SMALL AREA ESTIMATES OF THE POPULATION DISTRIBUTION BY ETHNIC GROUP IN ENGLAND: A PROPOSAL USING STRUCTURE PRESERVING ESTIMATORS

Luna, Angela; Zhang, Li-Chun; Whitworth, Alison; Piller, Kirsten Article SMALL AREA ESTIMATES OF THE POPULATION DISTRIBUTION BY ETHNIC GROUP IN ENGLAND: A PROPOSAL USING STRUCTURE PRESERVING ESTIMATORS Statistics in Transition New Series Provided in Cooperation with: Polish Statistical Association Suggested Citation: Luna, Angela; Zhang, Li-Chun; Whitworth, Alison; Piller, Kirsten (2015) : SMALL AREA ESTIMATES OF THE POPULATION DISTRIBUTION BY ETHNIC GROUP IN ENGLAND: A PROPOSAL USING STRUCTURE PRESERVING ESTIMATORS, Statistics in Transition New Series, ISSN 2450-0291, Exeley, New York, NY, Vol. 16, Iss. 4, pp. 585-602, https://doi.org/10.21307/stattrans-2015-034 This Version is available at: https://hdl.handle.net/10419/207792 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ STATISTICS IN TRANSITION new series and SURVEY METHODOLOGY 585 STATISTICS IN TRANSITION new series and SURVEY METHODOLOGY Joint Issue: Small Area Estimation 2014 Vol. 16, No. 4, pp. 585–602 SMALL AREA ESTIMATES OF THE POPULATION DISTRIBUTION BY ETHNIC GROUP IN ENGLAND: A PROPOSAL USING STRUCTURE PRESERVING ESTIMATORS Angela Luna, Li-Chun Zhang1, Alison Whitworth, Kirsten Piller2 ABSTRACT This paper addresses the problem of producing small area estimates of Ethnicity by Local Authority in England. A Structure Preserving approach is proposed, making use of the Generalized Structure Preserving Estimator. In order to identify the best way to use the available aggregate information, three fixed effects models with increasing levels of complexity were tested. Finite Population Mean Square Errors were estimated using a bootstrap approach. However, more complex models did not perform substantially better than simpler ones. A mixed-effects approach does not seem suitable for this particular application because of the very small sample sizes observed in many areas. Further research on a more flexible fixed-effects estimator is proposed. 1. Introduction Estimates of demographic characteristics are among the main outputs of National Statistical Institutes (NSIs). In addition to national and regional estimates, for topics such as Labour Force, Household composition or Ethnicity, periodic estimates at lower levels of geographic aggregation are in high demand both for public policy and research purposes. In census years, given the availability of data for almost all individuals in the population, it is straightforward to produce reliable estimates for small geographic domains. In contrast, during the inter-censal period, updated socio-demographic data can only be obtained via sample surveys or administrative systems. It is generally difficult to obtain reliable direct estimates for small geographic domains from sample surveys due to the small sample sizes. Data from administrative systems do not have this problem but, in contrast, may not cover the topics of interest. Moreover, definitions of the variables and domains in administrative 1 University of Southampton. 2 Office for National Statistics ONS-UK. 586 A. Luna, Li-Chun Zhang, A. Whitworth, K. Piller: Small area estimates of .... sources reflect the requirements of the administrative systems, which may be different from those for statistical purposes. This can result in comparability issues with figures obtained from population censuses or household surveys. From the statistical perspective, the estimation for small domains in the presence of limited, or even null domain-specific sampling data can be framed within the field of Small Area Estimation (SAE). Research in SAE has gained relevance in the last decades due to an increasing demand for small area outputs in the Official Statistics sector, as well as in many others. Readers interested in SAE can find a comprehensive account of methods in Rao (2003). For a review of the most important developments of the last decade, see Pfeffermann (2013). Implementation of SAE methods in the field of Official Statistics faces specific challenges and specialized research has been encouraged in the European context. Projects such as EURAREA (Eurostat, 2001-2004) and EU-SAE (ESSnet, 2009-2012) provide comprehensive reviews of the available SAE methods with potential applications in a broad set of topics covered by Official Statistics, taking into consideration the specific requirements and characteristics of European statistical systems. Special attention has been given to the use of SAE methods for the measurement of poverty, via collaborative