One of the major tools to collect data from humans, such as health states, behaviors or attitudes, are surveys. Typical communication channels used in surveys, so-called modes, include questionnaires issued in person, by telephone, online or on paper. These methods today are often combined in so-called mixed-mode surveys. In mixed-mode designs respondents are offered multiple modes to reply, which typically improves survey participation relative to a design using only a single mode.

Aim of the study
In this paper, we address the problem of measurement error which can occur in mixed-mode data. This denotes the problem when a mode measures with an error compared to a benchmark instrument (golden standard) because respondents do not give correct answers to a question. For example, individuals might answer less honestly or precisely when asked in person about the frequency of alcohol usage than they would or could online.

Methods
Measurement error can bias linear and non-linear estimates created using the mixed-mode data. We evaluate methodology to correct for this bias. Our approach assumes that in addition to a mixed-mode survey a re-interview is administered to a subset of respondents. For these respondents, the mode is switched such that the potential outcomes under both modes can be observed. Based on this sub-set of repeated measurements we construct six candidate estimators that exploit the re-interview information.

Results
In a simulation study, we show that one of the estimators, called the inverse regression estimator, performs well in all considered scenarios. Other estimators including the propensity score and the standard regression estimator only work well if the re-interview is not selective relative to the initial mode of interview. In contrast, the inverse regression estimator is guaranteed to perform well even when selectivity depends on the target variable, which is a common situation in survey practice. We recommend using the inverse regression estimator as long as the interview to re-interview correlation is moderately high.

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