For the most part, this document will present the functionalities of
the function surveysd::calc.stError() which generates point
estimates and standard errors for user-supplied estimation
functions.
Prerequisites
In order to use a dataset with calc.stError(), several
weight columns have to be present. Each weight column corresponds to a
bootstrap sample. In the following examples, we will use the data from
demo.eusilc() and attach the bootstrap weights using
draw.bootstrap() and recalib(). Please refer
to the documentation of those functions for more detail.
library(surveysd)
set.seed(1234)
eusilc <- demo.eusilc(prettyNames = TRUE)
dat_boot <- draw.bootstrap(eusilc, REP = 10, hid = "hid", weights = "pWeight",
strata = "region", period = "year")
dat_boot_calib <- recalib(dat_boot, conP.var = "gender", conH.var = "region",
epsP = 1e-2, epsH = 2.5e-2, verbose = FALSE)
dat_boot_calib[, onePerson := nrow(.SD) == 1, by = .(year, hid)]
## print part of the dataset
dat_boot_calib[1:5, .(year, povertyRisk, eqIncome, onePerson, pWeight, w1, w2, w3, w4, w5)]## year povertyRisk eqIncome onePerson pWeight w1 w2
## <num> <lgcl> <num> <lgcl> <num> <num> <num>
## 1: 2010 FALSE 16090.69 FALSE 504.5696 1008.6599936 1012.0421735
## 2: 2010 FALSE 16090.69 FALSE 504.5696 1008.6599936 1012.0421735
## 3: 2010 FALSE 16090.69 FALSE 504.5696 1008.6599936 1012.0421735
## 4: 2010 FALSE 27076.24 FALSE 493.3824 0.4390257 0.4410354
## 5: 2010 FALSE 27076.24 FALSE 493.3824 0.4390257 0.4410354
## w3 w4 w5
## <num> <num> <num>
## 1: 0.4503017 1039.1858437 0.4516434
## 2: 0.4503017 1039.1858437 0.4516434
## 3: 0.4503017 1039.1858437 0.4516434
## 4: 0.4405081 0.4525917 993.7730645
## 5: 0.4405081 0.4525917 993.7730645Estimator functions
The parameters fun and var in
calc.stError() define the estimator to be used in the error
analysis. There are two built-in estimator functions
weightedSum() and weightedRatio() which can be
used as follows.
povertyRate <- calc.stError(dat_boot_calib, var = "povertyRisk", fun = weightedRatio)
totalIncome <- calc.stError(dat_boot_calib, var = "eqIncome", fun = weightedSum)Those functions calculate the ratio of persons at risk of poverty (in percent) and the total income. By default, the results are calculated separately for each reference period.
povertyRate$Estimates## Key: <year, n, N, estimate_type>
## year n N estimate_type val_povertyRisk stE_povertyRisk
## <num> <int> <num> <char> <num> <num>
## 1: 2010 14827 8182222 direct 14.44422 0.6456405
## 2: 2011 14827 8182222 direct 14.77393 0.5173877
## 3: 2012 14827 8182222 direct 15.04515 0.4795197
## 4: 2013 14827 8182222 direct 14.89013 0.4722443
## 5: 2014 14827 8182222 direct 15.14556 0.5126322
## 6: 2015 14827 8182222 direct 15.53640 0.4889217
## 7: 2016 14827 8182222 direct 15.08315 0.5773682
## 8: 2017 14827 8182222 direct 15.42019 0.4083678
totalIncome$Estimates## Key: <year, n, N, estimate_type>
## year n N estimate_type val_eqIncome stE_eqIncome
## <num> <int> <num> <char> <num> <num>
## 1: 2010 14827 8182222 direct 162750998071 1224932244
## 2: 2011 14827 8182222 direct 161926931417 1355681349
## 3: 2012 14827 8182222 direct 162576509628 1101849682
## 4: 2013 14827 8182222 direct 163199507862 1245617252
## 5: 2014 14827 8182222 direct 163986275009 1333429301
## 6: 2015 14827 8182222 direct 163416275447 1612218047
## 7: 2016 14827 8182222 direct 162706205137 1529356073
## 8: 2017 14827 8182222 direct 164314959107 1291009642Columns that use the val_ prefix denote the point
estimate belonging to the “main weight” of the dataset, which is
pWeight in case of the dataset used here.
Columns with the stE_ prefix denote standard errors
calculated with bootstrap replicates. The replicates result in using
w1, w2, …, w10 instead of
pWeight when applying the estimator.
n denotes the number of observations for the year and
N denotes the total weight of those persons.
Custom estimators
In order to define a custom estimator function to be used in
fun, the function needs to have at least two arguments like
the example below.