projects such as SAMPLE (Small Area Methods for Poverty and Living conditions Estimates, European Commission, 2008-2011) or AMELI (Advanced Methodology for Laeken Indicators, 2008-2011). The deliverables of all the above mentioned projects are available online. At present, comparatively few official figures in the region are being produced using SAE methods. In the UK case, the Office for National Statistics (ONS) periodically disseminates small area estimates regarding three main topics: population estimates by age and sex using the Census and its coverage survey; average household income and households in poverty using the Family Resources Survey and administrative data maintained by the Department for Work and Pensions; and unemployment, making use of the Annual Population Survey and the administrative register for Jobseeker’s Allowance. Nonetheless, the interest in understanding the potential gains that can be obtained from a more extensive use of SAE methods in the context of official statistics remains. The ONS established the Census Transformation Programme in January 2015 to take forward the National Statistician’s recommendation to make the best use of all available data in the production of population statistics. This involves research into the potential use of administrative data as well as surveys to produce population, household and characteristic information currently provided in the Census. SAE methods provide a framework for intergrating sources. In this paper we investigate the problem of how to obtain estimates of the distribution of the population by ethnic group, in each Local Authority (LA) of England, using proxy and survey data. Such estimates are required by local and central government for planning services and formulating policy. More generally researchers, local authorities, health authorities and other public and private sector organisations could use them to gain an up-to-date picture of the ethnic STATISTICS IN TRANSITION new series and SURVEY METHODOLOGY 587 composition of local populations and to monitor diversity and anti-discrimination programmes. Ethnicity is a variable for which the use of Structure Preserving Estimators (SPREE) (Purcell and Kish, 1980) seems natural. Most SAE methods combine existing survey data for the variable of interest with relevant covariate information obtained from censuses or administrative sources, to obtain better estimates than those from the survey alone. For Labour Force status for instance, covariates such as sex, age or level of education can provide some explanatory power, see Molina et al. (2007) and Scealy (2010). In the case of ethnicity, on the other hand, it is difficult to identify such a set of covariates. Instead, for post-censal updates of the LA by ethnicity distribution, the corresponding aggregated census table can always be treated as a proxy for the table of interest. When a proxy is available, the SPREE approach allows for an intuitive modelling of the relationship between the so-called association structure, or simply the structure of both the proxy table and the table of interest. The SPREE approach is particularly compelling in the case where the margins of the table of interest are known in advance or can be accurately estimated because, given the margins, the structure is the only unknown component to be estimated. This will be explained in more detail in Section 2. This application addresses the particular problem of obtaining updated census tables of LA by ethnicity during the inter-censal period. However, it is important to notice that population censuses in general are going through a process of redesign in many European countries. More emphasis is being given to alternative operations based on demographic systems that use information from administrative sources alone or in combination with survey data. In such a context, the potential impact of SAE methods, including the SPREE approach and its extensions, is expected to increase considerably in the future. The rest of the paper is organised as follows. In the next section, the underpinning idea behind the SPREE approach and the GSPREE extension (Zhang and Chambers, 2004) is discussed in more detail. Section 3 describes the characteristics of the empirical exercise performed to obtain estimates of the distribution by ethnic group and LA in England. Section 4 presents the results of our analysis. Finally, Section 5 discusses the main results and points out some topics for future work. 2. SPREE approach 2.1. Structure Preserving Estimator (SPREE) Denote by Y the population table of interest, with