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2016 SURVEY AND DIARY OF CONSUMER PAYMENT CHOICE Sampling and Weighting (Marco Angrisani, USC, 1/26/2017) 1. Sample Selection The UAS is a panel of US households recruited through Address Based Sampling (ABS). Eligible individuals are all adults in the contacted household aged 18 and older. The UAS also includes a special purpose sample of Native Americans, recruited through ABS, targeting zip-codes with a higher proportion of Native Americans. In this case, eligible individuals are all adults in the contacted household aged 18 and older, whose ethnicity is Native American. Another special purpose sample includes families with young children in Los Angeles County. For the 2016 Survey of Consumer Payment Choice (SCPC) and Diary of Consumer Payment Choice (DCPC), all UAS members, with the exception of those belonging to the special purpose samples, were invited to take part in the study. The selection procedure was carried out in two steps. In the first step, panel members were asked about their willingness to participate in a twophase study consisting of the SCPC and the DCPC. In the second step, those who consented were invited to take the SCPC first and then the DCPC at designated dates. The SCPC was fielded on September 19, 2016. The fielding period for the DCPC was defined accordingly to run from September 28, 2016 to November 2, 2016. The number of UAS members available at the time of the sample selection (August 2016) who were part of the Nationally Representative core sample was 4,776. The consent form was filled in by 3,572 respondents, of which 3,361 were willing to participate in both the SCPC and the DCPC, 105 were willing to participate in the SCPC, but not in the DCPC, and 106 were not willing to participate at all. Out of the 3,466 who were invited to take the SCPC, 3,404 completed the survey for a response rate of 98%. Out of the 3,361 who were willing to take the DCPC, 3,048 actually did so for a response rate of 91%. Overall, the number of respondents who completed the SCPC, but did not take the DCPC is 356. 1 2. Weighting Procedure Sample weights for typical UAS surveys are constructed in two steps. In a first step, a base weight is assigned to each survey respondent in order to compensate for the disproportionate sampling of Native Americans in the UAS. In a second step, post-stratification weights are generated to bring the final survey sample in line with the reference population as far as the distribution of key variables of interest is concerned. Since the SCPC and DCPC samples only include UAS members from the Nationally Representative core sample, the aforementioned first step is not necessary and therefore skipped. 2.1. Categorization and imputation of variables As far as the UAS sample is concerned, we use demographic information taken from the most recent “My Household” survey, which is answered by the respondent every quarter. With the exception of age and number of household members, all other socio-demographic variables in the “My Household” survey are categorical and some, such as education and income, take values in a relatively large set. We recode all the variables used in the weighting procedure into new categorical variables with no more than 5 categories. The aim of limiting the categories is to prevent these variables from forming strata containing a very small fraction of the sample (less than 4-5%), which may cause sample weights to exhibit considerable variability. The categorization of variables used for the weighting procedure follows the same definitions adopted for the 2014 and 2015 SCPC/DCPC, in order to ensure comparability across years. The list of recoded categorical variables used in the weighting procedure is reported in Table 1. Table 1: List of Recoded Categorical Variables Used within the Weighting Procedure Recoded Variable Categories gender 1. Male; 2. Female age_cat 1. 18-34; 2. 35-44; 3. 45-54; 4. 55-64; 5. 65+ age_cat2 1. 18-44; 2. 45-64; 3. 65+ bornus 0. No; 1. Yes citizenus 0. No; 1. Yes marital_cat 1. Married; 2. Separated/Divorced/Widowed; 3. Never Married 2 education_cat 1. High School or Less; 2. Some College/Assoc. Degree; 3. Bachelor or More hisplatino 0. No; 1. Yes race_cat 1. White; 2. Non-White work_cat 1. Working; 2. Unemployed; 3. Retired; 4. On leave, Disabled, Other hhmembers_cat 1. One Member; 2. Two Members; 3. Three or More Members hhincome_cat 1. <$30,000; 2. $30,000-$59,999; 3. $60,000-$99,999; 4. $100,000+ hhincome_cat2 1. <$35,000; 2. $35,000-74,999; 3. $75,000+ Before implementing the weighting procedure, we employ the following imputation scheme to replace missing values of recoded socio-demographic variables. • We do not impute gender. Hence, respondents with missing gender are not assigned a sample weight. No respondent in the 2016 SCPC and DCPC samples has missing gender. • When actual age is missing, the variable agerange, available in the “My Household” survey, is used to impute age_cat. If agerange is also missing, the variable age_cat is assigned the mode for males or females, depending on the respondent’s gender. • For binary indicators, such as bornus, citizenus, and hisplatino, missing values are imputed using a logistic regression. • For ordered categorical variables, such as education_cat, hhmembers_cat, hhincome_cat and hhincome_cat2, missing values are imputed using an ordered logistic regression. • For non-ordered categorical variables, such as marital_cat, race_cat and work_cat, missing values are imputed using a multinomial logistic regression. Imputations are performed sequentially. That is, once age_cat has been imputed (if missing), the variable with the smallest number of missing values is the first one to be imputed by means of a regression featuring gender and age_cat as regressors. This newly imputed variable is then added to the set of regressors to impute the variable with the second smallest number of missing values. The procedure continues in this fashion until the variable with the most missing values (typically household income) is imputed using information on all other socio-demographic variables. The final 2016 SCPC and DCPC data sets contain a binary variable, imputation_flag, indicating whether any of the recoded socio-economic variables listed in Table 1 has been imputed. 