Fig. 2

Statistical diagram and model equations for importance of change conditional process analysis. Conditional process model equations: \(Y_{i} = c^{\prime}_{0} + c^{\prime}_{1} X_{i} + b_{1} M_{i} + b_{2} M_{i} + b_{3} M_{i} *W_{i} + b_{4} U_{1i} + b_{5} U_{2i} + e_{yi}\)_; \(M_{i} = a_{0} + a_{1} X_{i} + a_{2} U_{1i} + a_{c} U_{21} + e_{Mi}\)_; \(Y_{i} = 1.43 - 0.29X_{i} - 0.17M_{i} + 1.32W_{i} - 0.22M_{i} *W_{i} + 0.60U_{1i} + 0.03U_{2i} + e_{yi}\)_; \(M_{i} = 1.52 + 1.53X_{i} + 0.12U_{1i} + 0.58U_{2i} + e_{Mi}\). Intervention condition is a dichotomous variable (0 = control condition; 1 = brief alcohol intervention); alcohol problem severity factor represents participants’ severity factor score from a principal component analysis constructed via baseline measures and interviews; baseline importance of change and baseline drinks per day served as covariates; * indicates significance at the p < 0.05 level and ** at the p < 0.01 level