cells aj Y, where 1, ,aA indexes the set of areas and 1, ,jJ  indexes the categories of the 588 A. Luna, Li-Chun Zhang, A. Whitworth, K. Piller: Small area estimates of .... variable. Define log Y aj aj Y  . Ycan be represented in the form of a saturated loglinear model as: 0 Y YYYY aj a j aj    , (1) where (the dot indicating summing over the respective subscript), and 0 YYYYY aj aj a j    , for 1, , ,aA 1, , .jJ Following Purcell and Kish (1980), equation (1) can be used to decompose Y into two parts: the association structure and the allocation structure. The former corresponds to the terms  aj Y   , also called interactions, and determines the relationship between rows and columns in the table. In the theoretical case where rows and columns are independent, all the interaction terms are zero. The latter, given by the terms  0 Y ,  a Y   and  j Y   , carries information about the scale of the table and the disparities within the sets of rows and columns and is implicitly determined by the row and column margins of the table. Notice that in the SAE setting, it is easier to obtain information related to the allocation structure than to the association structure. Even if Y remains unknown, accurate estimates of the row marginal, i.e. the area sizes, can be obtained either from administrative sources or from population estimates. Similarly, given that the column marginal corresponds to the aggregation over the entire set of areas, it can usually be accurately estimated using survey data, if not available from other sources. Given the margins of Y , i.e., its allocation structure, a proxy of the table of interest, denoted by X, can be used to estimate the association structure of Y . The term proxy is used here in the customary sense of proxy variable as defined in Upton and Cook (2008): “A measured variable that is used in the place of a variable that cannot be measured”. A proxy table is therefore supposed to contain information for the same set of areas and regarding a similar characteristic as the table of interest. In particular, it is assumed to have the same dimension A  J . Notice that for demographic characteristics during inter-censal periods, the corresponding tables from the census year are obvious proxies. More generally, proxies can be derived not only from censuses but also from administrative sources. For the two-way case, the SPREE of Purcell and Kish (1980) simply uses the association structure of the proxy table as an estimate for the association structure of the table of interest. In other words, denoting by  aj X   the interaction terms for the proxy table X defined as in equation (1), the SPREE is characterised by the structural equation:  aj Y   aj X , for 1, , ,aA  1, , .jJ   The procedure proposed by Purcell and Kish (1980) to obtain the SPREE of Y is straightforward. The known margins of Y are imposed on X using a multiplicative raking procedure such as the Iterative Proportional Fitting (IPF) STATISTICS IN TRANSITION new series and SURVEY METHODOLOGY 589 algorithm (see for instance Agresti, 2013, p. 365-366). This ensures that the association structure of the estimated and proxy tables are the same. Fitting a saturated log-linear model with an offset term given by the interactions X aj  is an alternative way to obtain the same estimate (Noble et al., 2002). However, assuming that the proxy and the table of interest share exactly the same association structure is clearly restrictive in practice. Other estimators have been proposed to preserve in a more flexible way the association structure, leading to what we have called the SPREE approach. The modifications to the initial SPREE of Purcell and Kish (1980) go in two main directions: i) by relaxing the structural equation of SPREE to consider other types of relationship between the two association structures and ii) by including cell-specific random effects. Besides the SPREE, the following estimators can be framed within this approach: the Generalized Structure Preserving Estimator (GSPREE, Zhang and Chambers, 2004), the Extended Structure Preserving Estimator (ESPREE, Cinco, 2010) and the estimator proposed in Berg and Fuller (2014). Notice that in all the above mentioned cases the allocation structure is imposed by benchmarking the estimates to a set of known margins. The benchmarking has the additional advantage of providing some degree of protection against misspecification of the assumed model (Pfeffermann, 2013). 