@article{17a287db40f74a0b969f3ad1640c31cc,

title = "Multivariate Small Area Estimation of Multidimensional Latent Economic Well-being Indicators",

abstract = "Factor analysis models are used in data dimensionality reduction problems where the variability among observed variables can be described through a smaller number of unobserved latent variables. This approach is often used to estimate the multidimensionality of well-being. We employ factor analysis models and use multivariate empirical best linear unbiased predictor (EBLUP) under a unit-level small area estimation approach to predict a vector of means of factor scores representing well-being for small areas. We compare this approach with the standard approach whereby we use small area estimation (univariate and multivariate) to estimate a dashboard of EBLUPs of the means of the original variables and then averaged. Our simulation study shows that the use of factor scores provides estimates with lower variability than weighted and simple averages of standardised multivariate EBLUPs and univariate EBLUPs. Moreover, we find that when the correlation in the observed data is taken into account before small area estimates are computed, multivariate modelling does not provide large improvements in the precision of the estimates over the univariate modelling. We close with an application using the European Union Statistics on Income and Living Conditions data.",

keywords = "Factor analysis models, latent variables, model-based inference, multivariate EBLUP, multivariate multilevel models",

author = "Angelo Moretti and Natalie Shlomo and Sakshaug, {Joseph W.}",

note = "Funding Information: Here, we describe the main R packages that can be used to replicate the analysis. C.1 Estimation of small area means and MSE under univariate EBLUP approach. Although we programmed our functions manually, the sae package (Molina & Marhuenda,) may be used: Required packages: nlme, MASS Functions: eblupBHF() and pbmseBHF() nlme and MASS are still required. C.2 Running Mplus models in the R environment via MplusAutomation (Muth{\'e}n & Muth{\'e}n,; Hallquist & Wiley,) Functions: mplusObject(), mplusModeler() Mplus is required. C.3 Mapping using spdep, maptools, sp, Hmisc Functions: readShapePoly(), spplot(). C.4 Multivariate mixed-effects model ML fitting via mlmmm (Yucel,) Function: mlmmm.em(). C.5 On the implementation in Mplus C.1 Estimation of small area means and MSE under univariate EBLUP approach. Although we programmed our functions manually, the sae package (Molina & Marhuenda,) may be used: Required packages: nlme, MASS Functions: eblupBHF() and pbmseBHF() Required packages: nlme, MASS nlme and MASS are still required. C.2 Running Mplus models in the R environment via MplusAutomation (Muth{\'e}n & Muth{\'e}n,; Hallquist & Wiley,) Functions: mplusObject(), mplusModeler() Functions: mplusObject(), mplusModeler() Mplus is required. C.3 Mapping using spdep, maptools, sp, Hmisc Functions: readShapePoly(), spplot(). Functions: readShapePoly(), spplot(). C.4 Multivariate mixed-effects model ML fitting via mlmmm (Yucel,) Function: mlmmm.em(). Function: mlmmm.em(). Note that the following command, STRATIFICATION = strat and CLUSTER = psu are used to account for stratification and clustering in the estimation. In our work, after a sensitivity analysis, we decided not to include the commands in the software. We refer to Section for more details on the sampling design of the Italian SILC. Theory and more technical aspects on estimators used in this article but under complex sampling designs can be found in Muth{\'e}n & Satorra (). In particular, if weights are included in the analysis, a weighted sample mean vector and weighted sample covariance matrix are used in the estimators. Funding This research was financially supported by the United Kingdom Economic and Social Research Council (ESRC) (grant number ES/J500094/1). Funding Information: Note that the following command, STRATIFICATION = strat and CLUSTER = psu are used to account for stratification and clustering in the estimation. In our work, after a sensitivity analysis, we decided not to include the commands in the software. We refer to Section for more details on the sampling design of the Italian SILC. Theory and more technical aspects on estimators used in this article but under complex sampling designs can be found in Muth{\'e}n & Satorra ( ). In particular, if weights are included in the analysis, a weighted sample mean vector and weighted sample covariance matrix are used in the estimators. This research was financially supported by the United Kingdom Economic and Social Research Council (ESRC) (grant number ES/J500094/1). Funding Publisher Copyright: {\textcopyright} 2019 The Authors. International Statistical Review {\textcopyright} 2019 International Statistical Institute",

year = "2020",

month = apr,

day = "1",

doi = "10.1111/insr.12333",

language = "English",

volume = "88",

pages = "1--28",

journal = "International Statistical Review",

issn = "0306-7734",

publisher = "International Statistical Institute",

number = "1",

}