The R-package surveysd: Estimating standard errors for complex surveys with a rotating panel design

Abstract

Surveys with a rotating panel design are a prominent tool for producing more efficient estimates for indicators regarding trends or net changes over time. Variance estimation for net changes becomes however more complicated due to a possibly high correlation between the panel waves. Therefore, these estimates are quite burdensome to produce with traditional means. With the R-package surveysd, we present a tool which supports a straightforward way for producing estimates and corresponding standard errors for complex surveys with a rotating panel design. The package uses bootstrap techniques which incorporate the panel design and thus makes it easy to estimate standard errors. In addition the package supports a method for producing more efficient estimates by cumulating multiple consecutive sample waves. This method can lead to a significant decrease in variance assuming that structural patterns for the indicator in question remain fairly robust over time. The usability of the package and variance improvement, using this bootstrap methodology, is demonstrated on data from the user database (UDB) for the EU Statistics on Income and Living Conditions of selected countries with various sampling designs.

Keywords

Complex surveys variance estimation bootstrapping resampling R-programming

1. Introduction

Many sociodemographic population parameters are periodically estimated, for instance the unemployment rate, wealth distribution or poverty rate. One important aspect for the regular estimation of those parameters is to observe net changes over time and to consequently monitor the effect of related policies. Surveys with a rotating panel design are a prominent tool for measuring net changes of an indicator over time. They are a compromise between a single panel survey, which can suffer from cumulative effects of sample attrition, and a survey with independent samples, which exhibits a greater sampling error for measuring net changes and trends.

The overlapping panels do however increase the complexity for estimating net changes due to the possibly high correlation. For a statistical production process the estimation can become quite burdensome since estimates are produced not only for the whole survey population but also for many different sub-groupings.

One prominent sample with a rotating panel design is the so called EU Statistics on Income and Living Conditions (EU-SILC), launched 2004. It represents a European standardized survey to generate comparative measures of poverty and social exclusion among the EU Member States and social inclusion policies implemented by Member States are monitored mainly with comparative indicators based on EU-SILC data. The survey is conducted annually in each country with a rotating panel design of 4 waves [1]. In combination with a harmonized survey a set of common indicators, the so called Laeken indicators, were adopted for the countries of the EU [2].

In case of EU-SILC the ultimate cluster approach has been suggested during the second network project for the analysis of EU-SILC (Net-SILC2) as a pragmatic solution for estimating standard errors [3]. This method approximates total sampling variance from the variance between clusters at the first stage, which is called the ultimate cluster approach, see [4]. Standard errors for non-linear indicators are calculated upon linearised variables which have asymptotically the same variance properties as the indicators in question [5]. The approach has been implemented in an R-package called vardpoor [6], which is tailored specifically for the use with EU-SILC data.

The survey design and sample size of the EU-SILC is tuned to deliver qualitatively high well-being indicators at national or Nomenclature of Territorial Units for Statistics level 1 (NUTS1), but usually lacks the capability to do the same for smaller subgroups of the survey population, for example estimates on NUTS2 or NUTS3 level.

When it comes to regional indicators based on sample data such as EU-SILC three approaches are commonly known to improve their precision [7]:

Improved size, allocation or design of regional samples;

Improved estimation techniques which use auxiliary information;

Relaxing requirements of reporting by aggregating information over space, time for indicators.

The first approach requires changes in the data collection which imply considerable cost and needs time for implementation.

Small Area Estimation (SAE) has been developed as an alternative (or complementary) strategy to changes in sample design [8]. Depending on the model specifications and used auxiliary information the methods can yield different results, precision gains and also potential bias. Considering that EU-SILC is a harmonised survey comparing results on an EU-Level can be challenging for users when the underlying methodology can vary greatly. Another model based approach has for example been developed by the World Bank [9], it combines sample data and administrative information and produces regional estimates by mass imputing the variable of interest on a population census.

