Estimating Gamma Regression Model Parameters Using Fire Hawk Optimizer with Practical Application
DOI:
https://doi.org/10.31272/jae.i152.1566Keywords:
Gamma Regression, Fire Hawk Optimizer, Generalized Linear Models, Parameter Estimation, Mean Squared ErrorAbstract
This research addresses one of the most important regression models used in modeling positive data, which is the Gamma Regression model. This model is considered one of the Generalized Linear Models (GLMs) and is utilized when the dependent variable follows a Gamma distribution. The Fire Hawk Optimizer (FHO) algorithm was employed to maximize the log-likelihood function as an alternative to the well-known Iteratively Reweighted Least Squares (IWLS) method in the context of Generalized Linear Models.
A comparison was conducted between the two methods using simulation experiments with different sample sizes and various scenarios for the number of variables and the shape parameter ($\lambda$). The results showed that the FHO algorithm offers a competitive and comparable performance to the IWLS algorithm, especially in cases with small samples or complex parameters, with a clear decrease in the mean squared error (MSE) values as the sample size increases.
In the applied part, the impact of several variables on air quality was analyzed using 46 observations obtained from the Iraqi Meteorological Organization. The goodness-of-fit test results confirmed that the dependent variable follows the Gamma distribution. Furthermore, the estimates showed that all parameters were statistically significant, which reflects the model's adequacy and the efficiency of the FHO algorithm in tracking the true values and providing accurate and reliable estimates.
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