2.2. Generalized Structure Preserving Estimator (GSPREE) In some cases, it is possible to have access to a survey estimate of Y . Notice that the small area problem persists because the direct estimates of the cell totals are usually too unstable to be useful, due to small sample sizes. The GSPREE (Zhang and Chambers, 2004) proposes to use such information to update the association structure of the proxy table, aiming to reduce the bias of the SPREE. The GSPREE is characterised by the structural equation  aj Y   aj X for 1, , ,aA1, , .jJ   Clearly, the SPREE corresponds to the particular case  1 . An estimation procedure for  built directly from the structural equation involves several problems. Small sample sizes can lead to zero survey estimates for some of the cells, in which case the interaction terms for the survey estimate of Y are not defined. Moreover, even if all cells have a positive estimate, there is not a natural distribution that can be assumed for the interactions – as there is for the proportions or the counts – making it difficult to justify a standard approach such as Maximum Likelihood, for instance. Therefore, instead of formulating a model in the interaction scale, Zhang and Chambers (2004) propose to estimate  using the Generalized Linear Structural Model (GLSM), a model relating the within-area proportions of the proxy table and the table of interest, on the log scale centred around the average of the area. The equation that defines the GLSM is: 590 A. Luna, Li-Chun Zhang, A. Whitworth, K. Piller: Small area estimates of ....  aj Y   j   aj X (2) where and . The terms in the decomposition given in equation (1) satisfy and for Z  X,Y . Moreover,  j    j Y and  aj      aj Y  . Using these arguments it is straightforward to show that  aj Z   j Z   aj Z for ZX,Y , and therefore, that equation (2) is equivalent to the structural equation of the GSPREE. The  j are nuisance parameters with no practical interest. The GLSM is fitted via Iteratively Weighted Least Squares (IWLS) using direct estimates of the within-area proportions ˆ  aj Y and estimates of their variances. By doing so, it is implicitly assumed that the structural equation of the GSPREE holds for the table of direct estimates as well, or at least, that the value of  that better relates the table of interest and the proxy table does not change when the former is substituted by its direct estimate. Once the estimate ˆ  has been obtained, the GSPREE of Y is calculated by imposing the known row and column margins on the table of exponentiated estimated interactions , using IPF. In the absence of estimates of the variance of the direct estimators, it is also possible to obtain fully model-based estimates of  . One possibility, mentioned in Zhang and Chambers (2004), is to assume a multinomial distribution for the sampling cell counts in each area, and obtain an estimator of  using Maximum Likelihood (ML). Notice that this approach implicitly assumes that the sampling design of the survey is ignorable for Y . Otherwise, direct estimates of the proportions can be used instead of the observed proportions, assuming a multinomial distribution for the direct estimates of the cell totals. Despite not being mentioned in Zhang and Chambers (2004), fully model-based estimates of  under the GSPREE structural assumption can also be obtained assuming a Poisson distribution for the sampling counts y aj . It is straightforward to show that the equation: logY aj   a   j   aj X (3) with is also equivalent to the structural equation of the GSPREE. Both the  a and the  j terms for 1, , , 1, ,aAjJ   , are nuisance parameters. It is possible to fit (3) in a standard software using log-linear models and obtain the corresponding ML estimator of  . As with the fitting using the GLSM, this STATISTICS IN TRANSITION new series and SURVEY METHODOLOGY 591 approach assumes that the structural equation also holds for the table of sample counts. In the application presented in Section 4 we followed a fully model-based approach in order to simplify the fitting process. By doing so, we can be incurring in a misspecification of the variance structure of the sampling errors. Nevertheless, using an argument similar to that for the generalised estimating equation approach in Liang and Zeger (1986), it is possible to show that in such a case the estimator of β, although not fully efficient, would remain unbiased. 