# Analyzing Port State Control Data to Explore Future Improvements to GMDSS Training
## 3 Results
### Binary Regression Analysis Results Were Applied to Databases of Table 4  
Despite their recent extended use and success in many areas, machine learning algorithms perform poorly when they encounter (no stationary time series) distribution shifts at test time. When considering the gradual decrease over the years shown in Tables 1-3 in the number of samples, the truth is that the ratio between HRSC2 and HRSC3 subsets related to the total number of recorded inspections does not show a lack of stationarity, as shown in Figure 2. These last 3 years should probably be treated as anomalies caused by the end of the pandemic and the war in Ukraine. When applying the binary logistic regression in SPSS, the intercept-only model in all cases shows a lower explanatory capacity than when adding the independent variables. The categorical predictors are: Flag, Ship Type, and Port location, and the continuous predictors are: the ship's age and years. All of them are added to the study, but not all cases have explanatory power. Omnibus tests of Model Coefficients give Chi-square values with 7, 8, and 9 degrees of freedom with a significance beyond 0.001. So there is a significant improvement in fit after comparing with the intercept-only model. Using a Likelihood Ratio (LR) test to see if there is a significant improvement (\(p\)-value < 0.05) on the null model in the 'Model' row of the 'Omnibus Tests of Model Coefficients' Table 8. The number of explanatory analyses used depends on the behavior of some parameters. For example, when introducing more predictors, noticing that \(-2\) log Likelihood statistics increase or the pseudo-R-square decrease is a symptom that the expanded model performs worse than the previous one. Another indicator is the capacity of the model to provide a better success rate regarding classification. Figure 1: The age of the ships was calculated considering the 18 years of inspections. (**a**) The histogram of the ages of ships with which to define the subset HRSC2. (**b**) The histogram of the ages of ships with which to define the subset HRSC3. The list of explanatory variables is selected after comparing the behavior of the model after checking \(-2\) log Likelihood statistics and the pseudo-R-square:  
* For HRSC2 and HRSC2-expanded, the explanatory variables are Ship Flag, Ship Type, Ship Age, and Port situation. * For HRSC3 the explanatory variables are Ship Flag, Ship Type, Ship Age, Port situation, and Year. The results of the Chi-square show a large statistical significance with a \(p\)-value less than 0.05. The null hypothesis claims that adding these explanatory variables to the model does not significantly improve the capacity decision of the model. That is why the hypothesis is rejected and the predictors are added to the model. The [PERSON] and Lemeshow statistics indicate a poor fit if the significance value complies with the \(p\)-value \(<\) 0.05. Smaller Chi-square values with a larger \(p\)-value closer to 1 indicate a good logistic regression model fit. In this case, the null hypothesis states that there is no difference between the observed and predicted models. Following the Hosmer and Lemeshow tests, only HRSC2-extended shows a poor fit. Unfortunately, some doubts about the consistency of this test have been expressed in some studies, as this kind of test doesn't take overfitting into account, but it is preferred not to split the continuous explanatory variables into bins. The Nagelkerke Pseudo-R Square (approximately) estimates the value of the total variation explained by the full model. In this case, the calculation of pseudo-R\({}^{2}\) includes a correction so that the maximum value is equal to 1, suggesting that all predictions (R\({}^{2}\)HRSC2 = 0.11, R\({}^{2}\)HRSC2-extended = 0.21, and R\({}^{2}\)HRSC3 = 0.09) are NOT fairly reliable. Tables 9 and 10, show if any of the independent variables have a statistically significant effect on the dependent variable. Wald statistics test the significance of individual logistic regression coefficients for each independent variable.