In this work we present an R package which supports a harmonious approach for estimating standard errors on data collected through a survey with a rotating panel design. The methodology implemented uses bootstrapping techniques for error estimations which, contrary to jack knife replicates, yield consistent estimates for variance even for non-smooth estimators like the median. In order to mimic the panel design of the data requires that sample units must be linked over the panel waves through a unique identifier. Furthermore statistically significant estimates on subgroups of the population can be derived by using multiple consecutive panel waves. From a subject matter perspective this method is however only applicable if the structural patterns for the indicator changes slowly over time.

In a comprehensive study of poverty in NUTS2 regions [10] Statistics Austria has derived standard errors with a bootstrap replication method which partly drew on experience made in the Advanced Methodology for European Laeken Indicators (AMELI) project [11]. Results were compared over several years, indicators and estimation methods. Standard errors of EU-SILC estimates which are cumulated over three successive years were found to be about 25% below that of single years. This implies an increase of effective sample size by approximately 78%. The study in [10] also showed that results from more advanced SAE techniques could generally not provide more stable results.

2. Methodology

The following subsection presents the used methodology which is applied on multiple consecutive panels of survey data, for instance multiple years of EU-SILC. The methodology contains the following steps, in this order

Draw $B$ bootstrap replicates from data for each panel wave $y_{t}$ , $t=1,\ldots,n_{y}$ separately. For survey data with a rotating panel design the bootstrap replicate of a household are carried forward through the panel waves. That is, the bootstrap replicate of a sampling unit in the follow-up panel waves is set equal to the bootstrap replicate of the same sampling unit when it enters the survey.

Multiply each set of bootstrap replicates by the sampling weights to obtain uncalibrated bootstrap weights and calibrate each of the uncalibrated bootstrap weights using iterative proportional fitting.

Estimate the point estimate of interest $\theta$ , for each year and each calibrated bootstrap weight to obtain $\tilde{\theta}^{(i,y_{t})}$ , $t=1,\ldots,n_{y}$ , $i=1,\ldots,B$ . For fixed $y_{t}$ apply a filter with equal weights for each $i$ on $\tilde{\theta}^{(i,y^{*})}$ , $y^{*}\in\{y_{t-1},y_{t},y_{t+1}\}$ , to obtain $\tilde{\theta}^{(i,y_{t})}$ . Estimate the variance of $\theta$ using the distribution of $\tilde{\theta}^{(i,y_{t})}$ .

2.1 Rescaled Bootstrap

Bootstrapping has long been around and used widely to estimate confidence intervals and standard errors of point estimates, [12]. Given a random sample $(X_{1},\ldots,X_{n})$ drawn from an unknown distribution $F$ the distribution of a point estimate $\theta(X_{1},\ldots,X_{n};F)$ can in many cases not be determined analytically. However when using bootstrapping one can simulate the distribution of $\theta$ .

Let $s_{(.)}$ be a bootstrap sample, e.g. drawing $n$ observations with replacement from the sample $(X_{1},\ldots,X_{n})$ , then one can estimate the standard deviation of $\theta$ using $B$ bootstrap samples through

$\displaystyle sd\left(\theta\right)=\sqrt{\frac{1}{B-1}\sum_{i=1}^{B}(\theta% \left({s_{i}}\right)-\bar{\theta})^{2}},$

with $\bar{\theta}$ : $=\frac{1}{B}\sum^{B}_{i=1}\theta(s_{i})$ as the sample mean over all bootstrap samples.

sIn context of sample surveys naive bootstrap procedures are not applicable because they do not incorporate the specific sampling design. In the surveysd Package we implemented the rescaled bootstrap for stratified multistage sampling, see [13, 14]. For this procedure the bootstrap samples are selected without replacement and do incorporate stratification as well as clustering on multiple stages. Each of the bootstrap replicates $b_{j}^{i}$ for sample unit $Y_{j}$ , $j=1,\ldots,n\wedge i=1,\ldots,B$ , are multiplied with the corresponding weight $w_{j}$ which yields the $i$ -th uncalibrated bootstrap weight $\tilde{b}^{i}_{j}$ .

