# Skewed Binary Regression to Study Rental Cars by Tourists in the Canary Islands

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Logistic Specification

#### 2.2. Bayesian Symmetric Specification

#### 2.3. Bayesian Asymmetric Specification

## 3. Description of Database

- Origin spent. A quantitative variable defining expenses at origin per person and day. Expenditure of tourists is approximately 99.92 euros on average.
- Destination spent. A quantitative variable defining expenses at destination per person and day. Expenditure of tourists is approximately 40.68 euros on average.
- Nights. A quantitative variable representing the length of stay. It results in approximately nine days on average, with a minimum stay of one day and a maximum of 180.
- Previous visits. A dummy variable takes one whether the tourist has visited the Canary Islands before the current trip and 0 otherwise. Approximately 77% of visitors repeat visits.
- Accommodation. A dummy variable takes one if the tourist has been accommodated at a hotel and 0 otherwise.
- Party. A dummy variable takes 1 if the tourist has travelled with someone else and 0 otherwise.
- Booking. A dummy variable takes one if the tourist has booked the holidays at home and 0 otherwise.
- Low cost. A dummy variable, which takes one if the tourist has travelled in a low-cost carrier.
- Season. A categorical variable expressing the time of the year the tourist traveled: January–May, dummy variable which represents traveling from January to May; June–September, a dummy variable for traveling from June to September; and October–December, the reference dummy variable representing trips from October to December.

- 10.
- SunBeach. A dummy variable takes one whether the main reason for visiting the Islands is enjoying sun and beach, and 0, otherwise.
- 11.
- Holiday. A dummy variable takes 1 when the reason for traveling is holidays, and 0 otherwise.

- 12.
- Age in years. It can be seen in Table 1 that, on average, tourists are in their forties. The minimum age of those interviewed is 16 years old, and 9 are the oldest ones.
- 13.
- Gender. A dummy variable takes 1 for males. 49.5% of visitors are men.
- 14.
- Income. An ordered categorical variable which takes the following values: (1): from 12,000 to 24,000 euros; (2): from 24,001 to 36,000 euros; (3): from 36,001 to 48,000 euros; (4): from 48,001 to 60,000 euros; (5): from 60,001 to 72,000 euros; (6): from 72,001 to 84,000 euros; and (7): greater than 84,000 euros. The data reflect on Table 1 that on average, tourist’s income is between 36,000 euros and 48,000 euros.
- 15.
- Job. A dummy variable takes one if the tourist is employed and 0, otherwise. Approximately 82% of visitors are employed.
- 16.
- Nationality. Tourists are separated according to the following countries of residence: Germany, The United Kingdom, Spain, Nordic countries, and others. Mostly, incoming tourists are from the United Kingdom, followed by other countries, Spain, Germany, and Nordic countries. The dummy reference variable is ’Other’.

## 4. Empirical Results and Discussion

#### 4.1. Brief Explanation of the Computations

#### 4.2. Interpretation of the Results

#### 4.3. Checking the Models

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Cumulative density function (logistic kernel mean function) of the skewed logit model for special values of skewness parameter $\delta $. The case $\delta =0$ corresponds to the classical logistic distribution.

**Figure 2.**Marginal effect of the skewed logit model with different values of skewness parameter $\delta $. The case $\delta =0$ corresponds to the classical logistic distribution.

Variable | Minimum | Maximum | Mean/Mode | Standard Deviation |
---|---|---|---|---|

Renting | 0 | 1 | 0.223 | — |

(number of observations) | (21,933) | (6302) | ||

General variables | ||||

Origin spent | 0.52 | 1988.76 | 99.919 | 64.413 |

Destination spent | 0 | 500 | 40.679 | 37.105 |

Nights | 1 | 180 | 8.917 | 7.238 |

Previous visits | 0 | 1 | 0.767 | — |

Accommodation | 0 | 1 | 0.548 | — |

Party | 0 | 1 | 0.818 | — |

Booking | 0 | 1 | 0.985 | — |

Low cost | 0 | 1 | 0.518 | — |

Season: | ||||

Jan-May | 0 | 1 | 0.371 | — |

Jun-Sep | 0 | 1 | 0.295 | — |

Oct-Dec | 0 | 1 | 0.333 | — |

Trip motivation variables | ||||

SunBeach | 0 | 1 | 0.903 | — |

Holiday | 0 | 1 | 0.939 | — |

Socio-economic variables | ||||

Age | 16 | 92 | 44.827 | 14.275 |

Gender | 0 | 1 | 0.495 | — |

Income | 1 | 7 | 3.540 | 2.038 |

Job | 0 | 1 | 0.818 | — |

Nationality: | ||||

German | 0 | 1 | 0.173 | — |

British | 0 | 1 | 0.276 | — |

Spanish | 0 | 1 | 0.185 | — |

Nordic | 0 | 1 | 0.099 | — |

Other | 0 | 1 | 0.267 | — |

Observations | 28,235 |

Frequentist | Asymmetric Bayesian | |||||||
---|---|---|---|---|---|---|---|---|

Variables | $\widehat{\mathit{\beta}}$ | Robust sd | p-Value | ME | $\widehat{\mathit{\beta}}$ | sd | MC Error | ME |

Origin spending | −0.004 ${}^{***}$ | 3 × 10${}^{-4}$ | 0.000 | −6.4 × 10${}^{-4}$ | −3.246 ${}^{***}$ | 0.312 | 0.022 | −0.002 |

