# Modelling Freight Trip Generation Based on Deliveries for Brazilian Municipalities

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Freight Trip Generation Models—The Literature

^{®}. Google Scholar

^{®}was included since the authors knew beforehand that some classical papers would not be found in the other two databases. The search was limited to documents up to August 2021. Then, the search procedure yielded 708 documents: 160 in Scopus, 76 in Web of Science, and 476 in Google Scholar

^{®}. The inclusion criteria considered records (1) that were related to the research question and that estimated FTGM, (2) that were available online in full text, and (3) that were published in English or Portuguese. The exclusion criteria considered books, chapters, reports, and duplicated records. The inclusion and exclusion criteria resulted in 43 papers, whose abstracts were read. Another 21 papers were excluded, which led to 22 remaining papers for the analysis. Lastly, these 22 papers were read, categorised, and analysed.

## 3. Procedure for Estimating FTGM

#### 3.1. Step 1: Data Analysis

#### 3.2. Step 2: Estimation of the Linear Model

#### 3.3. Step 3: Evaluation of the OLS Assumptions

#### 3.4. Step 4: Estimation of Alternative Regression Models

#### 3.5. Step 5: Cross-Validation Analysis

## 4. Results

**all data**; (ii) state

**capital**cities (Belo Horizonte and Palmas); (iii)

**non-capital**cities (Betim, Caruaru, Contagem, Divinopolis, Itabira, Nova Lima, and Quixada); (iv)

**larger cities**, i.e., cities with a population greater than 50,000 inhabitants (Belo Horizonte, Betim, and Contagem); (v)

**medium cities**, i.e., cities with a population between 100,000 and 500,000 inhabitants (Caruaru, Divinopolis, Itabira, and Palmas); and (vi)

