...)
## S3 method for class 'svystatTM'
deff(object, ...)
## S3 method for class 'svystatTM'
confint(object, ...)
Arguments
design
Object of class analytic (or inheriting from it) containing survey data and sampling design metadata.
y
Formula defining the variables of interest. Only numeric or factor variables are allowed.
by
Formula specifying the variables that define the "estimation domains". If NULL
(the default option) estimates refer to the whole population.
estimator
character specifying the desired estimator: it may be 'Total' (the default) or
'Mean'.
vartype
character vector specifying the desired variability estimators. It is possible to choose
one or more of: standard error ('se', the default), coefficient of variation ('cv'),
percent coefficient of variation ('cvpct'), or variance ('var').
conf.int
Compute confidence intervals for the estimates? The default is
FALSE.
conf.lev
Probability specifying the desired confidence level: the default value is 0.95.
deff
Should the design effect be computed? The default is FALSE (see ‘Details’).
na.rm
Should missing values (if any) be removed from the variables of interest? The default is
FALSE (see ‘Details’).
object
An object of class svystatTM.
...
Additional arguments to coef, ..., confint methods (if any).
Details
This function computes weighted estimates for Totals and Means using suitable weights depending on the class of design: calibrated weights for class cal.analytic and direct weights otherwise. Standard errors for nonlinear estimators (e.g. calibration estimators) are calculated using the Taylor linearization technique.
The mandatory argument y identifies the variables of interest, that is the variables for which estimates are to be calculated. The corresponding formula should be of the type y=~var1+...+varn. The design variables referenced by y should be numeric or factor (variables of other types - e.g. character - will generate and error). It is admissible to specify for y "mixed" formulae that simultaneously contain quantitative (numeric) variables and qualitative (factor) variables.
To override the restriction to formulae of the type y=~var1+...+varn, the AsIs operator I() can be used (see ‘Examples’). Though the latter opportunity could appear quite useful in some occasion, actually it should be almost always possible to find a work-around by using other functions of the ReGenesees package.
The optional argument by specifies the variables that define the "estimation domains", that is the subpopulations for which the estimates are to be calculated. If by=NULL (the default option), the estimates produced by svystatTM refer to the whole population. Estimation domains must be defined by a formula: for example the statement by=~B1:B2 selects as estimation domains the subpopulations determined by crossing the modalities of variables B1 and B2. Notice that a formula like by=~B1+B2 will be automatically translated into the factor-crossing formula by=~B1:B2: if you need to compute estimates for domains B1 and B2 separately, you have to call svystatTM twice. The design variables referenced by by (if any) should be of type factor, otherwise they will be coerced.
The optional argument estimator makes it possible to select the desired estimator. If
estimator="Total" (the default option), svystatTM calculates, for a given variable of interest vark, the estimate of the total (when vark is numeric) or the estimate of the absolute frequency distribution (when vark is factor). Similarly, if estimator="Mean", the function calculates the estimate of the mean (when vark is numeric) or the the estimate of the relative frequency distribution (when vark is factor).
The conf.int argument allows to request the confidence intervals for the estimates. By default conf.int=FALSE, that is the confidence intervals are not provided.
Whenever confidence intervals are requested (i.e. conf.int=TRUE), the desired confidence level can be specified by means of the conf.lev argument. The conf.lev value must represent a probability (0<=conf.lev<=1) and its default is chosen to be 0.95.
The optional argument deff allows to request the design effect [Kish 1995] for the estimates. By default deff=FALSE, that is the design effect is not provided. The design effect of an estimator is defined as the ratio between the variance of the estimator under the actual sampling design and the variance that would be obtained for an 'equivalent' estimator under a hypothetical simple random sampling without replacement of the same size. To obtain an estimate of the design effect comparing to simple random sampling “with replacement”, one must use deff="replace".
Understanding what 'equivalent' estimator actually means is straightforward when dealing with Horvitz-Thompson estimators of Totals and Means. This is not the case when, on the contrary, the estimator to which the deff refers is a nonlinear estimator (e.g. for Calibration estimators of Totals and Means). In such cases, the standard approach is to use as 'equivalent' estimator the linearized version of the original estimator (that is: the estimator of the total of the linearized variable, aka "Woodruff transform").
