# Analyzing Port State Control Data to Explore Future Improvements to GMDSS Training
## Materials and Methods
### Statistical Tools and Data Analysis
#### 2.4.3 Binary Logistic Regression Analysis Using SPSS  
In this paper, a binary logistic regression is used to estimate the odds of having a high number of inspections with poor results in radiocommunications on a specific type of ship. This kind of regression was previously used by some authors to analyze PSC inspection records, for example [27; 47].  
In general, regression is used to look for significant relationships between variables. In particular, binary logistic regression is used basically for the following main purposes: (i) classifying the samples of a dataset according to at least two subsets; (ii) clarifying the existence of interaction between covariates with respect to the dependent variable; and (iii) explaining, quantifying, and even predicting the values of some binary outcome, the dependent variable, in its relationship with each of the covariates (explanatory variable). Therefore, the objective of logistic regression is not, as in linear regression, to predict the value of the variable from one or several predictor variables but to predict the probability of something known occurring from the values of the independent variables, so it will fail to predict continuous variables. Since the outcome is a probability, a logit transformation is applied to the odds of the dependent variable (natural logarithm of odds or log-odds). Odds is defined as the ratio of the probability of success to the probability of failure. The coefficients (beta parameters) generated in this kind of model are commonly estimated via Maximum Likelihood Estimation (MLE). Finally, a chi-square goodness of fit (or similar test) is used to evaluate how well the model predicts the dependent variable. The odd ratio compares the outcome of a model when a particular event takes place compared with the outcome in the absence of this event. When the Odds Ratio is greater than 1, then the event is associated with higher odds of occurrence, and when the odds ratio is less than 1, then the event is associated with lower odds.  
Although the possibility of using Ordinal Regression was initially considered, because the nature of the dependent variable was ordinal, it was soon discarded. Ordinal means two things: the categories can be ranked and the distance between a category and the adjacent one, which is the case. Unfortunately, the distribution of dependent variables recommends deciding between two levels instead of multiple levels, many of them with few-moderate sample sizes, and the test of parallel lines in SPSS recommends not choosing this model. Since the ordered logit model estimates one equation overall levels of the response variable, check whether the generated one-equation model is valid. Rejecting the null hypothesis based on the significance of the Chi-Square statistic means that ordered logit coefficients are not equal across the levels of the outcome, and it would be better to fit a less restrictive model as a binary logistic. Binary logistic regression models the relationship between a set of independent variables and a binary dependent variable. This study presents two dependent variables that are ordinal but perfectly associable with variables of a dichotomous nature (i.e., does the inspection detect a ship with radio deficiencies that led to detention? YES/NO).