L subscripts omitted for presentation clarity. This results in the linear logistic model: p ?a ?0 x logit ??log ? ?p?Eating occurrences. We defined no eating as no (zero minutes) primary eating or drinking–the ATUS does not distinguish between primary eating and primary drinking beverages –and no (zero minutes) of secondary eating. Although 4 percent of Americans age 15 and over had no primary eating/drinking BMS-986020 web occurrences on an average day over 2006?8, less than one percent (0.71 percent) had no eating under our definition that includes secondary eating, making this a rare situation.PLOS ONE | DOI:10.1371/journal.pone.0158422 July 13,9 /SNAP Benefit CycleMLN9708 mechanism of action because not eating for a whole day is a rare situation, we risk bias in using the standard logistic regression model [33]. However, estimation using a rare event approach (such as the Firth method) poses a problem with our data, at least with existing software. The ATUS has a complex sampling design, both stratified and clustered, and so is nonrandom. The ATUS treatment for this situation is the use of balanced replicate weights (BRR). The BRR method uses variation between primary sampling units within strata to estimate standard errors. Without BRR, the standard errors are underestimated. Available estimation methods for the Firth method do not accommodate the probability weights needed for estimation using the BRR, and so will produce underestimates of the standard errors. As a result, we use the standard logistical regression model, estimated with BRR in order to obtain correct estimates of standard errors. We also performed a “rare events” estimation of our model using the Firth method as a robustness test, which is discussed below. SNAP characteristics. The model included an indicator of SNAP participation, so the reference group is SNAP non-participants. Also included was the log of the number of days since benefit issuance, and also an interaction term between SNAP participation and the log variable. The log of the number of days since benefit issuance was used to capture the steep drawdown pattern of SNAP benefits redemption–in FY2009, 21 percent of benefits are redeemed on the first day of issuance, 59 percent at the end of the first week, and 79 percent at the end of the first two weeks [1]. The interaction term captures whether or not the effect of days since issuance is different for SNAP participants than others, or more generally, whether the marginal effect is different for SNAP participants than others at different values of issuance dates [34]. Calendar variables. We pooled the 2006?8 ATUS and EHM data, and because of this, we included dummy variables for 2006 and for 2007, with year 2008 as the reference group. These year dummies will control for any year-to-year effects, and in particular, the recent recession (December 2007 to June 2009, see National Bureau of Economic Research, U.S. Business Cycle Expansions and Contractions, http://www.nber.org/cycles/cyclesmain.html). In addition, we added day-of-the week dummies for Saturday, Sunday, and holidays (New Year’s Day, Easter, Memorial Day, Independence Day/Fourth of July, Labor Day, Thanksgiving Day, and Christmas Day) as eating patterns may be different on these days. We included season dummies for spring (March, April, May), summer (June, July, August), and fall (September, October, November), with winter (December, January, February) as the reference group. Household characteristics. In addition to household in.L subscripts omitted for presentation clarity. This results in the linear logistic model: p ?a ?0 x logit ??log ? ?p?Eating occurrences. We defined no eating as no (zero minutes) primary eating or drinking–the ATUS does not distinguish between primary eating and primary drinking beverages –and no (zero minutes) of secondary eating. Although 4 percent of Americans age 15 and over had no primary eating/drinking occurrences on an average day over 2006?8, less than one percent (0.71 percent) had no eating under our definition that includes secondary eating, making this a rare situation.PLOS ONE | DOI:10.1371/journal.pone.0158422 July 13,9 /SNAP Benefit CycleBecause not eating for a whole day is a rare situation, we risk bias in using the standard logistic regression model [33]. However, estimation using a rare event approach (such as the Firth method) poses a problem with our data, at least with existing software. The ATUS has a complex sampling design, both stratified and clustered, and so is nonrandom. The ATUS treatment for this situation is the use of balanced replicate weights (BRR). The BRR method uses variation between primary sampling units within strata to estimate standard errors. Without BRR, the standard errors are underestimated. Available estimation methods for the Firth method do not accommodate the probability weights needed for estimation using the BRR, and so will produce underestimates of the standard errors. As a result, we use the standard logistical regression model, estimated with BRR in order to obtain correct estimates of standard errors. We also performed a “rare events” estimation of our model using the Firth method as a robustness test, which is discussed below. SNAP characteristics. The model included an indicator of SNAP participation, so the reference group is SNAP non-participants. Also included was the log of the number of days since benefit issuance, and also an interaction term between SNAP participation and the log variable. The log of the number of days since benefit issuance was used to capture the steep drawdown pattern of SNAP benefits redemption–in FY2009, 21 percent of benefits are redeemed on the first day of issuance, 59 percent at the end of the first week, and 79 percent at the end of the first two weeks [1]. The interaction term captures whether or not the effect of days since issuance is different for SNAP participants than others, or more generally, whether the marginal effect is different for SNAP participants than others at different values of issuance dates [34]. Calendar variables. We pooled the 2006?8 ATUS and EHM data, and because of this, we included dummy variables for 2006 and for 2007, with year 2008 as the reference group. These year dummies will control for any year-to-year effects, and in particular, the recent recession (December 2007 to June 2009, see National Bureau of Economic Research, U.S. Business Cycle Expansions and Contractions, http://www.nber.org/cycles/cyclesmain.html). In addition, we added day-of-the week dummies for Saturday, Sunday, and holidays (New Year’s Day, Easter, Memorial Day, Independence Day/Fourth of July, Labor Day, Thanksgiving Day, and Christmas Day) as eating patterns may be different on these days. We included season dummies for spring (March, April, May), summer (June, July, August), and fall (September, October, November), with winter (December, January, February) as the reference group. Household characteristics. In addition to household in.
