Assessing the Efficiency of Generalized Additive Mixed Models (GAMMs) Using Milk Production Variables: Evidence from Tanzania’s National Panel Surveys

The study aimed to evaluate the performance of Generalized Additive Mixed Models (GAMMs) in fitting and predicting cattle milk production variables in Tanzania. The study used the National Panel Survey data collected between 2012 and 2021. GAMM (gamma), GAMM (lognormal), and GAMM (inverse normal) were fitted, and their performance was evaluated using Akaike Information Criterion (AIC), proportional of deviance explained, Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE). The findings show that the GAMM with the lognormal distribution performed best, having a balanced good fit and predictive performance (AIC=4714.36, deviance explained = 94%, RMSE = 4.72, and MAE=2.94). Although the GAMM with the gamma distribution had a slightly better prediction accuracy (RMSE = 4.27 and MAE =2.77), it had a higher AIC (5027.75) and a smaller proportion of deviance explained (59%), making it less suitable for identifying factors affecting cattle milk production. The GAMM with the inverse normal distribution showed the poorest performance, with the highest AIC (5366.34), lowest deviance explained (37.3%), and largest errors (RMSE = 13.64, MAE = 4.46). Despite the poor performance of the GAMM with the inverse normal distribution, the overall results demonstrate that GAMMs are an effective tool for fitting and predicting cattle milk production variables, particularly when data are collected repeatedly from the same units over time. The GAMM with the lognormal distribution not only provided accurate predictions but also offered valuable insights into nonlinear relationships between milk production and household inputs. These insights can guide dairy farmers and policymakers in optimizing milk production by focusing on key factors such as improved breeding practices, proper feeding, health management, and labour efficiency.