When dealing with domain estimation, the design effects referring to a given subpopulation are currently computed by taking the ratios between the actual variance estimates and those that would have been obtained if a simple random sampling were carried out within that subpopulation. This is the same as the srssubpop option for Stata's function estat.
Missing values (NA) in interest variables should be avoided. If na.rm=FALSE (the default) they generate NAs in estimates (or even an error, if design is calibrated). If na.rm=TRUE and estimator="Mean", observations containing NAs are dropped, and estimates get computed on non-missing values only. This implicitly assumes that missing values hit interest variables completely at random (MCAR): should this not be the case, computed estimates would be biased. Since, even under the MCAR assumption, estimates of totals and counts solely based on complete cases would be biased, function svystatTM adopts a model-based ratio estimator when na.rm=TRUE and estimator="Total". This is obtained by (i) first estimating the mean or proportion based on complete cases only, and (ii) then multiplying the result by the estimated population size based on all observations (i.e. both missing and non-missing). This model-based ratio estimator is asymptotically design-unbiased under the MCAR assumption. Notice that the na.rm=TRUE option is only allowed if y references a single interest variable.
Value
An object inheriting from the data.frame class, whose detailed structure depends on input parameters' values.
Author(s)
Diego Zardetto
References
Sarndal, C.E., Swensson, B., Wretman, J. (1992) “Model Assisted Survey Sampling”, Springer Verlag.
Kish, L. (1995). “Methods for design effects”. Journal of Official Statistics, Vol. 11, pp. 55-77.
European Commission, Eurostat, (2013). “Handbook on precision requirements and variance estimation for ESS households surveys: 2013 edition”, Publications Office. doi: 10.2785/13579
See Also
Estimators of Ratios between Totals svystatR, Shares svystatS, Ratios between Shares svystatSR, Quantiles svystatQ, Multiple Regression Coefficients svystatB, Complex Analytic Functions of Totals and/or Means svystatL, and all of the above svystat.
Examples
# Load survey data:
data(data.examples)
# Creation of a design object:
des<-e.svydesign(data=example,ids=~towcod+famcod,strata=~SUPERSTRATUM,
weights=~weight)
# Estimation of the total of 3 quantitative variables for the whole
# population:
svystatTM(des,~y1+y2+y3)
# Estimation of the total of the same 3 variables by region, with SE
# and CV%:
svystatTM(des,~y1+y2+y3,~regcod,vartype=c("se","cvpct"))
# Estimation of the mean of the same 3 variables by marstat and sex:
svystatTM(des,~y1+y2+y3,~marstat:sex,estimator="Mean")
# Estimation of the absolute frequency distribution of the qualitative
# variable age5c for the whole population, with the design effect:
svystatTM(des,~age5c,deff=TRUE)
# MARGINAL relative frequency distributions
# Estimation of the relative frequency distribution of the qualitative
# variable age5c for the whole population:
svystatTM(des,~age5c,estimator="Mean")
# CONDITIONAL relative frequency distributions
# Estimation of the relative frequency distribution of the qualitative
# variable marstat by sex:
svystatTM(des,~marstat,~sex,estimator="Mean")
# JOINT relative frequency distributions
# Estimation of the relative frequency of the joint distribution of sex
# and marstat:
# *First Solution* (using the AsIs operator I()):
svystatTM(des,~I(sex:marstat),estimator="Mean")
# *Second Solution* (adding a new variable to des):
des2 <- des.addvars(des, sex.marstat=sex:marstat)
svystatTM(des2,~sex.marstat,estimator="Mean")
# *Third Solution* (exploiting estimators of Shares, see also ?svystatS):
# Add new variable 'ones' to estimate counts of final units (individuals)
# and estimate the share of people for classes of sex and marstat
des2 <- des.addvars(des, ones=1)
svystatS(des2,~ones,classes=~sex:marstat)
# Estimation of the mean income inside provinces, with confidence intervals
# at a confidence level of 0.9:
svystatTM(des,~income,~procod,estimator="Mean",conf.int=TRUE,conf.lev=0.9)