2.1.1 Single primary sampling units (PSUs)

When dealing with multistage sampling designs the issue of single PSUs, e.g. a single response unit is present at a stage or in a strata, can occur. When applying bootstrapping procedures these single PSUs can lead to a variety of issues. The bootstrap procedure implemented in the Package surveysd automatically detects single PSUs and either merges them together with the strata or cluster with the next least number of PSUs or substitute with the mean value over all bootstrap replicates at the stage which did not contain single PSUs.

2.1.2 Considering panel rotation and split households

For a survey with a rotating penal design the $i$ -th bootstrap replicate weight $\tilde{b}^{i}_{j}$ for a unit $Y_{j}$ is taken forward until the unit $Y_{j}$ drops out of the sample. Meaning that the unit $Y_{j}$ , which enters the survey at panel $y_{1}$ and drops out at panel $y_{\tilde{t}}$ , the bootstrap replicates for the panel waves $y_{2},\ldots,y_{\tilde{t}}$ are set to the bootstrap replicate of the first panel wave $y_{1}$ .

This procedure is also extended to cases concerning so called split households. A split household occurs when a sampling unit changes address between consecutive panel waves and is followed up on, thus including other cohabitants at the new dress which were not originally in the sample. These new individuals in the split household will inherit the same bootstrap replicate as the sampling unit which changed dress.

2.2 Calibration

The uncalibrated bootstrap weights $\tilde{b}^{i}_{j}$ computed through the rescaled bootstrap procedure yields population statistics that differ from the known population margins of specified sociodemographic variables for which the base weights $w_{j}$ have been calibrated. To adjust for this, the bootstrap weights $\tilde{b}^{i}_{j}$ can be recalibrated using iterative proportional fitting [15], thus yielding calibrated bootstrap sample weights $b_{j}^{({i,y_{t}})}$ , $i=1,\ldots,B$ , for each panel $y$ and each sample unit $j$ .

2.3 Variance estimation

Using the calibrated bootstrap sample weights, $b_{j}^{({i,y_{t}})}$ , it is straight forward to compute the standard error of a point estimate $\theta(\text{X}^{y_{t}},\text{w}^{y_{t}})$ for panel $y_{t}$ with $\text{X}^{y_{t}}=(X_{1}^{y_{t}},\ldots,X_{n}^{y_{t}})$ as the vector of observations for the variable of interest in the survey and $\text{w}^{y_{t}}=(w_{1}^{y_{t}},\ldots,w_{n}^{y_{t}}$ ) as the corresponding weight vector, with

$\displaystyle sd\left(\theta\right)=\sqrt{\frac{1}{B-1}\sum_{i=1}^{B}(\theta^{% \left({i,y_{t}}\right)}-\overline{\theta^{\left({.,y_{t}}\right)}})^{2}}$

with

$\displaystyle\overline{\theta^{\left({.,y_{t}}\right)}}=\frac{1}{B}\sum_{i=1}^% {B}\theta^{\left({i,y_{t}}\right)},$

where $\theta^{(i,y_{t})}$ : $=\theta(\text{X}^{y_{t}},\text{b}^{(i,y_{t})})$ is the estimate of $\theta$ in panel $y_{t}$ using the $i$ -th vector of calibrated bootstrap weights.

As already mentioned the standard error estimation for indicators in EU-SILC yields high quality results for NUTS1 or country level. When estimation indicators on regional or other sub-aggregate levels one is confronted with point estimates yielding high variance.

