Supplement 1. R codes for the implementation of the predictions from empirical data.

File List ssize.csv (MD5: 5f7568ce74a8fbb8808614347bc21a94): Example ISD data sizeTL.csv (MD5: da8500a87c21284351543ba6318b66e7): Example size-TL relationship data SI_demonstration.r (MD5: e56272a18193777dd66ba3c1f1ef90c1): The demo main function. Prediction_func.r (MD5: 4ad59c0d3619d8e82d503c3766c63fba): The cross predictions function of the generalized MTE model. Random_Test.r (MD5: 21703f025baef51b1cc2cb305a8039b4): The randomization test of the generalized MTE model. Description Demonstration of the predictions of generalized MTE model can be carried out by executing the demo function, SI_demonstration.r, and then loading the example data sets, ssize.csv and sizeTL.csv, and prediction functions (Prediction_func.r and Random_Test.r) following the instructions in the demo function. The demon function, SI_demonstration.r, is the main function to demonstrate the implementation of two predictions from the example data sets and calculation of the 95% confidence interval. Prediction_func.r is the functions that produces the cross predictions between ISD and size-TL relationship (ISD→STL and STL→ISD) in the generalized MTE model. Random_Test.r is the function for the randomization test of the generalized MTE model.