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These are shortened instruments applied to nonrespondents, and aim to capture information that correlates with both: survey's main outcome variable(s), and respondent's propensity of participation.
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The observed spread-out shear transformations delaying strain localization and severe shear banding are explained in terms of the propensity for participation in deformation, while the tendency towards necking is attributed to the lack of strain hardening mechanism and inadequate strain rate hardening.
Rosenbaum and Rubin (1983) show that if the unconfoundedness assumption holds for X then it also holds for the conditional probability of participation or propensity score, P X) = Pr(T = 1|X).
We corrected the data for this bias on observable covariates of participation using the Propensity Score weighting approach [50].
We estimate the conditional probability of participation, i.e., the propensity score, with a logit functional form.
Propensity matching on baseline clinical and demographic variables, and country of participation, identified 1140 patients (570 from each cohort) who could be matched and compared at 12 months (Table 1 presents data for the matched groups).
The social participation subscale, covering propensity to participate in social interactions, consists of 4 items (e.g. "Converses with peers easily", α =.82).
The probability of participation was estimated using logistic model and used as a propensity score.
Instead of conditioning on single X, we use the propensity score p(X) = E(D = 1|X), i.e. the probability of participation in a program (see Rosenbaum and Rubin 1983).
We added this propensity score to the survival models as a covariate and examined if the probability of participation was associated with incident CVD or mortality.
Regarding the first question, we estimate effects of participation in a short-term training program during the first year on welfare using propensity score matching estimators in a dynamic setting, where treatment effects vary conditionally on the preceding duration in welfare.
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