## define custom estimator
myWeightedSum <- function(x, w) {
sum(x*w)
}
## check if results are equal to the one using `surveysd::weightedSum()`
totalIncome2 <- calc.stError(dat_boot_calib, var = "eqIncome", fun = myWeightedSum)
all.equal(totalIncome$Estimates, totalIncome2$Estimates)## [1] TRUEThe parameters x and w can be assumed to be
vectors with equal length with w being numeric weight
vector and x being the column defined in the
var argument. It will be called once for each period (in
this case year) and for each weight column (in this case
pWeight, w1, w2, …,
w10).
Custom estimators using additional parameters can also be supplied
and parameter add.arg can be used to set the additional
arguments for the custom estimator.
## use add.arg-argument
fun <- function(x, w, b) {
sum(x*w*b)
}
add.arg = list(b="onePerson")
err.est <- calc.stError(dat_boot_calib, var = "povertyRisk", fun = fun,
period.mean = 0, add.arg=add.arg)
err.est$Estimates## Key: <year, n, N, estimate_type>
## year n N estimate_type val_povertyRisk stE_povertyRisk
## <num> <int> <num> <char> <num> <num>
## 1: 2010 14827 8182222 direct 273683.9 15831.000
## 2: 2011 14827 8182222 direct 261883.6 13695.875
## 3: 2012 14827 8182222 direct 243083.9 5970.467
## 4: 2013 14827 8182222 direct 238004.4 11504.737
## 5: 2014 14827 8182222 direct 218572.1 5377.214
## 6: 2015 14827 8182222 direct 219984.1 9194.169
## 7: 2016 14827 8182222 direct 201753.9 8109.214
## 8: 2017 14827 8182222 direct 196881.2 5987.490
# compare with direct computation
compare.value <- dat_boot_calib[,fun(povertyRisk,pWeight,b=onePerson),
by=c("year")]
all((compare.value$V1-err.est$Estimates$val_povertyRisk)==0)## [1] TRUEThe above chunk computes the weighted poverty ratio for single person households.
Adjust variable depending on bootstrap weights
In our example the variable povertyRisk is a boolean and
is TRUE if the income is less than 60% of the weighted
median income. Thus it directly depends on the original weight vector
pWeight. To further reduce the estimated error one should
calculate for each bootstrap replicate weight
the weighted median income
and then define
as
$$ povertyRisk_w = \cases{1 \quad\text{if Income}<0.6\cdot medIncome_{w}\\ 0 \quad\text{else}} $$
The estimator can then be applied to the new variable . This can be realized using a custom estimator function.
# custom estimator to first derive poverty threshold
# and then estimate a weighted ratio
povmd <- function(x, w) {
md <- laeken::weightedMedian(x, w)*0.6
pmd60 <- x < md
# weighted ratio is directly estimated inside the function
return(sum(w[pmd60])/sum(w)*100)
}
err.est <- calc.stError(
dat_boot_calib, var = "povertyRisk", fun = weightedRatio,
fun.adjust.var = povmd, adjust.var = "eqIncome")
err.est$Estimates## Key: <year, n, N, estimate_type>
## year n N estimate_type val_povertyRisk stE_povertyRisk
## <num> <int> <num> <char> <num> <num>
## 1: 2010 14827 8182222 direct 14.44422 0
## 2: 2011 14827 8182222 direct 14.77393 0
## 3: 2012 14827 8182222 direct 15.04515 0
## 4: 2013 14827 8182222 direct 14.89013 0
## 5: 2014 14827 8182222 direct 15.14556 0
## 6: 2015 14827 8182222 direct 15.53640 0
## 7: 2016 14827 8182222 direct 15.08315 0
## 8: 2017 14827 8182222 direct 15.42019 0The approach shown above is only valid if no grouping variables are
supplied (parameter group = NULL). If grouping variables
are supplied one should use parameters fun.adjust.var and
adjust.var such that the
is first calculated for each period and then used for each
grouping in group.
