Deriving Small Area Estimates from Information Technology Business Surveys

Abstract

Summary Knowledge of the current state of the art in information and communication technology of businesses (ICTB) is an important issue for governments, markets and policy makers, because information technology improves access to information and plays an important role in firms' competitiveness. Statistical agencies use normalized surveys to provide harmonized statistics about the use of technology in enterprises. Classical design‐based estimators are appropriate for large domains, because direct estimates are consistent and easy to obtain by using sampling weights. However, to supply estimates for unplanned domains, where the sample size is random, model‐based estimators are usually required. In this paper, alternative logistic model‐based estimators are suggested to derive small area estimates from ICTB surveys. Final estimates are benchmarked to achieve coherence with direct estimates in larger domains, and standard errors are given by using bootstrap techniques. A Monte Carlo simulation study is conducted to compare the performance of the small area estimators proposed and to evaluate the behaviour of the mean‐squared error estimator. Results are illustrated with the 2010 ICTB survey of the Basque country (Spain).

Estimation of small area counts with the benchmarking property

“…We have also included an estimator based on a logistic regression model, without area random effects with a-posteriori ratio adjustment (LOGr). See [25].…”

$$\ell _2$$-penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency

“…Regarding the first aspect, since regional prevalence is usually stated as proportion (number of sick persons divided by the total number of persons), binomial, Poisson or negative binomial mixed models are canonical choices. The binomial-logit approach has been used for regional proportion estimation in the past, for instance by Molina et al (2007), Ghosh et al (2009), Chen and Lahiri (2012), Erciulescu and Fuller (2013), López-Vizcaíno et al (2013), López-Vizcaíno et al (2015), Burgard (2015), Militino et al (2015), Chambers et al (2016), Hobza and Morales (2016), Liu and Lahiri (2017) and Hobza et al (2018). The Poisson or negative binomial mixed models were applied to estimate small area counts or proportions by Berg (2010), Chambers et al (2014), , Tzavidis et al (2015) and Boubeta et al (2016Boubeta et al ( , 2017, among others.…”

l2-Penalized temporal logit-mixed models for the estimation of regional obesity prevalence over time

“…The binomial logit approach for regional proportions has been used. 13–23 Further, Poisson or negative binomial-mixed models were applied to SAE of counts or proportions by some authors, 24–27 among others. In addition to that, Shokoohi and Terabi 28 proposed a semi-parametric approach that combines generalized linear-mixed models (GLMMs) with penalized splines for SAE on cross-sectional and temporal data.…”