Statistical Analysis with Linked Data

Abstract

Summary Computerised Record Linkage methods help us combine multiple data sets from different sources when a single data set with all necessary information is unavailable or when data collection on additional variables is time consuming and extremely costly. Linkage errors are inevitable in the linked data set because of the unavailability of error‐free unique identifiers. A small amount of linkage errors can lead to substantial bias and increased variability in estimating parameters of a statistical model. In this paper, we propose a unified theory for statistical analysis with linked data. Our proposed method, unlike the ones available for secondary data analysis of linked data, exploits record linkage process data as an alternative to taking a costly sample to evaluate error rates from the record linkage procedure. A jackknife method is introduced to estimate bias, covariance matrix and mean squared error of our proposed estimators. Simulation results are presented to evaluate the performance of the proposed estimators that account for linkage errors.

High dimensional, robust, unsupervised record linkage

“…This is a non-trivial task, since the datasets are used multiple times in the process of linking, estimation of various quantities of interest, and then inference. The article HAN and LAHIRI (2019) provides review of the current state of the art in this direction of work. Some alternatives to fully Bayesian methods, for example regression analysis using linked data LAHIRI and LARSEN (2005); WINKLER (1997, 1993), have both computational efficiency and analytical tractability, which may make them attractive practical choices for applications.…”

A comparison of area level and unit level small area models in the presence of linkage errors

“…This might be a strong assumption and it might have an In this work, the linkage error adjusted unit level estimator is the one suggested in Di Consiglio and Tuoto (2016) and Briscolini et al (2018). In the adjustment, we assumed block specific probabilities of correct link are known and this is indeed a strong assumption (see remark 2 (3) of Han and Lahiri, 2018). Moreover, the proposed adjustment assumes the exchangeability of linkage errors, and the small areas coinciding with the blocks of the linkage process.…”

“…Clearly, the resulting unbiased estimators depend on the parameters of the linkage model. Recently, Han and Lahiri (2018) propose a general framework for statistical analysis with linked data under general assumptions. A different perspective is in Chambers (2009); secondary data users generally do not have detailed information on linkage model and parameters, in this setting, Chambers (2009) suggests an approximated Best Linear Unbiased Estimator and its empirical version and proposes a maximum likelihood estimator with application to linear and logistic regression functions.…”

“…In the future, we propose to expand our simulation experiment to include the framework proposed by Han and Lahiri (2018) to correct the unit level small area estimation and to benefit from the use of unit level information to improve estimators, even in the presence of linkage errors. One of the promising advantages of the Han and Lahiri's setting is that it does not require any exchangeability assumption.…”

Discussion of “Small area estimation: its evolution in five decades”, by Malay Ghosh

“…A brief description of the methodology is provided in the next section. Readers interested in the details are referred to Lahiri (2017), Han (2018), and Han and Lahiri (2019).…”