# using fun.adjust.var and adjust.var to estimate povmd60 indicator
# for each period and bootstrap weight before applying the weightedRatio
povmd2 <- function(x, w) {
md <- laeken::weightedMedian(x, w)*0.6
pmd60 <- x < md
return(as.integer(pmd60))
}
# set adjust.var="eqIncome" so the income vector is used to estimate
# the povmd60 indicator for each bootstrap weight
# and the resulting indicators are passed to function weightedRatio
group <- "gender"
err.est <- calc.stError(
dat_boot_calib, var = "povertyRisk", fun = weightedRatio, group = "gender",
fun.adjust.var = povmd2, adjust.var = "eqIncome")
err.est$Estimates## Key: <year, n, N, gender, estimate_type>
## year n N gender estimate_type val_povertyRisk stE_povertyRisk
## <num> <int> <num> <fctr> <char> <num> <num>
## 1: 2010 7267 3979572 male direct 12.02660 0.5340028
## 2: 2010 7560 4202650 female direct 16.73351 0.4478495
## 3: 2010 14827 8182222 <NA> direct 14.44422 0.4202035
## 4: 2011 7267 3979572 male direct 12.81921 0.4726545
## 5: 2011 7560 4202650 female direct 16.62488 0.5052391
## 6: 2011 14827 8182222 <NA> direct 14.77393 0.4285908
## 7: 2012 7267 3979572 male direct 13.76065 0.4920958
## 8: 2012 7560 4202650 female direct 16.26147 0.2953726
## 9: 2012 14827 8182222 <NA> direct 15.04515 0.3658453
## 10: 2013 7267 3979572 male direct 13.88962 0.4660053
## 11: 2013 7560 4202650 female direct 15.83754 0.4618770
## 12: 2013 14827 8182222 <NA> direct 14.89013 0.4462450
## 13: 2014 7267 3979572 male direct 14.50351 0.4831362
## 14: 2014 7560 4202650 female direct 15.75353 0.5056109
## 15: 2014 14827 8182222 <NA> direct 15.14556 0.4513984
## 16: 2015 7267 3979572 male direct 15.12289 0.4648867
## 17: 2015 7560 4202650 female direct 15.92796 0.3423830
## 18: 2015 14827 8182222 <NA> direct 15.53640 0.3127915
## 19: 2016 7267 3979572 male direct 14.57968 0.5532361
## 20: 2016 7560 4202650 female direct 15.55989 0.4666695
## 21: 2016 14827 8182222 <NA> direct 15.08315 0.4772422
## 22: 2017 7267 3979572 male direct 14.94816 0.5151348
## 23: 2017 7560 4202650 female direct 15.86717 0.5462449
## 24: 2017 14827 8182222 <NA> direct 15.42019 0.5171668
## year n N gender estimate_type val_povertyRisk stE_povertyRiskMultiple estimators
In case an estimator should be applied to several columns of the
dataset, var can be set to a vector containing all
necessary columns.
multipleRates <- calc.stError(dat_boot_calib, var = c("povertyRisk", "onePerson"), fun = weightedRatio)
multipleRates$Estimates## Key: <year, n, N, estimate_type>
## year n N estimate_type val_povertyRisk stE_povertyRisk
## <num> <int> <num> <char> <num> <num>
## 1: 2010 14827 8182222 direct 14.44422 0.7003471
## 2: 2011 14827 8182222 direct 14.77393 0.4938724
## 3: 2012 14827 8182222 direct 15.04515 0.4294296
## 4: 2013 14827 8182222 direct 14.89013 0.4150980
## 5: 2014 14827 8182222 direct 15.14556 0.4092522
## 6: 2015 14827 8182222 direct 15.53640 0.5463951
## 7: 2016 14827 8182222 direct 15.08315 0.5246169
## 8: 2017 14827 8182222 direct 15.42019 0.4284391
## val_onePerson stE_onePerson
## <num> <num>
## 1: 14.85737 0.7003471
## 2: 14.85737 0.4938724
## 3: 14.85737 0.4294296
## 4: 14.85737 0.4150980
## 5: 14.85737 0.4092522
## 6: 14.85737 0.5463951
## 7: 14.85737 0.5246169
## 8: 14.85737 0.4284391Here we see the relative number of persons at risk of poverty and the relative number of one-person households.
Grouping
The groups argument can be used to calculate estimators
for different subsets of the data. This argument can take the grouping
variable as a string that refers to a column name (usually a factor) in
dat. If set, all estimators are not only split by the
reference period but also by the grouping variable. For simplicity, only
one reference period of the above data is used.
dat2 <- subset(dat_boot_calib, year == 2010)
for (att in c("period", "weights", "b.rep"))
attr(dat2, att) <- attr(dat_boot_calib, att)To calculate the ratio of persons at risk of poverty for each federal
state of Austria, group = "region" can be used.
povertyRates <- calc.stError(dat2, var = "povertyRisk", fun = weightedRatio, group = "region")
povertyRates$Estimates## Key: <year, n, N, region, estimate_type>
## year n N region estimate_type val_povertyRisk
## <num> <int> <num> <fctr> <char> <num>
## 1: 2010 549 260564 Burgenland direct 19.53984
## 2: 2010 733 377355 Vorarlberg direct 16.53731
## 3: 2010 924 535451 Salzburg direct 13.78734
## 4: 2010 1078 563648 Carinthia direct 13.08627
## 5: 2010 1317 701899 Tyrol direct 15.30819
## 6: 2010 2295 1167045 Styria direct 14.37464
## 7: 2010 2322 1598931 Vienna direct 17.23468
## 8: 2010 2804 1555709 Lower Austria direct 13.84362
## 9: 2010 2805 1421620 Upper Austria direct 10.88977
## 10: 2010 14827 8182222 <NA> direct 14.44422
## stE_povertyRisk
## <num>
## 1: 3.0801817
## 2: 2.3092452
## 3: 2.3830009
## 4: 1.8283667
## 5: 1.5234799
## 6: 1.3010259
## 7: 1.1829950
## 8: 1.1390482
## 9: 1.3639079
## 10: 0.6456405The last row with region = NA denotes the aggregate over
all regions. Note that the columns N and n now
show the weighted and unweighted number of persons in each region.
