This study explores modeling approaches to assess dominant height growth for loblolly pine plantations in the Western Gulf region in the USA. Four Algebraic Difference Approaches (ADA) and two Generalized Algebraic Difference Approaches (GADA) site index models were used. Local parameters were estimated for each plot to ensure base-age invariance, and a residual variance model was incorporated to address heteroskedasticity. Biophysical variables, including water deficit, excess water, available water, and soil basic density, were identified through Lasso regression as significant predictors. In general, the inclusion of biophysical variables improved the performance of models, although this depends on their formulation. GADA2 evidenced the lowest root mean square error (RMSE) (5.68%) and bias (-1.42%) during the validation phase incorporating biophysical variables, while ADA3 exhibited the highest RMSE (12.77%) and bias (-8.79%). The GADA2 formulation effectively incorporated biophysical variables into both the asymptote and slope parameters, capturing site-specific variability and generating stable residual variance estimates. In contrast, ADA models without incorporated biophysical variables, although simpler to fit, were less adaptable and exhibited higher bias (between -6.77% and -7.83%). Thus, integrating biophysical variables as predictors into dominant height models improved their performance and applicability.