While poststratification typically adjusts based on demographic variables, propensity score adjustments often use demographic and webographic (lifestyle/attitudinal) questions. Webographic variables capture general attitudes or behaviors that are hypothesized to differ between the web sample and the general population.<sup>10</sup> <mark>An alternative to propensity score adjustment is matching. This technique utilizes a sample of cases representative of the population. This serves as the “target” sample. The aim of the matching exercise is to pair each case in the target sample with the most similar case from the online opt-in sample. When the closest match has been found for all of the cases in the target sample, any unmatched cases from the online opt-in Internet survey sample are discarded. At the end of the procedure, the matched cases from the Internet survey should be a set that closely resembles the target population.</mark> <mark>There are several ways to conduct the matching procedure. To perform the matching, the target sample and the online survey data can be combined and a selection model for the Internet survey can be implemented as before. A propensity score can be constructed as in the above section, and matching can be based on those. If there are many variables for selection, machine learning algorithms, such as random forest, can be employed. Random forest algorithms can measure the probability that each case belongs to either the target sample or the survey and produce a measure of the similarity between each case and every other case. The similarity measure can also be used for matching. Another approach is to match based on Mahalanobis distance (Diamond and Sekhon, 2005).</mark>

# **<mark>2.3. Review of Studies Applying the above Methods</mark>**

<mark>The selection of covariates for constructing propensity scores has been widely studied.</mark><sup>11</sup> <mark>Covariate selection is usually done in a variety of ways, such as stepwise regression that drops variables that are not significant (Berk and Newton 1985, Lieberman et al. 1996), or conducting one-step covariate selection based on theoretical and logical significance. Some studies argue that there are no serious errors if the model for propensity score adjustment is mis-specified (Drake, 1993), other studies note that the choice of covariates is critical for propensity score weighting (Isaksson and Forsman, 2003). Covariates may be country specific (Stenbjerre, 2002). In countries with homogenous populations and high Internet penetration, there could be fewer covariates that discriminate web survey participation, unlike in countries that have low Internet penetration. There is also a general consensus in the literature that webographic questions, in addition to regular demographic variables, are needed to calculate the propensity scores more accurately.</mark> Several studies examine non-economic averages and how adjusting can potentially reduce bias between volunteer Internet surveys and non-Internet probability-based surveys. Most studies indicate that various weighting schemes do not adequately reduce the difference between weighted Internet survey data and the reference survey. Varedian and Forsman (2003) investigate

> 10 Many Internet survey companies, such as, Harris Interactive, increasingly use webographic questions that are thought to best capture the differences between the general population and those willing to answer a web survey.

> 11 There is a tendency to use only those covariates that are statistically significantly different between treatment and comparison groups. Rosenbaum (2002) offered three cautions against this approach because the relationship between the outcome variable and one covariate is not important, statistical significance is not relevant always especially because it depends on the sample size.

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