Several grouping variables
In case more than one grouping variable is used, there are several
options of calling calc.stError() depending on whether
combinations of grouping levels should be regarded or not. We will
consider the variables gender and region as
our grouping variables and show three options on how
calc.stError() can be called.
Option 1: All regions and all genders
Calculate the point estimate and standard error for each region and each gender. The number of rows in the output is therefore
The last row is again the estimate for the whole period.
povertyRates <- calc.stError(dat2, var = "povertyRisk", fun = weightedRatio,
group = c("gender", "region"))
povertyRates$Estimates## Key: <year, n, N, gender, region, estimate_type>
## year n N gender region estimate_type val_povertyRisk
## <num> <int> <num> <fctr> <fctr> <char> <num>
## 1: 2010 549 260564 <NA> Burgenland direct 19.53984
## 2: 2010 733 377355 <NA> Vorarlberg direct 16.53731
## 3: 2010 924 535451 <NA> Salzburg direct 13.78734
## 4: 2010 1078 563648 <NA> Carinthia direct 13.08627
## 5: 2010 1317 701899 <NA> Tyrol direct 15.30819
## 6: 2010 2295 1167045 <NA> Styria direct 14.37464
## 7: 2010 2322 1598931 <NA> Vienna direct 17.23468
## 8: 2010 2804 1555709 <NA> Lower Austria direct 13.84362
## 9: 2010 2805 1421620 <NA> Upper Austria direct 10.88977
## 10: 2010 7267 3979572 male <NA> direct 12.02660
## 11: 2010 7560 4202650 female <NA> direct 16.73351
## 12: 2010 14827 8182222 <NA> <NA> direct 14.44422
## stE_povertyRisk
## <num>
## 1: 3.0801817
## 2: 2.3092452
## 3: 2.3830009
## 4: 1.8283667
## 5: 1.5234799
## 6: 1.3010259
## 7: 1.1829950
## 8: 1.1390482
## 9: 1.3639079
## 10: 0.7062000
## 11: 0.6653989
## 12: 0.6456405Option 2: All combinations of region and
gender
Split the data by all combinations of the two grouping variables. This will result in a larger output-table of the size
povertyRates <- calc.stError(dat2, var = "povertyRisk", fun = weightedRatio,
group = list(c("gender", "region")))
povertyRates$Estimates## Key: <year, n, N, gender, region, estimate_type>
## year n N gender region estimate_type val_povertyRisk
## <num> <int> <num> <fctr> <fctr> <char> <num>
## 1: 2010 261 122741.8 male Burgenland direct 17.414524
## 2: 2010 288 137822.2 female Burgenland direct 21.432598
## 3: 2010 359 182732.9 male Vorarlberg direct 12.973259
## 4: 2010 374 194622.1 female Vorarlberg direct 19.883637
## 5: 2010 440 253143.7 male Salzburg direct 9.156964
## 6: 2010 484 282307.3 female Salzburg direct 17.939382
## 7: 2010 517 268581.4 male Carinthia direct 10.552149
## 8: 2010 561 295066.6 female Carinthia direct 15.392924
## 9: 2010 650 339566.5 male Tyrol direct 12.857542
## 10: 2010 667 362332.5 female Tyrol direct 17.604861
## 11: 2010 1128 571011.7 male Styria direct 11.671247
## 12: 2010 1132 774405.4 male Vienna direct 15.590616
## 13: 2010 1167 596033.3 female Styria direct 16.964539
## 14: 2010 1190 824525.6 female Vienna direct 18.778813
## 15: 2010 1363 684272.5 male Upper Austria direct 9.074690
## 16: 2010 1387 772593.2 female Lower Austria direct 16.372949
## 17: 2010 1417 783115.8 male Lower Austria direct 11.348283
## 18: 2010 1442 737347.5 female Upper Austria direct 12.574206
## 19: 2010 14827 8182222.0 <NA> <NA> direct 14.444218
## stE_povertyRisk
## <num>
## 1: 2.9558393
## 2: 3.5819672
## 3: 2.5260206
## 4: 2.6804099
## 5: 1.9731209
## 6: 2.8596320
## 7: 1.4904660
## 8: 2.4199358
## 9: 1.6992510
## 10: 1.4994375
## 11: 1.4184052
## 12: 1.0860581
## 13: 1.5555397
## 14: 1.5269705
## 15: 1.4812521
## 16: 1.1879052
## 17: 1.3830320
## 18: 1.3266616
## 19: 0.6456405Option 3: Cobination of Option 1 and Option 2
In this case, the estimates and standard errors are calculated for
- every gender,
- every region and
- every combination of region and gender.
