7.2 Analysis for associations
7.2.1.1 Normality
First, to select the most appropriate correlation test for the assessment of associations of characteristics, the continuous data was tested for normality to justify whether the data shows a normal distribution. For association tests, the Spearmanβs rho method is preferred for the non-normally distributed data, since outliers are better incorporated compared to Pearsonβs r, because outliers are less weighted (Hauke & Kossowski, 2011). The results can be found in Appendix A7. As the figures show, none of the continuous data characteristics appeared to have normal distribution. Therefore, it was determined to use the Spearmanβs rho for association tests. For the correlations with the presence of Runway Status Lights, the MannβWhitney U Test was used, because of its binary character.
7.2.1.2 Outliers
To test the effect of outliers on the results, it was decided to create three separate datasets, one with all outliers included, one with outliers excluded and one with the exclusion of outliers which are no hub airports (semi-complete data set).
Model development Master Thesis 48 Outliers are defined as standardised residuals of at least 3.0 with regard to the mean. Conventionally, the effect of outliers is tested as an iterative effect during modelling. However, to assess the effects of the outlier removal it was decided to compare the association results per characteristics systematically. For instance, the correlation of hourly movements for total incursion rate is considered for each of the three datasets. Consequently, the semi-complete database could provide the best fit. After comparing all characteristics, the dataset providing the majority of the highest correlations is selected.
Off course, another way to deal with outliers, instead of the data point removal, is to treat these points as missing values. In this way, the outlier values are replaced with the means of the dataset. It was decided to not apply this method for hub airports, since transformation results in the loss of important characteristic information. The observed outliers in the final dataset are designated in the airport overview, which can be found in Appendix A12.
7.2.1.3 Associations
The following step is to test for associations between the airport characteristics and the incursion rates. Table 7-2 gives an overview of significant correlations between the characteristics and the total π πππ‘π, the rate for high severity, cat. D, and type OI, PD and V/PD incidents. The results are presented for the three datasets. The related correlations, significance levels and sample numbers can be found in Appendix A7.
Consideration of the outliers revealed that these airports are generally represented by non-hubs and other airport; these were thus removed in accordance to the previous explained assumption. Only 43 outliers are either L, M or S airports, of which HNL was found 9 times and HOU 8 times for high severity incursions. The data check resulted in no requirement for adaptions.
The exclusion of outliers influences the strength of the correlation between the airport attributes and the incursion rates. Exclusion of all outliers increased a major share of the correlations, however some correlations became less strong. For example, the correlation between the share of large aircraft versus the incursion rate for cat. D incidents showed to be stronger and more significant when the complete dataset including outliers was considered. However, for number of intersections versus high severity π πππ‘π, the ππ increased because of the outlier removal. Also, some data pairs became not significant for the 95% confidence interval after the outlier removal. Exclusion of only N and O airports, improved some of the significant correlations even further. For example, the share of commercial traffic became a significant indicator for high severity incidents. Since the semi-exclusion of outliers resulted in a stronger correlation matrix and a more representative sample of airports, this data set was preferred above the others. Next part elaborates on the analysis of this data set.
Table 7-2: Summary of significant associations per dataset
Characteristics
Complete data set Outliers excluded Semi-complete data set
ππ πΈπ ππ πΈπ ππ πΈπ T o ta l H ig h D OI PD V/P D T o ta l H ig h D OI PD V/P D T o ta l H ig h D OI PD V/P D Hourly movements β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
Share commercial traffic β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
Share heavy aircraft β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
Ratio intersecting runways β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
TWY-RWY intersections/RWY-km β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
Ratio non-right angled β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
Ratio RETs β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
Required crossings β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
Presence RSL β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
Hectare per runway-km β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’ β’β’β’β’
β Significant associations at 95% confidence interval
Incursion rates
Then, the correlations are considered per incursion rate. Surprisingly, according to the results in Table 7-2 and Appendix A7, more than half of the data pairs for the total π πππ‘π are not significant. Only the ππ of significant characteristic required
Model development Master Thesis 49 crossings is higher than 0.3. Because of the minimal number of significant airport attributes, it was decided to not further analyse the total π πππ‘π. The main reason for this is the absence of any operational component that describes the utilisation of an airport.
