Objectives Police-recorded crimes are used by police forces to document community differences in crime and design spatially targeted strategies. Nevertheless, crimes known to police are affected by selection biases driven by underreporting. This paper presents a simulation study to analyze if crime statistics aggregated at small spatial scales are affected by larger bias than maps produced for larger geographies. Methods Based on parameters obtained from the UK Census, we simulate a synthetic population consistent with the characteristics of Manchester. Then, based on parameters derived from the Crime Survey for England and Wales, we simulate crimes suffered by individuals, and their likelihood to be known to police. This allows comparing the difference between all crimes and police-recorded incidents at different scales. Results Measures of dispersion of the relative difference between all crimes and police-recorded crimes are larger when incidents are aggregated to small geographies. The percentage of crimes unknown to police varies widely across small areas, underestimating crime in certain places while overestimating it in others. Conclusions Micro-level crime analysis is affected by a larger risk of bias than crimes aggregated at larger scales. These results raise awareness about an important shortcoming of micro-level mapping, and further efforts are needed to improve crime estimates.
Small area estimation (SAE) plays a crucial role in the social sciences due to the growing need for reliable and accurate estimates for small domains. In the study of well-being, for example, policy makers need detailed information about the geographical distribution of a range of social indicators. We investigate data dimensionality reduction using factor analysis models and implement SAE on the factor scores under the empirical best linear unbiased prediction approach. We contrast this approach with the standard approach of providing a dashboard of indicators or a weighted average of indicators at the local level. We demonstrate the approach in a simulation study and a real data application based on the European Union Statistics for Income and Living Conditions for the municipalities of Tuscany.
This article deals with mean squared error (MSE) estimation of a multivariate empirical best linear unbiased predictor (MEBLUP) under the unit-level multivariate nested-errors regression model for small area estimation via parametric bootstrap. A simulation study is designed to evaluate the performance of our algorithm and compare it with the univariate case bootstrap MSE which has been shown to be consistent to the true MSE. The simulation shows that, in line with the literature, MEBLUP provides unbiased estimates with lower MSE than EBLUP. We also provide a short empirical analysis based on real data collected from the U.S. Department of Agriculture. Keywords: Multivariate empirical best linear unbiased predictor; Model-based inference; Multivariate small area estimation; Multivariate multilevel models; Resampling
Summary 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.
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