The number of rows in the output is therefore
povertyRates <- calc.stError(dat2, var = "povertyRisk", fun = weightedRatio,
group = list("gender", "region", c("gender", "region")))
povertyRates$Estimates## Key: <year, n, N, gender, region, estimate_type>
## year n N gender region estimate_type val_povertyRisk
## <num> <int> <num> <fctr> <fctr> <char> <num>
## 1: 2010 261 122741.8 male Burgenland direct 17.414524
## 2: 2010 288 137822.2 female Burgenland direct 21.432598
## 3: 2010 359 182732.9 male Vorarlberg direct 12.973259
## 4: 2010 374 194622.1 female Vorarlberg direct 19.883637
## 5: 2010 440 253143.7 male Salzburg direct 9.156964
## 6: 2010 484 282307.3 female Salzburg direct 17.939382
## 7: 2010 517 268581.4 male Carinthia direct 10.552149
## 8: 2010 549 260564.0 <NA> Burgenland direct 19.539837
## 9: 2010 561 295066.6 female Carinthia direct 15.392924
## 10: 2010 650 339566.5 male Tyrol direct 12.857542
## 11: 2010 667 362332.5 female Tyrol direct 17.604861
## 12: 2010 733 377355.0 <NA> Vorarlberg direct 16.537310
## 13: 2010 924 535451.0 <NA> Salzburg direct 13.787343
## 14: 2010 1078 563648.0 <NA> Carinthia direct 13.086268
## 15: 2010 1128 571011.7 male Styria direct 11.671247
## 16: 2010 1132 774405.4 male Vienna direct 15.590616
## 17: 2010 1167 596033.3 female Styria direct 16.964539
## 18: 2010 1190 824525.6 female Vienna direct 18.778813
## 19: 2010 1317 701899.0 <NA> Tyrol direct 15.308190
## 20: 2010 1363 684272.5 male Upper Austria direct 9.074690
## 21: 2010 1387 772593.2 female Lower Austria direct 16.372949
## 22: 2010 1417 783115.8 male Lower Austria direct 11.348283
## 23: 2010 1442 737347.5 female Upper Austria direct 12.574206
## 24: 2010 2295 1167045.0 <NA> Styria direct 14.374637
## 25: 2010 2322 1598931.0 <NA> Vienna direct 17.234683
## 26: 2010 2804 1555709.0 <NA> Lower Austria direct 13.843623
## 27: 2010 2805 1421620.0 <NA> Upper Austria direct 10.889773
## 28: 2010 7267 3979571.7 male <NA> direct 12.026600
## 29: 2010 7560 4202650.3 female <NA> direct 16.733508
## 30: 2010 14827 8182222.0 <NA> <NA> direct 14.444218
## year n N gender region estimate_type val_povertyRisk
## stE_povertyRisk
## <num>
## 1: 2.9558393
## 2: 3.5819672
## 3: 2.5260206
## 4: 2.6804099
## 5: 1.9731209
## 6: 2.8596320
## 7: 1.4904660
## 8: 3.0801817
## 9: 2.4199358
## 10: 1.6992510
## 11: 1.4994375
## 12: 2.3092452
## 13: 2.3830009
## 14: 1.8283667
## 15: 1.4184052
## 16: 1.0860581
## 17: 1.5555397
## 18: 1.5269705
## 19: 1.5234799
## 20: 1.4812521
## 21: 1.1879052
## 22: 1.3830320
## 23: 1.3266616
## 24: 1.3010259
## 25: 1.1829950
## 26: 1.1390482
## 27: 1.3639079
## 28: 0.7062000
## 29: 0.6653989
## 30: 0.6456405
## stE_povertyRiskGroup differences
If differences between groups need to be calculated, e.g difference
of poverty rates between gender = "male" and
gender = "female", parameter group.diff can be
utilised. Setting group.diff = TRUE the differences and the
standard error of these differences for all variables defined in
groups will be calculated.