To overcome this issue one can pool consecutive panels $\theta$ for 3 consecutive years using the calibrated bootstrap weights thus calculating $\{\theta^{({i,y_{t-1}})},\theta^{({i,y_{t}})}$ , $\theta^{({i,y_{t+1}})}\}$ , $i=1,\ldots,B$ . For fixed $i$ one can apply a filter with equal filter weights on the time series $\{{\theta^{({i,y_{t-1}})},\theta^{({i,y_{t}})},\theta^{({i,y_{t+1}})}}\}$ to create $\tilde{\theta}^{(i,y_{t})}$

$\displaystyle\tilde{\theta}^{(i,y_{t})}=\frac{1}{3}[\theta^{(i,y_{t-1})}+% \theta^{(i,y_{t})}+\theta^{(i,y_{t+1})}].$

Table 1
Section of the UDB data from Austria

Year	Hid	Pid	Nsuts2	Urban	AgeGroup	Sex	Weight
2008	4	s401	AT34	2	6	2	845.0613
2009	4	401	AT12	2	3	2	845.3711
2009	4	402	AT12	2	2	1	845.3711
2010	4	401	AT31	2	4	1	820.8616
2010	4	402	AT31	2	4	2	820.8616

Doing this for all $i$ , $i=1,\ldots,B$ , yields $\tilde{\theta}^{(i,y_{t})}$ , $i=1,\ldots,B$ . The standard error of $\theta$ can then be estimated as

$\displaystyle sd\left(\theta\right)=\sqrt{\frac{1}{B-1}\sum_{i=1}^{B}(\tilde{% \theta}^{(i,y_{t})}-\overline{\tilde{\theta}^{(i,y_{t})}})^{2}}$

with

$\displaystyle\overline{\tilde{\theta}^{(.,y_{t})}}=\frac{1}{B}\sum^{B}_{i=1}% \tilde{\theta}^{(i,y_{t})}.$

Applying the filter over the time series of estimated $\theta^{({i,y_{t}})}$ leads to a reduction of variance for $\theta$ since the filter reduces the noise in $\{{\theta^{({i,y_{t-1}})},\theta^{({i,y_{t}})},\theta^{({i,y_{t+1}})}}\}$ and thus leading to a more narrow distribution for $\tilde{\theta}^{(i,y_{t})}$ .

It should also be noted that estimating indicators from a survey with rotating panel design is in general not straight forward because of the high correlation between consecutive years. However with our approach to use bootstrap weights, which are independent from each other, we can bypass the cumbersome calculation of various correlations, and apply them directly to estimate the standard error [10] showed that using the proposed method on EU-SILC data for Austria the reduction in resulting standard errors corresponds in a theoretical increase in sample size by about 25%. Furthermore this study compared this method to the use of small area estimation techniques and on average the use of bootstrap sample weights yielded more stable results.

3. Application of surveysd

surveysd is a flexible R package for the estimation of standard errors for complex surveys with a rotating panel design. It is distributed under the GPL-2/GPL-3 license, see [16], and can be downloaded from the Comprehensive R Archive Network (CRAN), see https://CRAN.R-project.org/package=surveysd. As mentioned in the previous section the standard error estimation can be split up in three parts, namely

Drawing the bootstrap replicates

Calibrating bootstrap replicate weights

Estimating standard errors using bootstrap replicate weights

In the following subsections each of these steps is demonstrated using EU-SILC UDB data from Austria and Spain, containing the years 2008 till 2016. The EU-SILC sample for Austria contains a stratified sample design, whereas for Spain a 2-Stage sample design is used. The UDB data does not include all sample design variables and longitudinal identifiers, however they were provided by INE and Statistics Austria to augment the UDB data. Table 1 shows a snippet for the data from Austria, containing identifiers, like hid and pid, regional variables like nuts2 and degree of urbanisation (urban), as well as sociodemographic variables like sex and age groups (ageGroup).

Table 2
Results from the function calc.stError()

Year	$n$	$N$	val_AROPE	stE_AROPE
2008	13621	8241523	20.6109902	0.7010605
2009	13604	8262101	19.0881507	0.6657902
2010	14085	8283237	18.9036431	0.6570366
2011	13933	8315881	19.1581061	0.6817236
2012	13910	8344294	18.4801028	0.6833532
2013	13250	8368625	18.7844591	0.6367218
2014	12982	8403374	19.1505372	0.7117432
2015	13213	8476451	18.3001367	0.6761975
2016	13049	8590169	17.9541217	0.7442851
2016–2008	13335	8415846	$-$ 2.6568685	1.0403204
2016–2015	13131	8533310	$-$ 0.3460149	0.8044337

The following sections demonstrate how variance estimates for the amount of people at risk of poverty or social exclusion (AROPE) can be created.

