Model calibration and generalized regression estimation for domains and small areas

Risto Lehtonen, Carl-Erik Särndal, Ari Veijanen

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

In business surveys, generalized regression (GREG) and model-calibration (MC) estimation can be used for design-based estimation of totals for population subgroups or domains. In this paper, we consider the case of a binary response variable whose variation is modelled by logistic regression. Such settings are common in business surveys, for example in ICT surveys and business performance analysis. The sampling design is unequal probability πPS which is often used in business surveys. The classical GREG estimator of Särndal, Swensson and Wretman (1992) uses a fixed-effects linear assisting model. A multinomial logistic model was introduced as an assisting model for GREG in Lehtonen and Veijanen (1998). Logistic GREG has been examined further for domain estimation in Lehtonen, Särndal and Veijanen (2003, 2005) and Lehtonen and Veijanen (2009). Model calibration was introduced by Wu and Sitter (2001) and is further discussed in Särndal (2007). Montanari and Ranalli (2005) examined nonparametric MC. Chandra (2006) discusses MC in the context of business surveys. Lehtonen, Särndal and Veijanen (2008) extended MC to domain estimation. A key property of MC is that the weights are calibrated to the population total of the predictions derived via an assumed model. For comparability with the GREG approach, we use a logistic fixed-effects model. Under this model, GREG and MC require an access to unit-level auxiliary information. Both GREG and MC provide nearly design unbiased methods. In this paper, we present results on the accuracy of logistic GREG and MC estimators of domain totals of a binary response variable. The results are based on Monte Carlo experiments where repeated πPS samples were drawn from an artificially generated finite population.
Original languageEnglish
Title of host publicationProceedings of the SAE 2009 Conference on Small Area Estimation (CD rom)
Number of pages4
Place of PublicationElche, Spain
PublisherUniversitas Miguel Hernandez
Publication date2009
Publication statusPublished - 2009
MoE publication typeA4 Article in conference proceedings

Fields of Science

  • 112 Statistics and probability

Cite this

Lehtonen, R., Särndal, C-E., & Veijanen, A. (2009). Model calibration and generalized regression estimation for domains and small areas. In Proceedings of the SAE 2009 Conference on Small Area Estimation (CD rom) Elche, Spain: Universitas Miguel Hernandez.