povertyRates <- calc.stError(dat2, var = "povertyRisk", fun = weightedRatio,
group = c("gender", "region"),
group.diff = TRUE)
povertyRates$Estimates## Key: <year, n, N, gender, region, estimate_type>
## year n N gender region
## <num> <num> <num> <fctr> <fctr>
## 1: 2010 549.0 260564.0 <NA> Burgenland
## 2: 2010 641.0 318959.5 <NA> Burgenland - Vorarlberg
## 3: 2010 733.0 377355.0 <NA> Vorarlberg
## 4: 2010 736.5 398007.5 <NA> Burgenland - Salzburg
## 5: 2010 813.5 412106.0 <NA> Burgenland - Carinthia
## 6: 2010 828.5 456403.0 <NA> Salzburg - Vorarlberg
## 7: 2010 905.5 470501.5 <NA> Carinthia - Vorarlberg
## 8: 2010 924.0 535451.0 <NA> Salzburg
## 9: 2010 933.0 481231.5 <NA> Burgenland - Tyrol
## 10: 2010 1001.0 549549.5 <NA> Carinthia - Salzburg
## 11: 2010 1025.0 539627.0 <NA> Tyrol - Vorarlberg
## 12: 2010 1078.0 563648.0 <NA> Carinthia
## 13: 2010 1120.5 618675.0 <NA> Salzburg - Tyrol
## 14: 2010 1197.5 632773.5 <NA> Carinthia - Tyrol
## 15: 2010 1317.0 701899.0 <NA> Tyrol
## 16: 2010 1422.0 713804.5 <NA> Burgenland - Styria
## 17: 2010 1435.5 929747.5 <NA> Burgenland - Vienna
## 18: 2010 1514.0 772200.0 <NA> Styria - Vorarlberg
## 19: 2010 1527.5 988143.0 <NA> Vienna - Vorarlberg
## 20: 2010 1609.5 851248.0 <NA> Salzburg - Styria
## 21: 2010 1623.0 1067191.0 <NA> Salzburg - Vienna
## 22: 2010 1676.5 908136.5 <NA> Burgenland - Lower Austria
## 23: 2010 1677.0 841092.0 <NA> Burgenland - Upper Austria
## 24: 2010 1686.5 865346.5 <NA> Carinthia - Styria
## 25: 2010 1700.0 1081289.5 <NA> Carinthia - Vienna
## 26: 2010 1768.5 966532.0 <NA> Lower Austria - Vorarlberg
## 27: 2010 1769.0 899487.5 <NA> Upper Austria - Vorarlberg
## 28: 2010 1806.0 934472.0 <NA> Styria - Tyrol
## 29: 2010 1819.5 1150415.0 <NA> Tyrol - Vienna
## 30: 2010 1864.0 1045580.0 <NA> Lower Austria - Salzburg
## 31: 2010 1864.5 978535.5 <NA> Salzburg - Upper Austria
## 32: 2010 1941.0 1059678.5 <NA> Carinthia - Lower Austria
## 33: 2010 1941.5 992634.0 <NA> Carinthia - Upper Austria
## 34: 2010 2060.5 1128804.0 <NA> Lower Austria - Tyrol
## 35: 2010 2061.0 1061759.5 <NA> Tyrol - Upper Austria
## 36: 2010 2295.0 1167045.0 <NA> Styria
## 37: 2010 2308.5 1382988.0 <NA> Styria - Vienna
## 38: 2010 2322.0 1598931.0 <NA> Vienna
## 39: 2010 2549.5 1361377.0 <NA> Lower Austria - Styria
## 40: 2010 2550.0 1294332.5 <NA> Styria - Upper Austria
## 41: 2010 2563.0 1577320.0 <NA> Lower Austria - Vienna
## 42: 2010 2563.5 1510275.5 <NA> Upper Austria - Vienna
## 43: 2010 2804.0 1555709.0 <NA> Lower Austria
## 44: 2010 2804.5 1488664.5 <NA> Lower Austria - Upper Austria
## 45: 2010 2805.0 1421620.0 <NA> Upper Austria
## 46: 2010 7267.0 3979571.7 male <NA>
## 47: 2010 7413.5 4091111.0 male - female <NA>
## 48: 2010 7560.0 4202650.3 female <NA>
## 49: 2010 14827.0 8182222.0 <NA> <NA>
## year n N gender region
## estimate_type val_povertyRisk stE_povertyRisk
## <char> <num> <num>
## 1: direct 19.53983651 3.0801817
## 2: group difference 3.00252634 3.3440799
## 3: direct 16.53731017 2.3092452
## 4: group difference 5.75249330 3.5657838
## 5: group difference 6.45356876 3.9849262
## 6: group difference -2.74996696 2.9858980
## 7: group difference -3.45104242 3.2549609
## 8: direct 13.78734321 2.3830009
## 9: group difference 4.23164602 3.4914678
## 10: group difference -0.70107546 2.6010839
## 11: group difference -1.22911968 2.7299152
## 12: direct 13.08626775 1.8283667
## 13: group difference -1.52084728 1.6908612
## 14: group difference -2.22192274 2.6477620
## 15: direct 15.30819049 1.5234799
## 16: group difference 5.16519923 3.2532858
## 17: group difference 2.30515330 3.3224435
## 18: group difference -2.16267289 3.1952079
## 19: group difference 0.69737304 1.5035744
## 20: group difference -0.58729407 2.2538369
## 21: group difference -3.44734000 2.6436214
## 22: group difference 5.69621369 2.8540687
## 23: group difference 8.65006312 3.3806543
## 24: group difference -1.28836953 2.3703127
## 25: group difference -4.14841546 2.5772093
## 26: group difference -2.69368735 1.8955769
## 27: group difference -5.64753678 2.8355308
## 28: group difference -0.93355321 1.2952525
## 29: group difference -1.92649272 1.9246499
## 30: group difference 0.05627961 2.0082683
## 31: group difference 2.89756982 2.8351611
## 32: group difference -0.75735506 2.3045370
## 33: group difference 2.19649436 2.0993320
## 34: group difference -1.46456768 1.7378340
## 35: group difference 4.41841710 2.3174786
## 36: direct 14.37463728 1.3010259
## 37: group difference -2.86004593 2.2348640
## 38: direct 17.23468321 1.1829950
## 39: group difference -0.53101447 1.7555890
## 40: group difference 3.48486389 1.5978948
## 41: group difference -3.39106040 1.1153839
## 42: group difference -6.34490982 1.9960346
## 43: direct 13.84362281 1.1390482
## 44: group difference 2.95384943 1.6636062
## 45: direct 10.88977339 1.3639079
## 46: direct 12.02659998 0.7062000
## 47: group difference -4.70690810 0.4725442
## 48: direct 16.73350808 0.6653989
## 49: direct 14.44421817 0.6456405
## estimate_type val_povertyRisk stE_povertyRiskThe resulting output table contains 49 rows. 12 rows for all the direct estimators
and another 37 for all the differences within the variable
"gender" and "region" seperately. Variable
"gender" has 2 unique values
(unique(dat2$gender)) resulting in 1 difference, ~
gender = "male" - gender = "female" and
variable "region" has 9 unique values
(unique(dat2$region)) resulting in
estimates. Thus the output contains 1 + 36 = 37 estimates with respect to group differences.