3.1 Drawing bootstrap replicates

In order to draw bootstrap replicates, information about the sampling design, cluster and strata need to be available. In the case of the UDB data from Austria the stratification variable is equal to NUTS2. To reproduce the rotation for the bootstrap replicates the household id hid need to be fixed over time. First 1000 bootstrap replicates for the UDB data from Austria are drawn

library (surveysd) # load the package

# define stratified 1-Stage cluster sample

datAT_boot $<-$ draw.bootstrap(datAT, REP $=$ 1000, hid $=$ “hid”,

weights $=$ “weight”, strata $=$ “nuts2”,

period $=$ “year”, split $=$ TRUE, pid $=$ “pid”)

In the case of Spain the sampling design is more complex. At the first stage clusters were stratified and sampled from each strata separately. At the the second stage the households were sampled in each previously sampled cluster. For specifying this sampling design the number of clusters, a variable indicating clusters and stratification at the first stage need to be available in the data. Multiple stages can then be supplied using the arguments cluster and strata. The number of sampling units in each stage and strata must also be supplied, in this case total number of clusters (N.cluster) and households (N.households).

# define stratified 2-Stage cluster sample

datES_boot $<-$ draw.bootstrap(datES, REP $=$

1000, hid $=$ “hid”,

weights $=$ “weight”,

strata $=$ c(“Strata1”, “I”),

cluster $=$ c(“Cluster1”, “hid”),

totals $=$ c(“N.cluster”, “N.households”),

period $=$ “year”, split $=$ TRUE, pid $=$ “pid”)

Figure 1.

AROPE standard error for 2015 compared with 3 year average 2014–2016.

Note that the actual number of clusters was not contained in the UDB data but a rough estimate on the number of clusters was derived for the purpose of this demonstration.

3.2 Calibrating bootstrap replicate weights

With the function recalib() the bootstrap replicates weights are calculated and calibrated using the previously drawn bootstrap replicates. For both data sets we calibrate the replicates weights using the same population margins on personal- and household level, namely sex, ageGroup, hsize and nuts2. From the variables sex and ageGroup a combined cross table is used for calibration, see list(“sex”,“ageGroup”) in the code snippet below. The bootstrap replicate weights are calibrated on all population margins for each panel wave, e.g year, automatically.

datAT_calib $<-$ recalib(dat $=$ datAT_boot,

conP.var $=$ list(“sex”, “ageGroup”),

conH.var $=$ c(“hsize”, “nuts2”))

3.3 Estimating standard errors

Having the calibrated bootstrap replicate weights at hand we are interested in estimating the rate of persons who are at risk of poverty or social exclusion (AROPE), for each year as well as the net change of this estimate from 2016 to 2015 and from 2016 to 2008. The parameters fun and var in calc.stError() define the estimator to be used and the variable of interest.

est $<-$ calc.stError(datAT_calib, var $=$ “AROPE”,

fun $=$ weightedRatio,

period.diff $=$ c(“2016-2015”, “2016-2008”))

est$Estimates

Table 2 shows the results of the calculation. Columns that use the val_ prefix denote the point estimate belonging to the “main weight” of the dataset, which is weight in case of the dataset used here. Columns with the stE_ prefix denote standard errors calculated with bootstrap replicates. The replicates are calculated by using the replicate weights instead of weight when applying the estimator. n denotes the number of observations for the year and N denotes the total weight of those persons.