3 2.2. Post-stratification Weights The execution of the sampling process for a survey is typically less than perfect. Even if the sample of panel members invited to take a survey is representative of the population along a series of dimensions, the sample of actual respondents may exhibit discrepancies because of differences in response rates across groups and/or other issues related to the fielding time and content of the survey. Weighting is therefore needed to align the final survey sample to the reference population as far as the distribution of key variables is concerned. We perform iterative marginal weighting and assign survey respondents weights such that the weighted distributions of specific sociodemographic variables in the survey sample match their population counterparts (benchmark or target distributions). The benchmark distributions against which the 2016 SCPC and DCPC are weighted are derived from the Current Population Survey (CPS) Annual Social and Economic Supplement (ASEC) administered in March of 2016. The reference population is the U.S. population of those aged 18 and older, excluding institutionalized individuals and military personnel. We adopt a raking algorithm to generate post-stratification weights. This procedure involves the comparison of target population relative frequencies and actually achieved sample relative frequencies on a number of socio-demographic variables independently and sequentially. More precisely, starting from an initial weight of one, at each iteration of the algorithm weights are proportionally adjusted so that the distance between survey and population marginal distributions of each selected socio-demographic variable (or raking factor) decreases. The algorithm stops when survey and population distributions are perfectly aligned. A maximum of 50 iterations is allowed for perfect alignment of survey and population distributions to be achieved. If the process does not converge within 50 iterations, no sample weights are returned and attempts using different raking factors are made. 2.3. Trimming Our raking algorithm trims extreme weights in order to limit variability and improve efficiency of estimators. We follow the general weight trimming and redistribution procedure described by Valliant, Dever and Kreuter (2013). Specifically, indicating with 𝑤𝑤𝑖𝑖,𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 the raking weight for respondent i and with 𝑤𝑤 � 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 = 1 𝑁𝑁 ∑𝑁𝑁 𝑖𝑖=1 𝑤𝑤𝑖𝑖,𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 the sample average of raking weights, 4 I. We set the lower and upper bounds on weights equal to 𝐿𝐿 = 0.25𝑤𝑤 � 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 and 𝑈𝑈 = 4𝑤𝑤 � 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 , respectively. While these values are arbitrary, they are in line with those described in the literature and followed by other surveys (Izrael, Battaglia and Frankel, 2009). II. We reset any weights smaller than the lower bound to L and any weights greater than the upper bound to U: 𝐿𝐿 III. 𝑤𝑤𝑖𝑖,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = �𝑤𝑤𝑖𝑖,𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑈𝑈 𝑤𝑤𝑖𝑖,𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ≤ 𝐿𝐿 𝐿𝐿 < 𝑤𝑤𝑖𝑖,𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 < 𝑈𝑈 𝑤𝑤𝑖𝑖,𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 ≥ 𝑈𝑈 We compute the amount of weight lost by trimming as 𝑤𝑤𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = ∑𝑁𝑁 𝑖𝑖=1 𝑤𝑤𝑖𝑖,𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 − 𝑤𝑤𝑖𝑖,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 and distribute it evenly among the respondents whose weights are not trimmed. While raking weights can match population distributions of selected variables, trimmed weights typically do not. We therefore iterate the raking algorithm and the trimming procedure until a set of post-stratification weights is obtained that respect the weight bounds and align sample and population distributions of selected variables. This procedure stops after 50 iterations if an exact alignment respecting the weight bounds cannot be achieved. In this case, the trimmed weights will ensure the exact match between survey and population relative frequencies, but may take values outside the interval defined by the pre-specified lower and upper bounds. 2.4. Final Post-stratification Weights Indicate with 𝑤𝑤𝑖𝑖,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 the post-stratification weight for respondent i, obtained after iterating the raking algorithm and the trimming procedure as described above The final 2016 SCPC and DCPC data sets include post-stratification weights relative to their sample mean. That is: 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑖𝑖,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = where N is the survey sample size. 𝑤𝑤𝑖𝑖,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 1 �𝑁𝑁 ∑𝑁𝑁 𝑖𝑖=1 𝑤𝑤𝑖𝑖,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 � , These relative post-stratification weights, average to 1 and sum to the survey sample size N. 5 3. Produced Sample Weights We produce general weights for the SCPC and general and daily weights for the DCPC. With the exception of daily weights for the DCPC, all weights for the 2016 SCPC and DCPC are generated using the following set of raking factors: gender x race_cat gender x age_cat gender x education_cat hhmembers_cat x hhincome_cat The same set of raking factors was adopted to produce sample weights for the 2014 and 2015 SCPC/DCPC. Under this specification, both the raking and the trimming algorithms converge within the maximum number of allowed (50) iterations. Because of the limited number of respondents taking the diary at specific days, daily weights for the DCPC are generated using a reduced set of raking factors, namely: gender x age_cat2 education_cat hhincome_cat2 Again, this set of variables is the same as the one used for the 2015 DCPC so to ensure comparability. Under this specification, the raking algorithm converges within the maximum number of allowed (50) iterations. We do not apply trimming to daily weights. The complete list of weights and auxiliary variables provided with the final 2015 SCPC and DCPC data sets is reported below. 6 2016 SCPC: imputation_flag A binary variable indicating whether any of the variables listed in Table 1 has been imputed. rel_weight Relative post-stratification weights. 2016 DCPC: (note: the DCPC data set is in “long form” with 4 diary days (day 0-3) for each respondent) diary_day Variable taking values 0, 1, 2 and 3 for diary days 0, 1, 2, and 3, respectively. diarydate String variable recording the date of each diary day. diarydate_num Numeric variable recording the date of each diary day. survey_start Date and time when the online survey for each diary day started. survey_end Date and time when the online survey for each diary day ended. imputation_flag A binary variable indicating whether any of the variables listed in Table 1 has been imputed. rel_gen_weight Relative general post-stratification weights. rel_day_weight Relative daily post-stratification weights. 7