# Quantitative and qualitative variables together: estimation of the
# total of income and of the absolute frequency distribution of sex,
# by marstat:
svystatTM(des,~income+sex,~marstat)
# Estimating totals in domains for "incomplete" partitions: more on
# the AsIs operator I()
# Estimation of the total income (plus cvpct) ONLY in region 7:
svystatTM(des,~I(income*(regcod=="7")),vartype="cvpct")
# Alternative solution (adding a new variable to des):
des2 <- des.addvars(des, inc_reg7=I(income*(regcod=="7")))
svystatTM(des2,~inc_reg7,vartype="cvpct")
# Estimation of the total income (plus cvpct) ONLY in regions 6 and 10:
svystatTM(des,~I(income*as.numeric(regcod %in% c("6","10"))),vartype="cvpct")
# Alternative solution (adding a new variable to des):
des2 <- des.addvars(des, inc_reg6.10=I(income*(regcod %in% c("6","10"))))
svystatTM(des2,~inc_reg6.10,vartype="cvpct")
# Compare with the corresponding estimates for the "complete" partition,
# i.e. for regions:
svystatTM(des,~income,~regcod,vartype="cvpct")
# Under default settings lonely PSUs produce errors in standard
# errors estimation (notice we didn't pass the fpcs):
data(fpcdat)
des.lpsu<-e.svydesign(data=fpcdat,ids=~psu+ssu,strata=~stratum,
weights=~w)
## Not run:
svystatTM(des.lpsu,~x+y+z,vartype=c("se","cvpct"))
## End(Not run)
# This can be circumvented in different ways, namely:
old.op <- options("RG.lonely.psu"="adjust")
svystatTM(des.lpsu,~x+y+z,vartype=c("se","cvpct"))
options(old.op)
# or otherwise:
old.op <- options("RG.lonely.psu"="average")
svystatTM(des.lpsu,~x+y+z,vartype=c("se","cvpct"))
options(old.op)
# but see also ?collapse.strata for a better alternative.
####################################################
# Household-level estimation in household surveys. #
####################################################
# Large scale household surveys typically adopt a 2-stage sampling
# design with municipalities as PSUs and households as SSUs, in order
# to eventually collect information on each individual belonging to
# sampled SSUs. In such a framework (up to possible total nonresponse
# effects), each individual inside a sampled household shares the
# same direct weight, which, in turn, equals the household weight.
# This implies that it is very easy to build estimates referred to
# SSU-level (households) information, despite estimators actually
# involve only individual values. Some examples are given below.
# Load survey data:
data(data.examples)
# Define the survey design (variable famcod identifies households)
exdes<-e.svydesign(data=example,ids=~towcod+famcod,strata=~stratum,
weights=~weight)
# Collapse strata to eliminate lonely PSUs
exdes<-collapse.strata(design=exdes,block.vars=~sr:procod)
# Now add new convenience variables to the design object:
## 'ones': to estimate individuals counts
## 'housize': to classify individuals by household size
## 'houdensity': to estimate households counts
exdes<-des.addvars(exdes,
ones=1,
housize=factor(ave(famcod,famcod,FUN = length)),
houdensity=ave(famcod,famcod,FUN = function(x) 1/length(x))
)
# Estimate the total number of households:
nhou<-svystatTM(exdes,~houdensity,vartype="cvpct")
nhou
# Estimate the total number of individuals:
nind<-svystatTM(exdes,~ones,vartype="cvpct")
nind
# Thus the average number of individuals per household is:
coef(nind)/coef(nhou)
# ...which can be obtained also as a ratio (along with
# its estimated sampling variability):
svystatR(exdes,~ones,~houdensity,vartype="cvpct")
# Estimate the number and proportion of individuals living in households
# of given sizes:
nind.by.housize<-svystatTM(exdes,~housize,vartype="cvpct")
nind.by.housize
pind.by.housize<-svystatTM(exdes,~housize,estimator="Mean",var="cvpct")
pind.by.housize
# Estimate the number of households by household size:
nhou.by.housize<-svystatTM(exdes,~houdensity,~housize,vartype="cvpct")
nhou.by.housize
# Notice that estimates of individuals and household counts are consistent,
# indeed:
coef(nind.by.housize)/coef(nhou.by.housize)
DiegoZardetto/ReGenesees documentation built on Dec. 16, 2024, 2:03 p.m.
