Applying Prospect Theory to Participation in a CAPI/Web Panel Survey

Abstract Prospect theory states that the influential power of avoiding negative outcomes is stronger than that of achieving positive outcomes. In a survey context, this theory has been tested with respect to not only participation in a CATI survey, but also giving consent to data linkage in CATI surveys. No study, however, has tested the theory with respect to participation in a CAPI or web survey. This study does so in a mixed-mode panel context; it also tests the moderating effects of time-in-panel, response history, and mode protocol. Results show that the framing of the survey participation request influences participation propensity in a way consistent with prospect theory, but only for relatively recent panel entrants. The opposite effect is found for long-term panel participants. No difference is found between mode protocols.


A. Cumulative Wave 10 Response Rates
As described in section 4, the results presented in the paper are based on analysis of the 2,801 adult members of the three component samples who were issued to the field at wave 10 of the Understanding Society Innovation Panel. For illustrative purposes, section 3 presents the cumulative response rates for participation in wave 10. Out of the 2,801 issued sample members, 1,893 individual interviews were obtained at wave 10. The cumulative wave 10 response rates do not therefore reflect the proportion of the eligible sample included in the analysis base for the base, as the analysis base is not defined by participation at any particular wave. But they indicate levels of participation in the survey.
For each of the three samples, the cumulative response rate is estimated as the product of three components: = × × where is the estimated proportion of sample individuals whose household participated in the initial wave; is the estimated proportion of individuals in participating households for whom an individual interview was completed at the initial wave; and is the estimated proportion of individuals interviewed at the initial wave who were also interviewed at wave 10.
As the sampling frame does not include information on the number of residents at each address, the total number of individuals in the sample is unknown. The number of residents at each sample address is known only for the addresses where a successful household enumeration is carried out; not for (most) addresses where the household(s) did not respond. Therefore, cannot be directly calculated. It must be estimated by first estimating the expected number of individuals in the sample of addresses. (This step circumvents the need to assume that household response rate is independent of household size, an assumption that would be needed if the observed proportion of households participating were used in the calculation instead of .) The expected number of individuals in the sample is estimated as = ∑ , where is the proportion of households, according to the 2011 Census of Population, that contain individuals (except , which indicates the proportion of households containing seven or more individuals) and is the number of addresses in the selected sample, net of ineligible addresses (those at which no household resides). Thus, we estimate,

=
, where is the total number of persons in households that participated in the initial wave.
can be estimated in a more direct way, though note that only sample members aged 16 or over at the time of the respective survey wave are eligible for the individual interview, so the denominator is the total number of persons eligible for interview rather than the total number of sample members in sample households:

=
, where is the number of persons aged 16 or over in participating (enumerated) households, and is the number of completed individual interviews.
For , the denominator is the number of initial-wave respondents who are eligible to be interviewed again at wave 10. Thus, we should exclude initial-wave respondents who have either died or moved outside of the UK by the time of wave 10. The number expected to have died is estimated by applying age and gender-specific annual mortality rates, as published by the Office for National Statistics, to the age-gender distribution of the sample members interviewed at the initial wave. There is no reliable population information on the proportions of people who move abroad, so instead we exclude only the sample members who are known to have done so. This is likely to be a conservative approach as the survey is unlikely to have correctly identified all emigrants in the sample, so some will remain treated as non-respondents. Thus: where is the number of initial wave respondents estimated to have died by wave 10, ̂ is the number of initial wave respondents known to have emigrated by wave 10, and is the number of initial wave respondents who were interviewed also at wave 10.
Estimates of , , , and their components are presented in table A1 for each sample.

B. Logistic Regression Results
Here we present the full results of the models that underpin the P-values in table 2. Note: The dependent variable, survey outcome, is coded 1 for response and 0 for non-response. The predictor variable, framing, is coded 1 for the treatment (negative framing) and 0 for the control (positive framing). Thus, a positive coefficient for framing indicates that the treatment (negative framing) is associated with an increased tendency to respond.