If a combintaion of grouping variables is used in group
and group.diff = TRUE then differences between combinations
will only be calculated if one of the grouping variables differs. For
example the difference between the following groups would be
calculated
-
gender = "female" & region = "Vienna"-gender = "male" & region = "Vienna" -
gender = "female" & region = "Vienna"-gender = "female" & region = "Salzburg" -
gender = "male" & region = "Salzburg"-gender = "female" & region = "Salzburg"
The difference between
gender = "female" & region = "Vienna" and
gender = "male" & region = "Salzburg" however would not
be calculated.
Thus this leads to
results with respect to the differences. The Output contains an
additional column estimate_type and
povertyRates <- calc.stError(dat2, var = "povertyRisk", fun = weightedRatio,
group = list(c("gender", "region")),
group.diff = TRUE)
povertyRates$Estimates[,.N,by=.(estimate_type)]## estimate_type N
## <char> <int>
## 1: direct 19
## 2: group difference 81Differences between survey periods
Differences of estimates between periods can be
calculated using parameter period.diff.
period.diff expects a character vector (if not
NULL) specifying for which periods the
differences should be calcualed for. The inputs should be specified in
the form "period2" - "period1".
povertyRates <- calc.stError(dat_boot_calib[year>2013], var = "povertyRisk", fun = weightedRatio,
period.diff = c("2017 - 2016", "2016 - 2015", "2015 - 2014"))
povertyRates$Estimates## Key: <year, n, N, estimate_type>
## year n N estimate_type val_povertyRisk stE_povertyRisk
## <char> <num> <num> <char> <num> <num>
## 1: 2014 14827 8182222 direct 15.1455601 0.5126322
## 2: 2015 14827 8182222 direct 15.5364014 0.4889217
## 3: 2015-2014 14827 8182222 period difference 0.3908413 0.4704026
## 4: 2016 14827 8182222 direct 15.0831502 0.5773682
## 5: 2016-2015 14827 8182222 period difference -0.4532512 0.5194934
## 6: 2017 14827 8182222 direct 15.4201916 0.4083678
## 7: 2017-2016 14827 8182222 period difference 0.3370414 0.4919362If additional grouping variables are supplied to
calc.stError() die differences across periods
are also carried out for all variables in group.
povertyRates <- calc.stError(dat_boot_calib[year>2013], var = "povertyRisk", fun = weightedRatio,
group = "gender",
period.diff = c("2017 - 2016", "2016 - 2015", "2015 - 2014"))
povertyRates$Estimates## Key: <year, n, N, gender, estimate_type>
## year n N gender estimate_type val_povertyRisk
## <char> <num> <num> <fctr> <char> <num>
## 1: 2014 7267 3979572 male direct 14.5035068
## 2: 2014 7560 4202650 female direct 15.7535328
## 3: 2014 14827 8182222 <NA> direct 15.1455601
## 4: 2015 7267 3979572 male direct 15.1228904
## 5: 2015 7560 4202650 female direct 15.9279630
## 6: 2015 14827 8182222 <NA> direct 15.5364014
## 7: 2015-2014 7267 3979572 male period difference 0.6193836
## 8: 2015-2014 7560 4202650 female period difference 0.1744301
## 9: 2015-2014 14827 8182222 <NA> period difference 0.3908413
## 10: 2016 7267 3979572 male direct 14.5796824
## 11: 2016 7560 4202650 female direct 15.5598937
## 12: 2016 14827 8182222 <NA> direct 15.0831502
## 13: 2016-2015 7267 3979572 male period difference -0.5432080
## 14: 2016-2015 7560 4202650 female period difference -0.3680693
## 15: 2016-2015 14827 8182222 <NA> period difference -0.4532512
## 16: 2017 7267 3979572 male direct 14.9481591
## 17: 2017 7560 4202650 female direct 15.8671684
## 18: 2017 14827 8182222 <NA> direct 15.4201916
## 19: 2017-2016 7267 3979572 male period difference 0.3684767
## 20: 2017-2016 7560 4202650 female period difference 0.3072748
## 21: 2017-2016 14827 8182222 <NA> period difference 0.3370414
## year n N gender estimate_type val_povertyRisk
## stE_povertyRisk
## <num>
## 1: 0.5780030
## 2: 0.5222374
## 3: 0.5126322
## 4: 0.6723961
## 5: 0.3891856
## 6: 0.4889217
## 7: 0.5155048
## 8: 0.4741321
## 9: 0.4704026
## 10: 0.6775332
## 11: 0.5174284
## 12: 0.5773682
## 13: 0.5447479
## 14: 0.5414803
## 15: 0.5194934
## 16: 0.4374739
## 17: 0.4107798
## 18: 0.4083678
## 19: 0.5387920
## 20: 0.4810226
## 21: 0.4919362
## stE_povertyRiskAverages across periods
With parameter period.mean averages across
periods are calculated additional. The parameter accepts
only odd integer values. The resulting table will contain the direct
estimates as well as rolling averages of length
period.mean.
