Small Area Estimates of Disabled People in Poland Theoretical and Practical Aspects

Small area estimates of disabled people in Poland – theoretical and practical aspects

Keywords: small area estimation, disability, The National Census of Population and Housing 2011

1. Introduction

The phenomenon of disability is considered to be among the most serious social problems facing the modern world. The number of disabled people is consistently on the rise, which is the result of, among other things, population aging. The tasks associated with the possibly fullest inclusion of this social group in all kinds of social activities, including social and occupational activity, are becoming a growing challenge for modern societies. However, without detailed and up-to-date information, these tasks cannot be fulfilled at the national, regional or local level. There is a demand for data about disability at the level of local territorial units, which is accompanied by certain expectations about their quality expressed by different users.

The National Census of Population and Housing 2011 (NCPH 2011) is the basic source of information published by GUS (Central Statistical Office in Poland) about some characteristics of disability, both for the country as a whole and at the regional level. NCPH 2011 was carried out as a full-scale survey (administrative registers) and as a sample survey. Poland used the mixed model of data collection consisting of merging data from administrative registers with data obtained from direct statistical surveys. GUS decided to collect data using the mixed approach because it was safer and more effective, taking into consideration the present level of development of administrative sources, their quality, and the degree of advancement of methodological work concerning the estimation and imputation of missing data in administrative sources. Questions devoted to the problem of disability were measured in the Polish census in the survey based on a 20% sample. The size of the sample made it possible to publish information about disability at country level. However, in order to implement an appropriate social policy, one needs to measure disability and provide information about this phenomenon at lower levels of spatial aggregation. In this context information about disability is used to inform decisions concerning important political issues. Those decisions should be based on the most accurate disability indicators, estimates or numbers and should be delivered at the lowest level of spatial aggregation.

However, given the small sample size in the relevant subdomains of sample survey conducted as part of the NCPH 2011, it is necessary to use the latest techniques of indirect estimation that draw on alternative data sources to estimate the parameters of interest at low levels of spatial aggregation with acceptable precision. Since the NCPH 2011 survey does not adequately cover all the specific areas or population subgroups, the required information can only be obtained using small area estimation techniques based on the idea of ‘borrowing strength’. In Poland, for instance, NCPH 2011 data are only sufficient to publish information about disability at country or regional level. Owing to small sample sizes and a low precision of estimation, adequate estimates at lower levels of spatial aggregation cannot be delivered.

2. Definition of disability and the purpose of the presentation

The definition of the disabled person in NCPH 2011 can be expressed in the following way:

a person with a valid certificate issued by an authorised body – disabled in the legal sense,
a person without a certificate, who experiences functional limitations in activities of daily living that are typical for their age (playing, studying, work, self-care) –disabled only in the biological sense,
biologically and legally disabled people – people with a valid certificate and experiencing functional limitations in activities of daily living that are typical for their age,
disabled people only in the legal sense - people with a valid certificate but not experiencing functional limitations in activities of daily living.

The main purpose of the presentation is to evaluate the possibility of applying Small Area Estimation (SAE) methods to estimate basic information about disability in the province of Wielkopolska in Poland (cross-classified by LAU 1, level of education or labour market status).

3. Methods

SAE methodology has been developed to produce reliable estimates of different characteristics of interest, such as means, counts, quantiles or ratios, for domains with small sample sizes [1]. For some domains there may even be no samples available. SAE methodology also deals with the problem of how to assess the precision of estimation given small sample sizes in specific domains, when the precision of obtained direct estimates is rather low. As a consequence, indicators or figures published by the official statistical system cannot be based on direct estimation, including the Horvitz-Thompson approach. SAE methodology is used by different National Statistical Institutes (including GUS) in other fields. It is also useful in the context of disability.

In the field of disability there are different approaches to choose from. In particular, common SAE-based methods devoted to the problem of estimating disability include: direct estimates, which are in generally inefficient, calibration estimators (and its special case – GREG), EBLUP estimators, synthetic estimators, Structure Preserving Estimation (SPREE) or Generalized Structure Preserving Estimator (GSPREE).

All of these methods can be used to tackle the problem of estimating different parameters concerning disability. In particular, these methods enable the estimation of disability at lower levels of spatial aggregation and for some specific domains in Poland.

4. Selected Results

As already mentioned, the main aim of the presentation is to show the results of a study exploring the possibility of applying SAE methods to estimate basic information about disability in the province of Wielkopolska in Poland (cross-classified by LAU 1, level of education or labour market status). In our approach the domain of interest was defined as LAU1xLevel of education (higher, secondary, vocational and primary/no education) and LAU1xLabour market status (working, unemployed, inactive). All the calculations were carried out using the SAS software (Eurarea codes and SAS subroutine called IPF, performing iterative proportional fitting). In our study we applied the following estimators: direct, GREG, EBLUP_A and EBLUP_B, SYNTH_A and SYNTH_B (from Eurarea project [2]), SPREE [3] and GSPREE [4]. The following auxiliary variables were considered for some of the above models: sex, age group and place of residence. We used census data from 2002 and 2011. The variable of interest was the percentage of people who are both legally and biologically disabled. The abstract presents only the selected results for the domain defined by LAU1xLevel of education in the province of Wielkopolska and for selected estimators. Figure 1 presents the spatial distribution of the percentage of disabled people with primary/no education. Figure 2 presents a scatter plot of direct versus SPREE estimates, which shows that the SPREE estimator, compared to the direct one, is approximately unbiased.

Fig.1. The percentage of disabled people with primary/no education

Source: own elaboration

Fig.2. Direct vs SPREE estimator

Source: own elaboration

5. Conclusions

The main aim of this presentation is to highlight theoretical and practical aspects of applying small area estimation methods in the context of disability in Poland. Theoretical considerations will be illustrated with applications of SAE techniques at lower levels of spatial aggregation than those currently published by the Central Statistical Office in the area of disability. In fact, this is one of the first applications in which census unit level data are used to estimate disability in Poland at a lower level of spatial aggregation and for more detailed domains.

References

[1] J.N.K. Rao, I. Molina (2015), Small Area Estimation, 2nd Edition, Wiley.

[2] Eurarea Project (2004), Enhancing Small Area Estimation Techniques to Meet European Needs, Project documentation.

[3] T. Józefowski M. Szymkowiak (2013), Using a SPREE estimator to estimate the number of unemployed people across subregions (in Polish), Studia Oeconomica Posnaniensia, vol. 1, no. 10 (259).

[4] L.C. Zhang, R. Chambers (2004), Small area estimates for cross-classifications, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(2), 479-496.