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Abstract In small area estimation, different data sources are integrated in order to produce reliable estimates of target parameters (e.g., a mean or a proportion) for a collection of small subsets (areas) of a finite population. Regression models such as the linear mixed effects model or M-quantile regression are often used to improve the precision of survey sample estimates by leveraging auxiliary information for which means or totals are known at the area level. In many applications, the unit-level linkage of records from different sources is probabilistic and potentially error-prone. In this article, we present adjustments of the small area predictors that are based on either the linear mixed effects model or M-quantile regression to account for the presence of linkage error. These adjustments are developed from a two-component mixture model that hinges on the assumption of independence of the target and auxiliary variable given incorrect linkage. Estimation and inference is based on composite likelihoods and machinery revolving around the Expectation-Maximization Algorithm. For each of the two regression methods, we propose modified small area predictors and approximations for their mean squared errors. The empirical performance of the proposed approaches is studied in both design-based and model-based simulations that include comparisons to a variety of baselines. 

Modern predictive modeling tools, such as random forests (and related ensemble methods), have become almost ubiquitous in research applications involving innovative combinations of survey methodology and data science. However, an important potential flaw in the widespread application of these methods has not received sufficient research attention to date. Researchers at the junction of computer and survey science frequently leverage linked data sets to study relationships between variables, where the techniques used to link two (or more) data sets may be probabilistic and non-deterministic in nature. If frequent mismatch errors occur when linking two (or more) data sets, the commonly desired outputs of predictive modeling tools describing relationships between variables in the linked data sets (e.g., variable importance, confusion matrices, RMSE, etc.) may be negatively affected, and the true predictive performance of these tools may not be realized. We demonstrate a new methodology based on mixture modeling that is designed to adjust modern predictive modeling tools for the presence of mismatch errors in a linked data set. We evaluate the performance of this new methodology in an application involving the use of observed Twitter/X activity measures and predicted socio-demographic features of Twitter/X users to accurately predict linked measures of political ideology that were collected in a designed survey, where respondents were asked for consent to link any Twitter/X activity data to their survey responses (exactly, based on Twitter/X handles). We find that the new methodology, which we have implemented in R, is able to largely recover results that would have been seen prior to the introduction of mismatch errors in the linked data set. 

Abstract The advent of the information age has revolutionized data collection and has led to a rapid expansion of available data sources. Methods of data integration are indispensable when a question of interest cannot be addressed using a single data source. Record linkage (RL) is at the forefront of such data integration efforts. Incentives for sharing linked data for secondary analysis have prompted the need for methodology accounting for possible errors at the RL stage. Mismatch error is a common consequence resulting from the use of nonunique or noisy identifiers at that stage. In this paper, we present a framework to enable valid postlinkage inference in the secondary analysis setting in which only the linked file is given. The proposed framework covers a variety of statistical models and can flexibly incorporate information about the underlying RL process. We propose a mixture model for linked records whose two components reflect distributions conditional on match status, i.e. correct or false match. Regarding inference, we develop a method based on composite likelihood and the expectation-maximization algorithm that is implemented in the R package pldamixture. Extensive simulations and case studies involving contemporary RL applications corroborate the effectiveness of our framework. 

In the analysis of data sets consisting of (X, Y)-pairs, a tacit assumption is that each pair corresponds to the same observational unit. If, however, such pairs are obtained via record linkage of two files, this assumption can be violated as a result of mismatch error rooting, for example, in the lack of reliable identifiers in the two files. Recently, there has been a surge of interest in this setting under the term “Shuffled Data” in which the underlying correct pairing of (X, Y)-pairs is represented via an unknown permutation. Explicit modeling of the permutation tends to be associated with overfitting, prompting the need for suitable methods of regularization. In this paper, we propose an exponential family prior on the permutation group for this purpose that can be used to integrate various structures such as sparse and local shuffling. This prior turns out to be conjugate for canonical shuffled data problems in which the likelihood conditional on a fixed permutation can be expressed as product over the corresponding (X,Y)-pairs. Inference can be based on the EM algorithm in which the E-step is approximated by sampling, e.g., via the Fisher-Yates algorithm. The M-step is shown to admit a reduction from n^2 to n terms if the likelihood of (X,Y)-pairs has exponential family form. Comparisons on synthetic and real data show that the proposed approach compares favorably to competing methods. 

Opioid overdoses within the United States continue to rise and have been negatively impacting the social and economic status of the country. In order to effectively allocate resources and identify policy solutions to reduce the number of overdoses, it is important to understand the geographical differences in opioid overdose rates and their causes. In this study, we utilized data on emergency department opioid overdose (EDOOD) visits to explore the county-level spatio-temporal distribution of opioid overdose rates within the state of Virginia and their association with aggregate socio-ecological factors. The analyses were performed using a combination of techniques including Moran’s I and multilevel modeling. Using data from 2016–2021, we found that Virginia counties had notable differences in their EDOOD visit rates with significant neighborhood-level associations: many counties in the southwestern region were consistently identified as the hotspots (areas with a higher concentration of EDOOD visits) whereas many counties in the northern region were consistently identified as the coldspots (areas with a lower concentration of EDOOD visits). In most Virginia counties, EDOOD visit rates declined from 2017 to 2018. In more recent years (since 2019), the visit rates showed an increasing trend. The multilevel modeling revealed that the change in clinical care factors (i.e., access to care and quality of care) and socio-economic factors (i.e., levels of education, employment, income, family and social support, and community safety) were significantly associated with the change in the EDOOD visit rates. The findings from this study have the potential to assist policymakers in proper resource planning thereby improving health outcomes.