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| svystatTM | R Documentation |
Estimation of Totals and Means in Subpopulations
Description
Computes estimates, standard errors and confidence intervals for Totals and Means in subpopulations.
Usage
svystatTM(design, y, by = NULL, estimator = c("Total", "Mean"),
vartype = c("se", "cv", "cvpct", "var"),
conf.int = FALSE, conf.lev = 0.95, deff = FALSE,
na.rm = FALSE)
## S3 method for class 'svystatTM'
coef(object, ...)
## S3 method for class 'svystatTM'
SE(object, ...)
## S3 method for class 'svystatTM'
VAR(object, ...)
## S3 method for class 'svystatTM'
cv(object, ...)
## S3 method for class 'svystatTM'
deff(object, ...)
## S3 method for class 'svystatTM'
confint(object, ...)
Arguments
design |
Object of class |
y |
Formula defining the variables of interest. Only |
by |
Formula specifying the variables that define the "estimation domains". If |
estimator |
|
vartype |
|
conf.int |
Compute confidence intervals for the estimates? The default is
|
conf.lev |
Probability specifying the desired confidence level: the default value is |
deff |
Should the design effect be computed? The default is |
na.rm |
Should missing values (if any) be removed from the variables of interest? The default is
|
object |
An object of class |
... |
Additional arguments to |
Details
This function computes weighted estimates for Totals and Means using suitable weights depending on the class of design: calibrated weights for class cal.analytic and direct weights otherwise. Standard errors for nonlinear estimators (e.g. calibration estimators) are calculated using the Taylor linearization technique.
The mandatory argument y identifies the variables of interest, that is the variables for which estimates are to be calculated. The corresponding formula should be of the type y=~var1+...+varn. The design variables referenced by y should be numeric or factor (variables of other types - e.g. character - will generate and error). It is admissible to specify for y "mixed" formulae that simultaneously contain quantitative (numeric) variables and qualitative (factor) variables.
To override the restriction to formulae of the type y=~var1+...+varn, the AsIs operator I() can be used (see ‘Examples’). Though the latter opportunity could appear quite useful in some occasion, actually it should be almost always possible to find a work-around by using other functions of the ReGenesees package.
The optional argument by specifies the variables that define the "estimation domains", that is the subpopulations for which the estimates are to be calculated. If by=NULL (the default option), the estimates produced by svystatTM refer to the whole population. Estimation domains must be defined by a formula: for example the statement by=~B1:B2 selects as estimation domains the subpopulations determined by crossing the modalities of variables B1 and B2. Notice that a formula like by=~B1+B2 will be automatically translated into the factor-crossing formula by=~B1:B2: if you need to compute estimates for domains B1 and B2 separately, you have to call svystatTM twice. The design variables referenced by by (if any) should be of type factor, otherwise they will be coerced.
The optional argument estimator makes it possible to select the desired estimator. If
estimator="Total" (the default option), svystatTM calculates, for a given variable of interest vark, the estimate of the total (when vark is numeric) or the estimate of the absolute frequency distribution (when vark is factor). Similarly, if estimator="Mean", the function calculates the estimate of the mean (when vark is numeric) or the the estimate of the relative frequency distribution (when vark is factor).
The conf.int argument allows to request the confidence intervals for the estimates. By default conf.int=FALSE, that is the confidence intervals are not provided.
Whenever confidence intervals are requested (i.e. conf.int=TRUE), the desired confidence level can be specified by means of the conf.lev argument. The conf.lev value must represent a probability (0<=conf.lev<=1) and its default is chosen to be 0.95.
The optional argument deff allows to request the design effect [Kish 1995] for the estimates. By default deff=FALSE, that is the design effect is not provided. The design effect of an estimator is defined as the ratio between the variance of the estimator under the actual sampling design and the variance that would be obtained for an 'equivalent' estimator under a hypothetical simple random sampling without replacement of the same size. To obtain an estimate of the design effect comparing to simple random sampling “with replacement”, one must use deff="replace".
Understanding what 'equivalent' estimator actually means is straightforward when dealing with Horvitz-Thompson estimators of Totals and Means. This is not the case when, on the contrary, the estimator to which the deff refers is a nonlinear estimator (e.g. for Calibration estimators of Totals and Means). In such cases, the standard approach is to use as 'equivalent' estimator the linearized version of the original estimator (that is: the estimator of the total of the linearized variable, aka "Woodruff transform").