povertyRates <- calc.stError(dat_boot_calib[year>2013], var = "povertyRisk", fun = weightedRatio,
period.mean = 3)
povertyRates$Estimates## Key: <year, n, N, estimate_type>
## year n N estimate_type val_povertyRisk stE_povertyRisk
## <char> <num> <num> <char> <num> <num>
## 1: 2014 14827 8182222 direct 15.14556 0.5126322
## 2: 2014_2015_2016 14827 8182222 period average 15.25504 0.4496982
## 3: 2015 14827 8182222 direct 15.53640 0.4889217
## 4: 2015_2016_2017 14827 8182222 period average 15.34658 0.4028768
## 5: 2016 14827 8182222 direct 15.08315 0.5773682
## 6: 2017 14827 8182222 direct 15.42019 0.4083678if in addition the parameters group and/or
period.diff are specified then differences and groupings of
averages will be calculated.
povertyRates <- calc.stError(dat_boot_calib[year>2013], var = "povertyRisk", fun = weightedRatio,
period.mean = 3, period.diff = "2016 - 2015",
group = "gender")
povertyRates$Estimates## Key: <year, n, N, gender, estimate_type>
## year n N gender estimate_type
## <char> <num> <num> <fctr> <char>
## 1: 2014 7267 3979572 male direct
## 2: 2014 7560 4202650 female direct
## 3: 2014 14827 8182222 <NA> direct
## 4: 2014_2015_2016 7267 3979572 male period average
## 5: 2014_2015_2016 7560 4202650 female period average
## 6: 2014_2015_2016 14827 8182222 <NA> period average
## 7: 2015 7267 3979572 male direct
## 8: 2015 7560 4202650 female direct
## 9: 2015 14827 8182222 <NA> direct
## 10: 2015_2016_2017 7267 3979572 male period average
## 11: 2015_2016_2017 7560 4202650 female period average
## 12: 2015_2016_2017 14827 8182222 <NA> period average
## 13: 2016 7267 3979572 male direct
## 14: 2016 7560 4202650 female direct
## 15: 2016 14827 8182222 <NA> direct
## 16: 2016-2015 7267 3979572 male period difference
## 17: 2016-2015 7560 4202650 female period difference
## 18: 2016-2015 14827 8182222 <NA> period difference
## 19: 2016-2015_mean 7267 3979572 male difference between period averages
## 20: 2016-2015_mean 7560 4202650 female difference between period averages
## 21: 2016-2015_mean 14827 8182222 <NA> difference between period averages
## 22: 2017 7267 3979572 male direct
## 23: 2017 7560 4202650 female direct
## 24: 2017 14827 8182222 <NA> direct
## year n N gender estimate_type
## val_povertyRisk stE_povertyRisk
## <num> <num>
## 1: 14.50350682 0.57800303
## 2: 15.75353283 0.52223739
## 3: 15.14556006 0.51263215
## 4: 14.73535987 0.57119384
## 5: 15.74712982 0.39010598
## 6: 15.25503720 0.44969824
## 7: 15.12289042 0.67239613
## 8: 15.92796296 0.38918560
## 9: 15.53640136 0.48892172
## 10: 14.88357729 0.51877021
## 11: 15.78500836 0.32734186
## 12: 15.34658105 0.40287678
## 13: 14.57968239 0.67753324
## 14: 15.55989368 0.51742844
## 15: 15.08315018 0.57736817
## 16: -0.54320803 0.54474787
## 17: -0.36806928 0.54148025
## 18: -0.45325118 0.51949345
## 19: 0.14821741 0.09132724
## 20: 0.03787854 0.11858738
## 21: 0.09154385 0.09465179
## 22: 14.94815906 0.43747385
## 23: 15.86716845 0.41077980
## 24: 15.42019160 0.40836780
## val_povertyRisk stE_povertyRisk