Destination spending | 0.004 ${}^{***}$ | 4 × 10${}^{-4}$ | 0.000 | 6.4 × 10${}^{-4}$ | 1.791 ${}^{***}$ | 0.187 | 0.013 | 9.9 × 10${}^{-4}$ |

Nights | 0.008 ${}^{***}$ | 0.002 | 0.000 | 1.3 × 10${}^{-3}$ | 0.698 ${}^{***}$ | 0.184 | 0.010 | 3.5 × 10${}^{-4}$ |

Repeat | −0.002 | 0.035 | 0.958 | −3.2 × 10${}^{-4}$ | −0.121 | 0.449 | 0.034 | −6.9 × 10${}^{-5}$ |

Accommodation | −0.100 ${}^{***}$ | 0.033 | 0.001 | -0.016 | −1.422 ${}^{***}$ | 0.434 | 0.029 | −8.03 × 10${}^{-4}$ |

Party | 0.591 ${}^{***}$ | 0.045 | 0.000 | 0.087 | 7.383 ${}^{***}$ | 0.727 | 0.066 | 0.004 |

Booking | 0.470 ${}^{***}$ | 0.143 | 0.001 | 0.067 | 4.734 ${}^{***}$ | 1.462 | 0.144 | 0.002 |

Low cost | 0.217 ${}^{***}$ | 0.031 | 0.000 | 0.035 | 2.775 ${}^{***}$ | 0.414 | 0.030 | 0.001 |

Jan-May | −0.098 ${}^{***}$ | 0.036 | 0.007 | −0.016 | −1.285 ${}^{***}$ | 0.456 | 0.029 | −7.3 × 10${}^{-4}$ |

Jun-Sep | −0.039 | 0.037 | 0.289 | −0.006 | −0.507 | 0.472 | 0.031 | −2.9 × 10${}^{-4}$ |

SunBeach | −0.069 | 0.054 | 0.198 | −0.011 | −0.968 ${}^{*}$ | 0.635 | 0.057 | −5.6 × 10${}^{-4}$ |

Holiday | 0.977 ${}^{***}$ | 0.083 | 0.000 | 0.125 | 12.33 ${}^{***}$ | 1.119 | 0.108 | 0.006 |

Age | −0.004 ${}^{***}$ | 0.001 | 0.000 | −6.4 × 10${}^{-4}$ | −0.823 ${}^{***}$ | 0.226 | 0.013 | −4.5 × 10${}^{-4}$ |

Gender | 0.141 ${}^{***}$ | 0.030 | 0.000 | 4.7 × 10${}^{-4}$ | 1.760 ${}^{***}$ | 0.387 | 0.024 | 0.001 |

Income | 0.072 ${}^{***}$ | 0.008 | 0.000 | 0.012 | 1.865 ${}^{***}$ | 0.241 | 0.016 | 9.4 × 10${}^{-4}$ |

Job | 0.217 ${}^{***}$ | 0.044 | 0.000 | 0.034 | 2.791 ${}^{***}$ | 0.601 | 0.052 | 0.0015 |

German | 0.142 ${}^{***}$ | 0.044 | 0.001 | 0.023 | 1.806 ${}^{***}$ | 0.565 | 0.038 | 0.001 |

British | −1.053 ${}^{***}$ | 0.044 | 0.000 | −0.150 | −13.770 ${}^{***}$ | 0.977 | 0.087 | −0.007 |

Spanish | 0.469 ${}^{***}$ | 0.044 | 0.000 | 0.081 | 5.881 ${}^{***}$ | 0.688 | 0.056 | 0.003 |

Nordic | −0.767 ${}^{***}$ | 0.629 | 0.000 | −0.106 | −9.944 ${}^{***}$ | 1.001 | 0.074 | −0.005 |

Intercept | −3.079 ${}^{***}$ | 0.183 | 0.000 | −58.330 ${}^{***}$ | 3.765 | 3.765 | ||

$\delta $ | 29.090 ${}^{***}$ | 1.767 | 0.176 | |||||

Observations | 28,235 | 28,235 | ||||||

% Correct fit | 77.61 | 99.99 | ||||||

DIC | 27,862.584 | 4647.380 | ||||||

AIC | 27,904.584 | 2369.000 | ||||||

BIC | 28,077.798 | 2550.000 |

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**MDPI and ACS Style**

Dávila-Cárdenes, N.; Pérez-Sánchez, J.M.; Gómez-Déniz, E.; Boza-Chirino, J.
Skewed Binary Regression to Study Rental Cars by Tourists in the Canary Islands. *J. Risk Financial Manag.* **2021**, *14*, 541.
https://doi.org/10.3390/jrfm14110541

**AMA Style**

Dávila-Cárdenes N, Pérez-Sánchez JM, Gómez-Déniz E, Boza-Chirino J.
Skewed Binary Regression to Study Rental Cars by Tourists in the Canary Islands. *Journal of Risk and Financial Management*. 2021; 14(11):541.
https://doi.org/10.3390/jrfm14110541

**Chicago/Turabian Style**

Dávila-Cárdenes, Nancy, José María Pérez-Sánchez, Emilio Gómez-Déniz, and José Boza-Chirino.
2021. "Skewed Binary Regression to Study Rental Cars by Tourists in the Canary Islands" *Journal of Risk and Financial Management* 14, no. 11: 541.
https://doi.org/10.3390/jrfm14110541