3. Empirical exercise: distribution of the population by Ethnicity at LA level in England An empirical exercise was conducted with the aim of producing small area estimates of the distribution of the population by ethnic group for each LA in England. Given that some of the sources of information used in this exercise are subject to disclosure control, it was necessary to perform all the data analysis in a Safe Room of the Virtual Microdata Laboratory (VML) of ONS. Thus, in accordance with ONS standards and the principles set out in the Code of Practice for Official Statistics, full account has been taken of requirements to safeguard confidentiality and uphold relevant data security standards. All the calculations hereby presented are the responsibility of the authors. This section starts with a description of the data sources used: the proxy table, the table of survey estimates and the benchmark totals for the columns and row margins. A description of the variable of interest and the definition of categories across the different sources is then provided. Finally, the models that were involved in the fitting process are presented. 3.1. Sources of information Proxy Information Proxy information for the distribution of Ethnicity at the LA level can be obtained for England from several sources. For this empirical exercise, aggregate data from the 2011 Census and the English School Census3 were used. The 2011 Census provides estimates of the counts of persons and households who are defined as usual residents of England and Wales on the 27th March. The estimated coverage rate for persons in the 2011 Census was 93%. The observed counts were adjusted by over and undercount, taking into account the characteristics of individuals and households who were missed from the Census enumeration. 3 Access to and use of information from the School Census is authorised by data sharing regulations i.e. Statistics and Registration Service Act 2007 (Disclosure of Pupil Information) (England) Regulations 2009. 592 A. Luna, Li-Chun Zhang, A. Whitworth, K. Piller: Small area estimates of .... The English School Census targets the population attending school in England and it is carried out every year. It mostly covers the population between 2 and 19 years old, with almost full coverage of children between the compulsory school ages of 5 and 15. The main school census in January collects information on the pupil’s ethnicity, which is not asked about in the two other collection periods in June and August. Whereas state maintained schools and non-maintained special schools are included, independent schools are not covered. This can result in some differences between the population estimates for children in compulsory school age obtained from this and other sources. As the English School Census only provides a good coverage for children between 5 and 15 years old, it could be said that for the empirical exercise there is one source of proxy information for individuals in the ages 0-4 and 16 or more, and two sources for those between 5 and 15 years. In order to use the appropriate models for each age group, age-group specific Census tables of LA by Ethnic group were produced. Regarding the School Census, the empirical exercise hereby presented used information collected in January 2013. Survey estimates Most household surveys carried out by the ONS collect demographic data. For this empirical exercise, the Annual Population Survey (APS) is used for the updated estimates for the population by ethnic group. The APS contains detailed information on ethnicity, has the biggest sample size among the periodic surveys and, except for the Isle of Scilly, it includes information for all Local Authorities in England. The APS is a household survey that is designed to provide information at a local level, on many demographic and socio-economic topics. The data sets are published quarterly (January to December; April to March; July to June; and October to September) and contain approximately 250,000 individuals. They contain the Labour Force Survey (LFS) data and the boost samples to the LFS. The boost for England is called the English Local LFS (ELLFS) and has been designed to give a minimum sample size of economically active individuals for each local education authority. The APS data set for England therefore consists of four successive quarters from the LFS, plus the ELLFS boost. Both the LFS and the ELLFS use a rotational sampling design involving waves. For the LFS, a sample of households is interviewed quarterly for five waves, inducing an 80% of overlap between samples of consecutive quarters. For the ELLFS a sample is interviewed once a year for four waves. Notice that the households are included in the APS only the first time they are interviewed, so that each respondent only appears in the data set once. Non-private households (some communal establishments, armed forces