Factor analysis (FA) 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 wellbeing. We employ FA models and use multivariate EBLUP (MEBLUP) to predict a vector of means of factor scores representing wellbeing for small areas. We compare this approach to the standard approach whereby we use SAE (univariate and multivariate) to estimate a dashboard of EBLUPs on 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 MEBLUPs 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 EU Survey on Income and Living Conditions data.

中文翻译：

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多维潜在经济福利指标的多变量小区域估计

因子分析 (FA) 模型用于数据降维问题，其中观察变量之间的可变性可以通过较少数量的未观察到的潜在变量来描述。这种方法通常用于估计幸福感的多维性。我们采用 FA 模型并使用多元 EBLUP (MEBLUP) 来预测代表小区域幸福感的因子得分均值向量。我们将此方法与标准方法进行比较，标准方法使用 SAE（单变量和多变量）来估计原始变量上的 EBLUP 仪表板，然后取平均值。我们的模拟研究表明，与标准化 MEBLUP 和单变量 EBLUP 的加权和简单平均值相比，使用因子分数提供的估计具有更低的可变性。而且，我们发现，当在计算小区域估计值之前考虑观察数据中的相关性时，多变量建模与单变量建模相比，在估计精度方面没有大的改进。我们以使用欧盟收入和生活条件调查数据的应用程序结束。