**small cities**, i.e., cities with a population lower than 100,000 inhabitants (Nova Lima and Quixada).

## 5. Discussion of Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- van Wee, B.; Annema, J.A.; Banister, D. Accessibility: Perspectives, Measures and Applications. In The Transport System and Transport Policy; Edward Elgar: Cheltenham, UK, 2013. [Google Scholar]
- McLeod, S.; Schapper, J.H.M.; Curtis, C.; Graham, G. Conceptualizing Freight Generation for Transport and Land Use Planning: A Review and Synthesis of the Literature. Transp. Policy
**2019**, 74, 24–34. [Google Scholar] [CrossRef] - Lindholm, M.; Behrends, S. Challenges in Urban Freight Transport Planning—A Review in the Baltic Sea Region. J. Transp. Geogr.
**2012**, 22, 129–136. [Google Scholar] [CrossRef] - Holguín-Veras, J.; Amaya Leal, J.; Sanchez-Diaz, I.; Browne, M.; Wojtowicz, J. State of the Art and Practice of Urban Freight Management Part II: Financial Approaches, Logistics, and Demand Management. Transp. Res. Part A Policy Pract.
**2020**, 137, 383–410. [Google Scholar] [CrossRef] - Holguín-Veras, J.; Amaya Leal, J.; Sánchez-Diaz, I.; Browne, M.; Wojtowicz, J. State of the Art and Practice of Urban Freight Management: Part I: Infrastructure, Vehicle-Related, and Traffic Operations. Transp. Res. Part A Policy Pract.
**2020**, 137, 360–382. [Google Scholar] [CrossRef] - Cassiano, D.R.; Bertoncini, B.V.; de Oliveira, L.K. A Conceptual Model Based on the Activity System and Transportation System for Sustainable Urban Freight Transport. Sustainability
**2021**, 13, 5642. [Google Scholar] [CrossRef] - Comi, A.; Site, P.D.; Filippi, F.; Nuzzolo, A. Urban Freight Transport Demand Modelling: A State of the Art. Eur. Transp. Trasp. Eur.
**2012**, 51, 1–17. [Google Scholar] - Sahu, P.K.; Pani, A. Freight Generation and Geographical Effects: Modelling Freight Needs of Establishments in Developing Economies and Analyzing Their Geographical Disparities. Transportation
**2020**, 47, 2873–2902. [Google Scholar] [CrossRef] - Gasparini, A.; Campos, V.B.G.; D’agosto, M.D.A. Modelos Para Estimativa Da Demanda de Viagens de Veículos de Carga Para Supermercados e Shopping-Centers. Transportes
**2010**, 18, 58–65. [Google Scholar] [CrossRef] - Oliveira, L.K.; Oliveira, R.L.M.; Ramos, C.M.F.; Ebias, D.G. Modelo de Geração de Viagens de Carga Em Áreas Urbanas: Um Estudo Para Bares, Restaurantes e Supermercados. Transportes
**2016**, 24, 53–67. [Google Scholar] [CrossRef] - Oliveira, L.K.; Herédia, R.T.; Bertoncini, B.V.; Oliveira, R.L.M. Freight Trip Generation to Buildings under Construction: A Comparative Analysis with Linear Regression and Generalised Linear Regression. Transportes
**2020**, 28, 28–42. [Google Scholar] [CrossRef] - de Oliveira, L.K.; Lopes, G.P.; de Oliveira, R.L.M.; Bracarense, L.; dos, S.F.P.; Pitombo, C.S. An Investigation of Contributing Factors for Warehouse Location and the Relationship between Local Attributes and Explanatory Variables of Warehouse Freight Trip Generation Model. Transp. Res. Part A Policy Pract.
**2022**, 162, 206–219. [Google Scholar] [CrossRef] - Silva, K.; da Silva Lima, R.; Alves, R.; Yushimito, W.F.; Holguín-Veras, J. Freight and Service Parking Needs in Historical Centers: A Case Study in São João Del Rei, Brazil. Transp. Res. Rec.
**2020**, 2674, 352–366. [Google Scholar] [CrossRef] - Ferreira, B.L.G.; Silva, M.A.V. Truck Trips in Urban Areas and Its Relation to Socioeconomic Variables. Rev. Gestão Da Produção Operações E Sist.
**2016**, 11, 197–212. [Google Scholar] [CrossRef] - Barbosa, M.W.; de Sousa, P.R.; de Oliveira, L.K. The Effects of Barriers and Freight Vehicle Restrictions on Logistics Costs: A Comparison before and during the COVID-19 Pandemic in Brazil. Sustainability
**2022**, 14, 8650. [Google Scholar] [CrossRef] - Alho, A.R.; Silva, J.D.A.E. Freight-Trip Generation Model: Predicting Urban Freight Weekly Parking Demand from Retail Establishment Characteristics. Transp. Res. Rec.
**2014**, 2411, 45–54. [Google Scholar] [CrossRef] - Alho, A.R.; Silva, J.A. Modeling Retail Establishments’ Freight Trip Generation: A Comparison of Methodologies to Predict Total Weekly Deliveries. Transportation
**2015**. [Google Scholar] [CrossRef] - Mommens, K.; van Lier, T.; Macharis, C. Loading Unit in Freight Transport Modelling. Procedia Comput. Sci.
**2016**, 83, 921–927. [Google Scholar] [CrossRef] - Sánchez-Díaz, I. Modeling Urban Freight Generation: A Study of Commercial Establishments’ Freight Needs. Transp. Res. Part A Policy Pract.
**2017**, 102, 3–17. [Google Scholar] [CrossRef] - Holguín-Veras, J.; Sánchez-Díaz, I. Freight Demand Management and the Potential of Receiver-Led Consolidation Programs. Transp. Res. Part A Policy Pract.
**2016**, 84, 109–130. [Google Scholar] [CrossRef] - Venkadavarahan, M.; Raj, C.T.; Marisamynathan, S. Development of Freight Travel Demand Model with Characteristics of Vehicle Tour Activities. Transp. Res. Interdiscip. Perspect.
