On Misspecification of Spatial Weight Matrix for Small Area Estimation in Longitudinal Analysis

• Authors: Tomasz Żądło
• Languages of publication: EN

Abstracts

EN

The problem of prediction of subpopulation (domain) total is studied as in Rao (2003). Considerations are based on spatially correlated longitudinal data. The domain of interest can be defined after sample selection what implies its random sample size. The special case of the General Linear Mixed Model is proposed where two random components obey assumptions of spatial and temporal moving average process respectively. Moreover, it is assumed that the population may change in time and elements’ affiliations to subpopulation may change in time as well. The proposed model is a generalization of longitudinal models studied by e.g. Verbeke, Molenberghs (2000) and Hedeker, Gibbons (2006). The best linear unbiased predictor (BLUP) is derived. It may be used even if the sample size in the subpopulation of interest in the period of interest is zero. In the Monte Carlo simulation study the accuracy of the empirical version of the BLUP will be studied in the case of correct and incorrect specification of the spatial weight matrix. Two cases of model misspecification are studied. In the first case the misspecified spatial weight is used. In the second case independence of random components is assumed but the variable which is used to compute elements of spatial weight matrix in the correct case will be used as auxiliary variable in the model.

• Publisher: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
• Journal: Comparative Economic Research. Central and Eastern Europe
• Year: 2012
• Volume: 15
• Issue: 4
• Pages: 305-318

Dates

published

2012-12-01

online

2013-03-08

Contributors

author

Tomasz Żądło

• Ph.D., University of Economics in Katowice

References

• Hedeker D., Gibbons R.D. (2006), Longitudinal Data Analysis, John Wiley, New Jersey
• R Development Core Team (2011), A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna
• Rao J.N.K (2003), Small area estimation, John Wiley and Sons, New Jersey
• Royall R.M. (1976), The linear least squares prediction approach to two-stage Sampling, Journalof the American Statistical Association, 71, 657-473
• Verbeke G., Molenberghs G. (2000), Linear Mixed Models for Longitudinal Data, Springer- Verlag, New York
• Żądło T. (2004), On unbiasedness of some EBLU predictor, [in:] J. Antoch (ed.), Proceedings inComputational Statistics, Physica-Verlag, Heidelberg-New York, 2019-2026
• Żądło T. (2009), On prediction of domain totals based on unbalanced longitudinal data, [in:] Wywiał J., Żądło T. (eds.) Survey Sampling in Economic and Social Research, University of Economic in Katowice, Katowice
• Żądło T. (2011), On accuracy of two predictors for spatially and temporally correlatedlongitudinal data, submitted to publication

Identifiers

DOI

10.2478/v10103-012-0043-5