Fig 3. Aggregation of three “prior” study regressions across four scenarios.
a) Estimated parameters of a linear generating process (meta-model) y = β0+β1x1+β2x2+β3x3+ε. Three prior studies of the form y = β0+βixi+βjxj+ε; (i,j = {1,2,3}; i ≠ j) are estimated and their coefficients are reported within the gray bars. b) Similar to a, but prior studies estimate models of the form y = β0+βixi+ε; (i = {1,2,3}). c) Similar to a, but using binary outcomes and logistic regression meta-model of the form Pr(y = 1) = (1+exp(−(β0+β1x1+β2x2+β3x3)))−1 with prior studies including only two of the three explanatory variables and a constant. d) Similar to c, but only including one explanatory variable and a constant in each prior study. In (a), (b), (c), and (d), γ1 represents the intercept and γ2, γ3, and γ4 represent the coefficients of x1, x2, and x3, respectively, both in “prior” study regressions and meta-model. In (a) and (b), γ5 represents MSE in “prior” study regressions and the estimated standard deviation of the error term in the meta-model.