**2020**, 8, 100241. [Google Scholar] [CrossRef] - Middela, M.S.; Ramadurai, G. Incorporating Spatial Interactions in Zero-Inflated Negative Binomial Models for Freight Trip Generation. Transportation
**2021**, 48, 2335–2356. [Google Scholar] [CrossRef] - Sanchez-Diaz, I. Assessing the Magnitude of Freight Traffic Generated by Office Deliveries. Transp. Res. Part A Policy Pract.
**2020**, 142, 279–289. [Google Scholar] [CrossRef] - Wang, X.C.; Zhou, Y. Deliveries to Residential Units: A Rising Form of Freight Transportation in the U.S. Transp. Res. Part C Emerg. Technol.
**2015**, 58, 46–55. [Google Scholar] [CrossRef] - Sánchez-Díaz, I.; Holguín-Veras, J.; Wang, X. An Exploratory Analysis of Spatial Effects on Freight Trip Attraction. Transportation
**2016**, 43, 177–196. [Google Scholar] [CrossRef] - Ducret, R.; Gonzalez-Feliu, J. Connecting Demand Estimation and Spatial Category Models for Urban Freight: First Attempt and Research Implications. Transp. Res. Procedia
**2016**, 12, 142–156. [Google Scholar] [CrossRef] - Pani, A.; Sahu, P.K.; Chandra, A.; Sarkar, A.K. Assessing the Extent of Modifiable Areal Unit Problem in Modelling Freight (Trip) Generation: Relationship between Zone Design and Model Estimation Results. J. Transp. Geogr.
**2019**, 80, 102524. [Google Scholar] [CrossRef] - Wooldridge, J.M. Introductory Econometrics: A Modern Approach; Cengage Learning: Boston, MS, USA, 2012. [Google Scholar]
- Gujarati, D.N.; Damodar, G.; Porter, D. Basic Econometrics; Irwin/McGraw-Hill: New York, NY, USA, 2008. [Google Scholar]
- Washington, S.P.; Karlaftis, M.G.; Mannering, F.; Anastasopoulos, P. Statistical and Econometric Methods for Transportation Data Analysis; Chapman and Hall/CRC: Boca Raton, FL, USA, 2020. [Google Scholar]
- Motuba, D.; Tolliver, D. Truck Trip Generation in Small-And Medium-Sized Urban Areas. Transp. Plan. Technol.
**2017**, 40, 327–339. [Google Scholar] [CrossRef] - Lawson, C.T.; Holguín-Veras, J.; Sánchez-Díaz, I.; Jaller, M.; Campbell, S.; Powers, E.L. Estimated Generation of Freight Trips Based on Land Use. Transp. Res. Rec.
**2012**, 2269, 65–72. [Google Scholar] [CrossRef] - Dhonde, B.; Patel, C.R. Implementing Circular Economy Concepts for Sustainable Urban Freight Transport: Case of Textile Manufacturing Supply Chain. Acta Logist.
**2020**, 7, 131–143. [Google Scholar] [CrossRef] - Gonzalez-Feliu, J.; Peris-Pla, C. Impacts of Retailing Land Use on Both Retailing Deliveries and Shopping Trips: Modelling Framework and Decision Support System. IFAC-Pap.
**2018**, 51, 606–611. [Google Scholar] [CrossRef] - Campbell, S.; Holguín-Veras, J.; Ramirez-Rios, D.G.; González-Calderón, C.; Kalahasthi, L.; Wojtowicz, J. Freight and Service Parking Needs and the Role of Demand Management. Eur. Transp. Res. Rev.
**2018**, 10, 47. [Google Scholar] [CrossRef] - Gonzalez-Feliu, J.; Sánchez-Díaz, I. The Influence of Aggregation Level and Category Construction on Estimation Quality for Freight Trip Generation Models. Transp. Res. Part E Logist. Transp. Rev.
**2019**, 121, 134–148. [Google Scholar] [CrossRef] - Puente-Mejia, B.; Palacios-Argüello, L.; Suárez-Núñez, C.; Gonzalez-Feliu, J. Freight Trip Generation Modeling and Data Collection Processes in Latin American Cities. Modeling Framework for Quito and Generalization Issues. Transp. Res. Part A Policy Pract.
**2020**, 132, 226–241. [Google Scholar] [CrossRef] - Oliveira, L.K.; Barraza, B.; Bertocini, B.V.; Isler, C.A.; Pires, D.R.; Madalon, E.C.N.; Lima, J.; Vieira, J.G.V.; Meira, L.H.; Bracarense, L.S.F.P.; et al. An Overview of Problems and Solutions for Urban Freight Transport in Brazilian Cities. Sustainability
**2018**, 10, 1233. [Google Scholar] [CrossRef] - Ramsey, J.B. Tests for Specification Errors in Classical Linear Least-Squares Regression Analysis. J. R. Stat. Society. Ser. B (Methodol.)
**1969**, 31, 350–371. [Google Scholar] [CrossRef] - Zeileis, A.; Hothorn, T. Diagnostic Checking in Regression Relationship. R News
**2002**, 2, 7–10. [Google Scholar] - Cook, R.D. Detection of Influential Observation in Linear Regression. Technometrics
**1977**, 19, 15–18. [Google Scholar] [CrossRef] - Hastie, T.; Tibshirani, R.; Friedman, J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction; Springer: Berlin/Heidelberg, Germany, 2016. [Google Scholar]
- Schwarz, G. Estimating the Dimension of a Model. Ann. Stat.
**1978**, 6, 461–464. [Google Scholar] [CrossRef] - Zhu, L.; Cui, H. A Semi-Parametric Regression Model with Errors in Variables. Scand. J. Stat.
**2003**, 30, 429–442. [Google Scholar] [CrossRef] - Venables, V.M.; Ripley, B.D. Modern Applied Statistics with S-PLUS; Springer: Berlin/Heidelberg, Germany, 2002. [Google Scholar]
- Yee, T.W. Vector Generalized Linear and Additive Models: With an Implementation in R; Springer: Berlin/Heidelberg, Germany, 2015. [Google Scholar]
- Cheah, L.; Mepparambath, R.M.; Ricart Surribas, G.M. Freight Trips Generated at Retail Malls in Dense Urban Areas. Transp. Res. Part A Policy Pract.
**2021**, 145, 118–131. [Google Scholar] [CrossRef]

