Calculating empirical best linear unbiased predictors (EBLUPs) for nonlinear mixed effects models in Excel/Solver

Nonlinear mixed-effects models have become common in the forestry literature. Calibration of these models for a new subject (one not used in the fitting of the model) involves estimating the values of the of random-effects parameters. Estimators can be obtained by taking a Taylor-series expansion of the nonlinear model around the expected value or the conditional expectation of the random-effects parameters. The conditional expectation method requires an iterative technique to find the estimates, which can be a complicated programming exercise. This note describes a relatively easy way to do the calculations necessary for both the zero expansion and conditional expectation methods in Excel and demonstrates the procedure on a small example.