Fig 1.
Prior studies provide the vector of empirical signatures, . The hypothesized meta-model is estimated by simulating those signatures and matching them against empirical ones.
Fig 2.
GMA and its inputs and outputs.
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.
Fig 4.
Comparison of two linear models and the nonlinear meta-model with the underlying true model.
The predicted outcome is fluid leakage rate and its expected value under the true data generating process (left), and each model is shown using color maps. Black dots in the two middle charts identify the original data points used in estimation of the two linear models. However, these “raw” data points are not used in GMA estimation, only the coefficients of the two linear models (3+2 coefficients) and two R2 terms (total of 7 signatures) are used for estimation of the non-linear meta-model (graphed on the right).
Table 1.
Estimates for alternative BMR meta-model specifications.