Contrary to the total incursion rate, many of the attributes show a significant correlation with high severity rates. This once again explains the influence of D incidents on the total incursion numbers, in line with the assumption from the previous chapter that D incidents less relate to geometrics. Apparently, high severity incidents could be better modelled and predicted separately from the total number of incursions. Wilke et al. (2015a); (2015b) and Claros et al. (2017) also noted the different associations per severity level. Therefore, it was chosen to not further elaborate on the π πππ‘π of D. It is chosen to further analyse the high severity model, because of the higher correlations and the fact that all types of incidents are captured.
The table also learns that most of significant associations are found for operational incidents (OI) and that vehicle/pedestrian deviations (V/PD) is the most complicated to predict, because of the less associations. A possible explanation for this result is that airport vehicles naturally use the infrastructure in a different way than aircraft. Also for ground vehicles, often dedicated roads are available, which minimise the need for to use the taxiways. These infrastructure variables are not captured by the analysis.
Airport characteristics
Also, the correlations with airport characteristics are clarified individually. Some remarkable results are explained below. The share commercial traffic is only correlated to the frequency of severity D incidents. This could be caused by the share of GA aviation, which might be more vulnerable to D incidents. Furthermore, it shows correlation with OI and PD incidents, and not with V/PD. In line with Hypotheses H8, the incursion rate with pilot errors shows a decrease when the share of commercial air traffic increases. Furthermore, it shows negative correlations for all π πππ‘π values, except of OI. Remarkably, the share of heavy aircraft is correlated with all incursion rates, except of high severity incidents. Thus, an increasing share of heavy aircraft seem to be correlated with an increasing OI rate.
Also, higher ratios of non-right-angled intersections and RETs relate to higher incursion numbers, which is in line with
Hypotheses H5. The variable required crossings is the only characteristic that correlates to all incursion rates, and is
apparently an important determinant, such as was expected (Hypotheses H1). Hectare per runway-km only correlates with high severity rates and OI rates. There is a negatively relationship, thus, the more surface area per runway km, the larger the lower the incursion rates. This justifies the assumption from the high-level analysis.
Lastly, for the presence of Runway Status Lights, a correlation was found for D incidents and PD. This can be substantiated by the fact that RSL is especially implemented for the main users; the pilots. Low severity D incidents imply the unauthorised presence of aircraft or vehicles on the runway, often without danger for collisions. The aim of RSL is to prevent this from happening. For arrival aircraft, which contribute for a large share to the high severity incursion statistics, the presence of RSL is not directly useful.
7.2.2 Concluding
To conclude this paragraph, the potential for characteristics to be used as model attributes has been indicated for certain incursion groups. As explained, only the high severity interactions are modelled using the semi-complete dataset. Association results validate some of the hypotheses, which contributes to the answering of the research questions. One of these shows the need to exclude share of heavy aircraft and the presence of RSL as model variable, and are therefore not further examined. Thus, now the final selection of model attributes and the estimation variable are known for the estimation in the next part.
7.3
Model estimation
Throughout this paragraph, the process of the model estimation is discussed. The described steps include the definition of assumptions, the stepwise modelling, the improvement of the model fit and the consideration of interactions. The final selection of potential model attributes to be assessed can be found in Table 7-3.
7.3.1 Collinearity
During the regression modelling, not only the model fits π 2 are examined. Also, a collinearity check is taken into consideration for the review of the model. The models are tested for collinearity, by observing the collinearity coefficients
Model development Master Thesis 50 given in SPSS. The tolerance per variable should be higher than 0.10 and the variance inflation factor lower than 10.0. Furthermore, correlations between variables in the model should not exceed 0.70.