When dealing with domain estimation, the design effects referring to a given subpopulation are currently computed by taking the ratios between the actual variance estimates and those that would have been obtained if a simple random sampling were carried out within that subpopulation. This is the same as the srssubpop option for Stata's function estat.
Missing values (NA) in interest variables should be avoided. If na.rm=FALSE (the default) they generate NAs in estimates (or even an error, if design is calibrated). If na.rm=TRUE and estimator="Mean", observations containing NAs are dropped, and estimates get computed on non-missing values only. This implicitly assumes that missing values hit interest variables completely at random (MCAR): should this not be the case, computed estimates would be biased. Since, even under the MCAR assumption, estimates of totals and counts solely based on complete cases would be biased, function svystatTM adopts a model-based ratio estimator when na.rm=TRUE and estimator="Total". This is obtained by (i) first estimating the mean or proportion based on complete cases only, and (ii) then multiplying the result by the estimated population size based on all observations (i.e. both missing and non-missing). This model-based ratio estimator is asymptotically design-unbiased under the MCAR assumption. Notice that the na.rm=TRUE option is only allowed if y references a single interest variable.
Value
An object inheriting from the data.frame class, whose detailed structure depends on input parameters' values.
Author(s)
Diego Zardetto
References
Sarndal, C.E., Swensson, B., Wretman, J. (1992) “Model Assisted Survey Sampling”, Springer Verlag.
Kish, L. (1995). “Methods for design effects”. Journal of Official Statistics, Vol. 11, pp. 55-77.
European Commission, Eurostat, (2013). “Handbook on precision requirements and variance estimation for ESS households surveys: 2013 edition”, Publications Office. doi: 10.2785/13579
See Also
Estimators of Ratios between Totals svystatR, Shares svystatS, Ratios between Shares svystatSR, Quantiles svystatQ, Multiple Regression Coefficients svystatB, Complex Analytic Functions of Totals and/or Means svystatL, and all of the above svystat.
Examples
# Load survey data:
data(data.examples)
# Creation of a design object:
des<-e.svydesign(data=example,ids=~towcod+famcod,strata=~SUPERSTRATUM,
weights=~weight)
# Estimation of the total of 3 quantitative variables for the whole
# population:
svystatTM(des,~y1+y2+y3)
# Estimation of the total of the same 3 variables by region, with SE
# and CV%:
svystatTM(des,~y1+y2+y3,~regcod,vartype=c("se","cvpct"))
# Estimation of the mean of the same 3 variables by marstat and sex:
svystatTM(des,~y1+y2+y3,~marstat:sex,estimator="Mean")
# Estimation of the absolute frequency distribution of the qualitative
# variable age5c for the whole population, with the design effect:
svystatTM(des,~age5c,deff=TRUE)
# MARGINAL relative frequency distributions
# Estimation of the relative frequency distribution of the qualitative
# variable age5c for the whole population:
svystatTM(des,~age5c,estimator="Mean")
# CONDITIONAL relative frequency distributions
# Estimation of the relative frequency distribution of the qualitative
# variable marstat by sex:
svystatTM(des,~marstat,~sex,estimator="Mean")
# JOINT relative frequency distributions
# Estimation of the relative frequency of the joint distribution of sex
# and marstat:
# *First Solution* (using the AsIs operator I()):
svystatTM(des,~I(sex:marstat),estimator="Mean")
# *Second Solution* (adding a new variable to des):
des2 <- des.addvars(des, sex.marstat=sex:marstat)
svystatTM(des2,~sex.marstat,estimator="Mean")
# *Third Solution* (exploiting estimators of Shares, see also ?svystatS):
# Add new variable 'ones' to estimate counts of final units (individuals)
# and estimate the share of people for classes of sex and marstat
des2 <- des.addvars(des, ones=1)
svystatS(des2,~ones,classes=~sex:marstat)
# Estimation of the mean income inside provinces, with confidence intervals
# at a confidence level of 0.9:
svystatTM(des,~income,~procod,estimator="Mean",conf.int=TRUE,conf.lev=0.9)
