Comparison between Highly Complex Location Models and GAMLSS.

Area of Science:

• Statistics
• Econometrics
• Data Science

Background:

• Regression models are crucial for analyzing relationships between variables.
• Complex probability distributions in regression do not always yield superior results.
• The need for interpretable yet effective statistical models is paramount.

Purpose of the Study:

• To evaluate the performance of simple probability distributions against complex ones in regression.
• To demonstrate the utility of the reverse Gumbel distribution within the GAMLSS framework.
• To advocate for parsimonious model selection in statistical analysis.

Main Methods:

• Utilized the generalized additive models for location, scale, and shape (GAMLSS) framework.
• Applied the reverse Gumbel (RG) distribution as a simple location model.
• Compared RG model performance against other location models using three real-world datasets.

Main Results:

• The reverse Gumbel distribution, when used within GAMLSS, provided competitive or superior results compared to more complex location models.
• Demonstrated that a simpler distribution with a sophisticated regression structure can be more effective.
• Highlighted the interpretability benefits of using simpler distributions.

Conclusions:

• Simple distributions, such as the reverse Gumbel, can be highly effective in regression analysis, particularly within flexible modeling frameworks like GAMLSS.
• Model complexity is not always correlated with improved performance; parsimony should be considered.
• The GAMLSS framework effectively accommodates simpler distributions for robust statistical modeling.