Analytic Strategy Clause Samples
Analytic Strategy. Analyses were conducted in stata 16 using the N-SSATS survey data. A difference in differences approach using two-way fixed effects models with logistic regression examined the effect of Medicaid expansion on the likelihood of SUD treatment facilities offering criminal justice programs [162]. As a dichotomous dependent variable, the implications of this policy are measured using logistic regressions. A stepwise approach helped determine significance of the variables of interest, with the progressive addition of covariates across the four specifications. Specification 1 was the bivariate logistic regression estimating the relationship between Medicaid expansion on the likelihood of a facility offering a CJ program. Specification 2 controlled for state and facility characteristics. Specification 3, shown in Equation 1, added state and year fixed effects to the model used in Specification 2. Equation 1 Pr[CJfst = 1] = F(β0 + β1Expansionst + β2Xft + β3Zst + δs + τt + εfst) Expansionfst—my key independent variable of interest—is a dichotomous measure indicating a state’s Medicaid expansion status in state s and year t. Xft is a vector of facility f- year characteristics (accepts health service payment, receives specialty funding, offers payment assistance, ownership, offers wrap-around services), and Zst is a vector of state-year characteristics (race/ethnicity, political ideology, state budget, JAG Award, SUD rate, and socioeconomic status variables). State fixed effects, 𝜹s, controlled for time-invariant state characteristics such as geographic location; while, the year fixed effects, 𝜏t, addressed secular time trends in SUD treatment that affect the nation [163,164]. 𝜀fst is the error term. Finally, as shown in Equation 2, Specification 4 updated Specification 3 to include an interaction between Medicaid expansion and a state-year measure of SUD burden. Equation 2 Pr[CJfst = 1] = F(β0 + β1Expansionst × SUDst + β2Expansionfst + β3Xft + β4Zst + δs + τt + εfst) Expansionst x SUDst is an interaction between a state’s expansion status and its SUD rate. Based on results from Specification 4, marginal effects were calculated across a range of SUD rates to delve further into differential impact of expansion based on SUD burden. It is important to note that as a difference-in-difference model, the treatment and control groups were assumed to reflect similar trends in the outcome variable in the period prior to expansion. This assumption was tested using data gathered...
Analytic Strategy. We consider the following: (1) the association between recent paternal incarceration and fathers’ parenting; (2) the association between recent paternal incarceration and mothers’ parenting; (3) the mechanisms underlying the association between recent paternal incarceration and fathers’ parenting; and (4) the association between recent paternal incarceration and mothers’ repartnering. The OLS models estimating fathers’ parenting are an important first step because they provide a baseline estimate of how paternal incarceration is associated with parenting after adjusting for observed differences between individuals. Model 1 adjusts for a wide array of control variables that precede recent incarceration, including prior incarceration. Model 2 includes these controls and also adjusts for a lagged dependent variable. Model 3 is restricted to fathers who reported prior incarceration. By examining only those who experienced prior incarceration, we diminish unobserved heterogeneity and strengthen causal inference. Note that limiting the sample to previously incarcerated men necessitates estimating the link between an additional incarceration and parenting. These and all models include city fixed-effects. Then, we take two additional steps to diminish unobserved and observed heterogeneity. In Model 4, we present fixed-effects models that estimate how entry into recent incarceration (n = 97 for residential fathers, n = 246 for nonresidential fathers) is associated with changes in fathers’ parenting between the three- and five-year surveys, net of unobserved stable characteristics and observed time-varying characteristics. By examining within-person changes, we account for the possibility that some individuals may simply have a greater stable propensity for criminal activity or have other unobserved disadvantages associated with parenting, and we consider these our most robust estimates. Finally, in Model 5, we present results from propensity score matching models estimating changes in parenting between the three- and five-year survey (▇▇▇▇▇▇▇▇▇ and ▇▇▇▇▇ 1983). Propensity score matching, an alternative way of minimizing selection, approximates an experimental design by using observed variables to comprise a treatment group and a control group. Though this method does not eliminate unobserved heterogeneity, it makes the distribution of covariates between the treatment and control groups as similar as possible, which is especially beneficial given the ▇▇▇▇▇ differenc...
Analytic Strategy