3.3.1 Grouping

Usually estimates need to be produced not only for each panel wave but also for many different subgroups of the underlying population, for instance for each NUTS2 region, age group, sex and a combination of those. Using the group argument this can easily be supplied to the function calc.stError()

groups $<-$ list(“nuts2”, “ageGroup”, “sex”,

c(“ageGroup”, “sex”))

resGroup $<-$ calc.stError(datAT_calib, var $=$

“AROPE”, fun $=$ weightedRatio,

group $=$ groups,

period.diff $=$ c(“2016-2015”, “2016-2008”))

resGroup

## Calculated point estimates for variable(s)

## AROPE

## Results hold 297 point estimates for 9 periods in

27 subgroups

## Estimated standard error exceeds 10 % of the the

point estimate in 86 cases

From the output we see that we have calculated 297 point estimates for 27 different groupings, which result from

$\displaystyle\left({n_{\text{years}}+n_{\text{diff}}}\right)\cdot(n_{\text{% nuts2}}+n_{\text{sex}}+n_{\text{ageGroup}}+n_{\text{sex}\times\text{ageGroup}}% +1)={\left({9+2}\right)\cdot\left({9+2+5+2\cdot 5+1}\right)}={297}$

3.3.2 Custom estimators

There are two built-in estimator functions in calc. stError(): weightedSum() and weightedRatio(). In order to define a custom estimator function to be used in fun, the function needs to have two arguments like the example below.

## define custom estimator

myWeightedRatio $<-$ function(x, w) {

sum(x*w)/sum(w)*100

}

est2 $<-$ calc.stError(datAT_calib, var $=$

“AROPE”, fun $=$ myWeightedRatio,

period.diff $=$ c(“2016-2015”, “2016-2008”))

all.equal(est$Estimates, est2$Estimates)

## [1] TRUE

The parameters x and w can be assumed to be vectors with equal length with w being numeric 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 weight and the replicate weights).

3.3.3 Comparison with 3-year averages

When producing point estimates for subgroups of the population the underlying sample size might not suffice to produce reliable estimates. As mentioned in the methodological section one can overcome this issue by estimating averages over multiple consecutive panel waves. Using the argument period.mean averages are constructed for each panel wave and grouping, resulting in $k$ -year averages.

groups $<-$ list(c(“nuts2”,“urban”))

resAT $<-$ calc.stError(datAT_calib, var $=$

“AROPE”, fun $=$ weightedRatio,

period.mean $=$ 3, group $=$ groups)

resES $<-$ calc.stError(datES_calib, var $=$

“AROPE”, fun $=$ weightedRatio,

period.mean $=$ 3, group $=$ groups)

Figure 1 shows the comparison of the standard error of AROPE for each region (nuts2) by degree of urbanisation (urban) when using a single year, 2015, and 3 consecutive years, 2014 to 2016. The dotted line represents the 25% improvement that is to be expected for using the mean over 3 consecutive years [10]. Most estimates are indeed gathering around that line.

4. Conclusion and outlook

Surveys with a rotating panel design are commonly used when net changes or trends over time of sociodemographic indicators are of interest. The introduction of rotating panels does have a decreasing effect on the variance but results in increasing complexity of the standard error estimates due to the possibly high correlations between panel waves. Using the R package surveysd estimates for standard errors for surveys with a rotating panel design can be derived in a straight forward way. Step by step instructions for the usage of the package are available at https://statistikat.github.io/surveysd/. The underlying methodology does not depend on auxiliary information and supports a harmonious approach for producing estimates on sociodemographic indicators on an EU level. Furthermore the use of averaging over multiple consecutive panel waves is supported yielding a significant reduction in standard error. Contrary to SAE this approach does not need auxiliary information or expert knowledge. It is however only applicable if the structural patterns for the indicator in question remain fairly robust over time.

Given the computational flexibility of the replication approach, the surveysd package may be easily extended, including the following examples:

Technical improvement of the replication method may be necessary to represent the actual longitudinal sampling by rotational group. In the present version of the algorithm, bootstrap replicates are generated independently for each wave and only afterwards taken forward for individuals from the same original sample household.

Results from bootstrapping and calibration could be displayed in a more userfriendly way. This would require additional classes and possibly some interfaces to the rmarkdown package. Similarly, markup methods for the results of calc.stError() could be added.