accommodation, etc.) are excluded from the sampling frame. For England the households are sampled through the Royal Mail Postcode Address File (PAF) and the National Health Service (NHS) communal accommodation list. This empirical exercise uses the data STATISTICS IN TRANSITION new series and SURVEY METHODOLOGY 599 samples were generated for each age group, and the aggregate of the three samples was used to fit the Fixed and Mixed effects estimators under Model 1. The initial idea was to generate the population composition under a mixed effects model split by age. However, as mentioned before, it was impossible to obtain positive variance estimates for those models, and even in the case of Model 1, only three of the six categories have a positive variance component estimate. Using such variance components estimates could lead to an overly optimistic scenario for the GSPREE because of a lack of heterogeneity. An alternative set of variance components was obtained from the two proxy tables, School Census 2012-2013 and Census 2011, by considering the School Census as a big sample from the true population in the age group 5-15 and using the methodology of the mixed effects GSPREE estimator. The estimated variance components are 0 for White, 0.02 for Mixed, 0.05 for Asian, 0.12 for Chinese, 0 for Black and 0.79 for Other. To allow for extra heterogeneity in all the categories, the two zero estimates were replaced by the minimum positive estimated value, 0.02. These estimates were used in all age groups, to generate the population composition from which the bootstrap samples are generated. Despite the two zero estimates, we have found the set of variance components estimated using the two auxiliary sources more plausible than the one obtained from the sampling data under Model 1 in section 4.1, when taking into consideration the category specific heterogeneity observed in Figure 2. This could be seen as evidence against the performance of the mixed effects estimator presented in the previous section. It is possible that, even under Model 1, a synthetic estimator needs to be used given the small sample sizes in the cells of the survey composition. The results in terms of FP-Bias and FP-MSE obtained under Poisson or Multinomial sampling were very similar, possibly due to the impact of the benchmarking on reducing the variability associated to the random area sample size in the case of the Poisson sampling. We will therefore omit one set of the results. The results for the Multinomial sampling are presented in Table 2 and Figures 5, 6 and 7. Table 2. Average FP-Bias and Square root FP-MSE Ethnicity Measure Model White Mixed Asian Chinese Black Other Average FP-Bias Model 1 FE -0.00157 0.00013 0.00162 0.00028 -0.0001 -0.00036 Model 2 FE -0.0008 -0.00001 0.00119 0.00022 -0.0002 -0.0004 Model 3 FE -0.00156 0.00011 0.00164 0.00029 -0.00009 -0.0004 Model 1 ME -0.00158 0.00018 0.0016 0.00031 -0.00013 -0.00039 Average Square Root FPMSE Model 1 FE 0.00948 0.00195 0.00691 0.00158 0.00354 0.00717 Model 2 FE 0.01177 0.00251 0.00895 0.00161 0.00418 0.00651 Model 3 FE 0.00951 0.00189 0.007 0.00162 0.00357 0.00717 Model 1 ME 0.00974 0.00187 0.00709 0.00167 0.00355 0.00716 600 A. Luna, Li-Chun Zhang, A. Whitworth, K. Piller: Small area estimates of .... Overall, there is no estimator that performs substantially better than the others, either in terms of FP-Bias or FP-MSE. Even though the average bias for each category is close to zero, according to Table 2, for specific areas there is bias in the estimation of the within-area distribution in all the fixed effects estimators, as it can be seen from Figure 5. The mixed effects estimator under Model 1 seems unable to correct this bias, given that the estimates with bigger biases are those for LAs with small sampling fractions. See Figure 6. Figure 5. FP-Bias with respect to the simulated population composition. Red triangle: Mean Figure 6. Implicit sampling fraction Vs. FP-Bias of the mixed effects estimator (Model 1) 1 FE 2 FE 3 FE 1 ME -0.10 0.00 0.05 0.10 White Model Bias 1 FE 2 FE 3 FE 1 ME -0.10 0.00 0.05 0.10 Mixed Model Bias 1 FE 2 FE 3 FE 1 ME -0.10 0.00 0.05 0.10 Asian Model Bias 1 FE 2 FE 3 FE 1 ME -0.10 0.00 0.05 0.10 Chinese Model Bias 1 FE 2 FE 3 FE 1 ME -0.10 0.00 0.05 0.10 Black Model Bias 1 FE 2 FE 3 FE 1 ME -0.10 0.00 0.05 0.10 Other Model Bias STATISTICS IN TRANSITION new series and SURVEY METHODOLOGY 601 5. Discussion In this paper, we present a feasibility study to produce Small Area estimates of the within-area distribution of Ethnicity by LA in England, using the GSPREE. It is the first time