An Extension of the Mixed Effects Model that Includes Correlation within Group Errors

Mixed effect models allow for a great deal of flexibility in defining random outcomes, but they limit within-group errors to independent disbursed random variables with a zero mean and constant variance. In addition to its random outcomes for the implied structure, this model is expanded in this paper by including within-group correlated errors. We demonstrate how to accurately predict the model's parameters using a marginal maximum probability (ML) method. The model's accuracy is demonstrated by a real-world example. Additionally, we provide several instructions for correlation systems to represent serial and spatial correlation. Finally, we define how to combine variance features and correlation systems to flexibly model the within-group variance-covariance shape. We also discuss how the lme function can be used to maintain the prolonged linear mixed effects model. And, when compared to other models, the exponential spatial correlation version has the smallest AIC and BIC, making it appear to be the best within-group correlation model.