# Quantitative and qualitative variables together: estimation of the
# total of income and of the absolute frequency distribution of sex,
# by marstat:
svystatTM(des,~income+sex,~marstat)
# Estimating totals in domains for "incomplete" partitions: more on
# the AsIs operator I()
# Estimation of the total income (plus cvpct) ONLY in region 7:
svystatTM(des,~I(income*(regcod=="7")),vartype="cvpct")
# Alternative solution (adding a new variable to des):
des2 <- des.addvars(des, inc_reg7=I(income*(regcod=="7")))
svystatTM(des2,~inc_reg7,vartype="cvpct")
# Estimation of the total income (plus cvpct) ONLY in regions 6 and 10:
svystatTM(des,~I(income*as.numeric(regcod %in% c("6","10"))),vartype="cvpct")
# Alternative solution (adding a new variable to des):
des2 <- des.addvars(des, inc_reg6.10=I(income*(regcod %in% c("6","10"))))
svystatTM(des2,~inc_reg6.10,vartype="cvpct")
# Compare with the corresponding estimates for the "complete" partition,
# i.e. for regions:
svystatTM(des,~income,~regcod,vartype="cvpct")
# Under default settings lonely PSUs produce errors in standard
# errors estimation (notice we didn't pass the fpcs):
data(fpcdat)
des.lpsu<-e.svydesign(data=fpcdat,ids=~psu+ssu,strata=~stratum,
weights=~w)
## Not run:
svystatTM(des.lpsu,~x+y+z,vartype=c("se","cvpct"))
## End(Not run)
# This can be circumvented in different ways, namely:
old.op <- options("RG.lonely.psu"="adjust")
svystatTM(des.lpsu,~x+y+z,vartype=c("se","cvpct"))
options(old.op)
# or otherwise:
old.op <- options("RG.lonely.psu"="average")
svystatTM(des.lpsu,~x+y+z,vartype=c("se","cvpct"))
options(old.op)
# but see also ?collapse.strata for a better alternative.
####################################################
# Household-level estimation in household surveys. #
####################################################
# Large scale household surveys typically adopt a 2-stage sampling
# design with municipalities as PSUs and households as SSUs, in order
# to eventually collect information on each individual belonging to
# sampled SSUs. In such a framework (up to possible total nonresponse
# effects), each individual inside a sampled household shares the
# same direct weight, which, in turn, equals the household weight.
# This implies that it is very easy to build estimates referred to
# SSU-level (households) information, despite estimators actually
# involve only individual values. Some examples are given below.
# Load survey data:
data(data.examples)
# Define the survey design (variable famcod identifies households)
exdes<-e.svydesign(data=example,ids=~towcod+famcod,strata=~stratum,
weights=~weight)
# Collapse strata to eliminate lonely PSUs
exdes<-collapse.strata(design=exdes,block.vars=~sr:procod)
# Now add new convenience variables to the design object:
## 'ones': to estimate individuals counts
## 'housize': to classify individuals by household size
## 'houdensity': to estimate households counts
exdes<-des.addvars(exdes,
ones=1,
housize=factor(ave(famcod,famcod,FUN = length)),
houdensity=ave(famcod,famcod,FUN = function(x) 1/length(x))
)
# Estimate the total number of households:
nhou<-svystatTM(exdes,~houdensity,vartype="cvpct")
nhou
# Estimate the total number of individuals:
nind<-svystatTM(exdes,~ones,vartype="cvpct")
nind
# Thus the average number of individuals per household is:
coef(nind)/coef(nhou)
# ...which can be obtained also as a ratio (along with
# its estimated sampling variability):
svystatR(exdes,~ones,~houdensity,vartype="cvpct")
# Estimate the number and proportion of individuals living in households
# of given sizes:
nind.by.housize<-svystatTM(exdes,~housize,vartype="cvpct")
nind.by.housize
pind.by.housize<-svystatTM(exdes,~housize,estimator="Mean",var="cvpct")
pind.by.housize
# Estimate the number of households by household size:
nhou.by.housize<-svystatTM(exdes,~houdensity,~housize,vartype="cvpct")
nhou.by.housize
# Notice that estimates of individuals and household counts are consistent,
# indeed:
coef(nind.by.housize)/coef(nhou.by.housize)
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