this approach has been attempted for this type of problem in the UK. Unlike other demographic and socio-economic characteristics, Ethnicity is a variable for which there is no clear set of covariates identified in the literature, which could be used as a predictor. In fact, unless a proxy is involved, it seems difficult to expect good performance of a Small Area Estimator in this context. Structure Preserving Estimators can be used, given that proxy compositions can be obtained either from the last population census or from other sources, such as the School Census. Figure 7. Square root FP-MSE with respect to the simulated population composition. Red triangle: Mean In this work, we formulated three alternative models to produce the desired estimates with the GSPREE. However, in terms of Bias and FP-MSE, no substantial improvement was obtained by using more complex models or different sources of information. Moreover, given the small sample sizes available from the APS, synthetic estimates seem the only possible alternative in this case. Notice that the lack of sample size to fit a mixed effects model is not a problem only of this application but rather one which all applications of SAE face sooner or later, if the aim is to produce estimates at increasingly lower levels of aggregation. In this sense, work to improve the synthetic predictor is of highest priority. Currently, we are working on a more flexible version of the fixed effects GSPREE and we expect to be able to evaluate it against the other estimators included in this paper, in the near future. When it comes to mixed effects modelling, a particular problem we encountered with these data is that the variance component estimate can be 1 FE 2 FE 3 FE 1 ME 0.00 0.04 0.08 0.12 White Model Square root MSE 1 FE 2 FE 3 FE 1 ME 0.00 0.04 0.08 0.12 Mixed Model Square root MSE 1 FE 2 FE 3 FE 1 ME 0.00 0.04 0.08 0.12 Asian Model Square root MSE 1 FE 2 FE 3 FE 1 ME 0.00 0.04 0.08 0.12 Chinese Model Square root MSE 1 FE 2 FE 3 FE 1 ME 0.00 0.04 0.08 0.12 Black Model Square root MSE 1 FE 2 FE 3 FE 1 ME 0.00 0.04 0.08 0.12 Other Model Square root MSE 602 A. Luna, Li-Chun Zhang, A. Whitworth, K. Piller: Small area estimates of .... negative for some but not all the categories, when the model allows for categoryspecific variance components. A possible remedy is to impose a common variance component. However, further study is needed in order to determine whether this or another random effects modelling strategy can be suitable. Evaluation of the estimators in terms of their Bias and FP-MSE is also a topic for future work. The conclusions and quality of the evaluation is closely related to the plausibility of the characteristics of the artificial finite population, or as in our case, of the artificial population composition, from which the bootstrap samples are extracted. Additional work is still necessary in this area in order to formulate alternative scenarios that can be used to select a model, as well as to increase our knowledge on the performance of the proposed estimators. REFERENCES AGRESTI, A., (2013). Categorical Data Analysis. John Wiley & Sons. BERG, E. J., FULLER,W. A., (2014). Small Area Prediction of Proportions with Applications to the Canadian Labour Force Survey. Journal of Survey Statistics and Methodology, 2 (3), 227–56. CINCO, M., (2010). Intercensal Updating of Small Area Estimates. Unpublished PhD thesis. Massey University. LIANG, K-Y., ZEGER, S. L., (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22. MOLINA, I., AYOUB S., LOMBARDIA, M. J., (2007). Small Area Estimates of Labour Force Participation under a Multinomial Logit Mixed Model. Journal of the Royal Statistical Society: Series A (Statistics in Society), 170 (4), 975– 1000. NOBLE, A., HASETT, S., ARNOLD, G., (2002). Small Area Estimation via Generalized Linear Models. Journal of Official Statistics, 18(1):45–68. PFEFFERMANN, D., (2013). New Important Developments in Small Area Estimation. Statistical Science, 28 (1), 40–68. PURCELL, N., KISH, L., (1980). Postcensal estimates for local areas (or domains). International Statistical Review, 48(1), 3–18. RAO, J. N. K., (2003). Small Area Estimation. John Wiley & Sons. SCEALY, J., (2010). Small Area Estimation Using a Multinomial Logit Mixed Model with Category Specific Random Effects. Research paper, Australian Bureau of Statistics. UPTON, G., COOK, I., (2008). A Dictionary of Statistics. Oxford University Press. ZHANG, L. C., CHAMBERS, R., (2004). Small area estimates for crossclassifications, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(2), 479–496.