Currently, there is no way to obtain the actual distribution of bootstrap replicates. Only derived estimates (standard errors and confidence intervals) are returned by calc.stError(). A more flexible approach would be to return the replicates and to define methods that summarize or visualize those replicates.

Footnotes

Acknowledgments

Early parts of the R package surveysd were initially developed in the course of the third Network for the analysis of EU-SILC (Net-SILC3), funded by Eurostat. Authors gratefully acknowledge generous support from several colleagues. Alexander Kowarik, Angelika Meraner and Matthias Till provided fruitfull feedback and extended testing of the softwares.

References

Verma

Betti

. EU statistics on income and living conditions (eu-silc): Choosing the survey structure and sample design. Statistics in Transition 2006; 7: 935-70.

Atkinson

Cantillon

Marlier

Nolan

. Social indicators: The eu and social inclusion. 2002, doi: 10.1093/0199253498.001.0001.

Berger

Osier

Goedemé

. Standard error estimation and related sampling issues. In:. Monitoring social inclusion in europe, 2017, pp. 465-78. doi: 10.2785/60152.

Särndal

Swensson

Wretman

. Model assisted survey sampling. Springer-Verlag; 1992, doi: 10.1007/978-1-4612-4378-6.

Deville

J-C

. Variance estimation for complex statistics and estimators: Linearization and residual techniques. Survey Methodology 1999; 25: 219-30.

Breidaks

Liberts

Ivanova

. Vardpoor: Estimation of indicators on social exclusion and poverty and its linearization, variance estimation. Riga, Latvia: Central Statistical Bureau of Latvia, 2017.s

Verma

Lemmi

Betti

Gagliardi

Piacentini

. How precise are poverty measures estimated at the regional level? Regional Science and Urban Economics 2017; 66. doi: 10.1016/j.regsciurbeco.2017.06.007.

Tzavidis

Zhang

L-C

Hernandez

Schmid

Rojas-Perilla

. From start to finish: A framework for the production of small area official statistics. Freie Universität Berlin, Fachbereich Wirtschaftswissenschaft, 2016. doi: 10.1111/rssa.12364s.

Elbers

Lanjouw

Chesher

Cogneau

Deaton

, et al. Micro-level estimation of poverty and inequality, 2002.

10.

Bauer

Till

Heuberger

Bilgili

Glaser

Kafka

, et al. Studie zu armut und sozialer eingliederung in den bundesländern. Statistik Austria [in German], 2013.

11.

Alfons

Templ

. Estimation of social exclusion indicators from complex surveys: The r package laeken. Journal of Statistical Software, Articles 2013; 54: 1-25. doi: 10.18637/jss.v054.i15.

12.

Efron

. Bootstrap methods: Another look at the jackknife. Ann Statist 1979; 7: 1-26. doi: 10.1214/aos/1176344552.

13.

Chipperfield

Preston

. Efficient bootstrap for business surveys. Survey Methodology 2007; 33: 167-72.

14.

Preston

. Rescaled bootstrap for stratified multistage sampling. Survey Methodology 2009; 35: 227-34.

15.

Meraner

Gumprecht

Kowarik

. Weighting procedure of the austrian microcensus using administrative data. Austrian Journal of Statistics 2016; 45: 3. doi: 10.17713/ajs.v45i3.120s.

16.

GNU general public license 2007.

The R-package surveysd: Estimating standard errors for complex surveys with a rotating panel design

Abstract

Keywords

1. Introduction

2. Methodology

2.1 Rescaled Bootstrap

2.1.1 Single primary sampling units (PSUs)

2.1.2 Considering panel rotation and split households

2.2 Calibration

2.3 Variance estimation

Table 1 Section of the UDB data from Austria

Table 2 Results from the function calc.stError()

3.3 Estimating standard errors

3.3.1 Grouping

3.3.2 Custom estimators

3.3.3 Comparison with 3-year averages

4. Conclusion and outlook

Footnotes

Acknowledgments

References

Table 1
Section of the UDB data from Austria

Table 2
Results from the function calc.stError()