# Modeling Public Transportation Use Among Short-Term Rental Guests in Madrid
## 3 Results
### Ordered Logistic Regression Marginal Effects  
Table 6 presents the marginal effects of the ordered logistic regression model estimating the probability of low, medium, and high levels of public transport use among tourists, extracted from Model 1 (Table 5). The reported marginal effects reflect the discrete change in the predicted probability of each outcome category when the independent variable changes, holding all other variables constant. Bolded values denote statistically significant effects at the 10% level. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Model 1**} & \multicolumn{3}{c}{**Model 2**} & \multicolumn{3}{c}{**Model 3**} \\ \multicolumn{2}{c}{**Variable**} & \multicolumn{3}{c}{**Use of Public Transport**} & \multicolumn{3}{c}{**Use of Bus**} & \multicolumn{3}{c}{**Use of Metro**} \\ \cline{2-9}  & \(\beta\) & \(p\) & \(\beta\) & \(p\) & \(\beta\) & \(p\) & \\ \hline
**First time in the city: Yes** & \(-\)0.3939 & 0.0188 & ** & \(-\)0.6951 & 0.0001 & *** & \(-\)0.4607 & 0.0067 & *** \\
**Group type: Solo** & 0.2691 & 0.5077 & & \(-\)0.0177 & 0.9682 & & 0.4619 & 0.2775 & \\
**Group type: Couple** & 0.0215 & 0.9042 & & \(-\)0.0789 & 0.6872 & & 0.0393 & 0.8289 & \\
**Origin: Europe** & \(-\)0.7256 & 0.0072 & *** & \(-\)0.2305 & 0.4270 & & \(-\)0.8799 & 0.0015 & *** \\
**Origin: America** & \(-\)0.4144 & 0.1483 & & 0.1203 & 0.6952 & & \(-\)0.4468 & 0.1281 & \\
**Origin: Rest** & \(-\)0.9805 & 0.0240 & ** & \(-\)0.9840 & 0.0986 & * & \(-\)1.0634 & 0.0145 & ** \\
**Access to city: Land-based** & \(-\)0.2987 & 0.2448 & & \(-\)0.2003 & 0.4763 & & \(-\)0.4558 & 0.0822 & * \\
**Access to city: Private car** & \(-\)0.6245 & 0.1044 & & \(-\)0.6512 & 0.1600 & & \(-\)0.6286 & 0.1090 & \\
**Number of nights** & 0.0476 & 0.1729 & & 0.0151 & 0.6690 & & 0.0452 & 0.1919 & \\
**Number of visited touristic attractions** & 0.1650 & 0.0000 & *** & 0.2260 & 0.0000 & *** & 0.1923 & 0.0000 & *** \\
**Importance of transport: Medium** & 0.9893 & 0.0002 & ** & 0.8250 & 0.0061 & *** & 1.3833 & 0.0000 & *** \\
**Importance of transport: High** & 1.2933 & 0.0000 & *** & 0.7904 & 0.0065 & *** & 1.6109 & 0.0000 & *** \\
**Accommodation zone: Central Almond** & 0.6440 & 0.0128 & ** & \(-\)0.6346 & 0.0389 & ** & 0.7472 & 0.0045 & *** \\
**Accommodation zone: Periphery** & 1.1320 & 0.0018 & *** & 0.3329 & 0.3402 & & 1.0207 & 0.0045 & *** \\
**Distance to metro** & 0.0006 & 0.3923 & & & & 0.0008 & 0.2961 & \\
**Distance to bus** & \(-\)0.0027 & 0.1109 & & \(-\)0.0025 & 0.1905 & & & \\ \hline \(\alpha_{1}\) & 0.4091 & & & 1.4127 & & 1.2365 & & \\ \(\alpha_{2}\) & 2.2428 & & & 3.0385 & & 2.9955 & & \\ \hline
**Sample size (n)** & 610 & & 547 & & 604 & & \\ \hline
**Log likelihood intercept only** & \(-\)661.1 & & \(-\)569.6 & & \(-\)660.9 & & \\
**Log likelihood at convergence** & \(-\)613.1 & & \(-\)528.0 & & \(-\)600.9 & & \\ \(\chi^{2}\) & 95.9 & & 83.3 & 120.1 & & \\
**AIC** & 1262 & & 1090 & & 1236 & & \\ \hline \hline \end{tabular} Statistical significance codes: *** for 1%, *** for 5%, and *** for 10%. AIC is the Akaike information criterion.  
\end{table} 
Table 5: Results of the ordered logistic regression. First-time visitors to the city are significantly more likely to be in the low-use (+7.0%, \(p=0.02\)) and mid-use (+1.9%, \(p=0.04\)) categories and less likely to be in the high-use category (\(-8.9\%,p=0.02\)). Regarding geographic origin, tourists from Europe and the rest of the world show a significantly higher probability of low public transport use (+13.2% and +20.9%, respectively) and a lower probability of high use (\(-16.1\%\) and \(-18.6\%\), respectively) relative to tourists from Spain. For American tourists, only a weakly significant increase in the probability of medium use is observed (+1.5%, \(p=0.06\)), suggesting regional disparities in public transport use among international tourists. Arriving by private car is associated with a lower likelihood of high public transport use (\(-12.9\%,p=0.07\)), although the effect is only marginally significant.