Table 1.

True values of the parameters used for data generation

Parameter	True value(s)	Description
Equation 1a (Logistic sub-model)
$b_{0\left(B\right)}$	2.94, 2.20, 1.10	Non-varying intercept corresponding with probability of any drinking in the control condition. The three values correspond with a 5%, 10%, and 25% rate of zeroes, respectively
$b_{1\left(B\right)}$	0.14	Non-varying slope for treatment
$b_{2\left(B\right)}$	3.16	Covariate effect of baseline drinking (not drinking vs. any drinking)
$b_{3\left(B\right)}$	−0.91	Covariate effect of baseline drinking (quantity of drinking)
${\sigma }_{0\left(B\right)}$	1.06	SD of study-level varying intercept
${\sigma }_{1\left(B\right)}$	0.16	SD of study-level varying slope for treatment
${\sigma }_{r_0\left(B\right)}$	1.60	SD of participant-level varying intercept
${\rho }_{01\left(B\right)}$	0.09	Correlation of the varying intercept and varying treatment slope
Equation 1b (Zero-truncated negative binomial sub-model)
$b_{0\left(C\right)}$	0.72	Non-varying intercept corresponding with mean number of drinks when drinking in the control condition.
$b_{1\left(C\right)}$	−0.01	Non-varying slope for treatment
$b_{2\left(C\right)}$	0.16	Covariate effect of baseline drinking (not drinking vs. any drinking)
$b_{3\left(C\right)}$	0.38	Covariate effect of baseline drinking (quantity of drinking)
${\sigma }_{0\left(C\right)}$	0.14	SD of study-level varying intercept
${\sigma }_{1\left(C\right)}$	0.05	SD of study-level varying slope for treatment
${\sigma }_{r_0\left(C\right)}$	0.24	SD of participant-level varying intercept
${\rho }_{01\left(C\right)}$	−0.19	Correlation of the varying intercept and varying treatment slope
${\alpha }_{\left(C\right)}$	330.00	Dispersion parameter

Notes. Correlations between the two hurdle sub-models were not modeled in the data generation, to minimize non-convergence in the simulation analyses. (B) = Logistic sub-model parameter; (C) = Zero-truncated negative binomial sub-model parameter; SD = standard deviation.