An Error Function-Based Regression Model for Depressogenic Reasoning Data Analysis

This study proposes a flexible three-parameter distribution to capture complex patterns in continuous positive data. By combining the generalized log-logistic odd generator with an error function distribution, our model successfully accommodates various density shapes, including strong skewness and bimodality. Using Monte Carlo simulations and maximum likelihood estimation, we validate our regression model’s estimators and confirm that larger sample sizes yield high precision, consistency, and inferential stability. Using data from hospitalized depression patients, we demonstrate the model’s practical application. This new distribution fits the data better than competing models, supported by lower statistical metrics and likelihood ratio tests. Furthermore, the variables’ “simplicity” and “fatalism” significantly influence observed depression levels.