Forecasting Repeated-Measures Trajectories Using Nonlinear Mixed-Effects Models: A Comparison of Population-Averaged, Subject-Specific, and Autocorrelation-Based Predictions

Nonlinear mixed-effects models (NLMMs) provide a flexible framework for modeling repeated-measures trajectories. However, how best to forecast future observations, especially at ages well beyond those represented in the data, remains relatively underexamined. In this study, we develop a Chapman–Richards NLMM with a spatial-power autocorrelation structure for irregularly spaced repeated measures and compare three forecasting strategies: (i) population-averaged forecasts based on the fixed-effects component only; (ii) subject-specific forecasts in which empirical best linear unbiased predictors (EBLUPs) of the random effects are obtained via a first-order Taylor series expansion with an iterative Newton–Raphson update, including the case of new progenies not used in model fitting; and (iii) forecasts that combine the population-averaged prediction with prior repeated measures through the fitted autocorrelation matrix. Forecast accuracy was assessed with progeny-level validation under fully held-out and partially observed scenarios, using root mean square prediction error (RMSPE) and mean absolute error (MAE), and was examined as a function of: (i) the number of available prior measures and (ii) the accuracy of the fixed-effects component of the NLMM. The methods were illustrated with repeated-measures data from hybrid spruce (Picea engelmannii Parry ex Engelmann × Picea glauca (Moench) Voss) progeny trials at three planting sites in British Columbia, Canada, with measurement ages from 2 to 42 years. Subject-specific forecasts had the lowest prediction errors when sufficient prior measures were available and were also the least affected by misspecification of the fixed-effects component. With only two prior measurements, autocorrelation-based forecasts had the lowest or tied-lowest observed errors, although differences among the three approaches were small. Using all measurements taken before age 42, subject-specific forecasts of height at age 42 achieved an RMSPE of 0.50 m. With only two prior measurements, the corresponding RMSPEs were approximately 1.31–1.33 m across the forecasting approaches. Although demonstrated with a single hybrid spruce dataset from three planting sites, the comparison is, in principle, applicable to other repeated-measures settings in which long-horizon predictions are required from short observation histories; broader applicability remains to be confirmed.