**Figure 6.**Histogram of the explanatory variable, by subset. (

**a**) Brazil data, (

**b**) capital cities, (

**c**) non-capital cities, (

**d**) larger cities, (

**e**) medium cities, (

**f**) small cities.

Issues Analysed in the Papers | References | ||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

[10] | [11] | [13] | [16] | [25] | [32] | [33] | [8] | [34] | [17] | [35] | [36] | [26] | [18] | [19] | [20] | [21] | [22] | [23] | [24] | [27] | [31] | ||

Technique | OLS | • | • | • | • | • | • | • | • | • | • | ||||||||||||

Standard trip generation rates | • | • | • | ||||||||||||||||||||

Weighted linear regression | |||||||||||||||||||||||

Generalised linear regression | • | • | • | • | |||||||||||||||||||

Logit or probit models | • | • | • | ||||||||||||||||||||

Negative binomial regression | • | • | • | ||||||||||||||||||||

Multiple classification analysis | • | • | |||||||||||||||||||||

Covariance analysis | • | ||||||||||||||||||||||

Non-linear regression | • | • | • | • | |||||||||||||||||||

Spatial techniques | • | • | • | • | • | ||||||||||||||||||

Independent variables | Employee | • | • | • | • | • | • | • | • | • | • | • | |||||||||||

Establishment area | • | • | • | • | • | • | • | ||||||||||||||||

Number of establishments | • | ||||||||||||||||||||||

Type of establishment | • | • | • | ||||||||||||||||||||

Population | • | ||||||||||||||||||||||

Goodness-of-fit measures | t-test | • | • | • | • | • | • | ||||||||||||||||

F-test | • | • | • | • | • | • | |||||||||||||||||

R-squared | • | • | • | • | • | • | • | ||||||||||||||||

AIC | • | • | |||||||||||||||||||||

BIC | • | ||||||||||||||||||||||

RMSE | • | • | • | • | |||||||||||||||||||

MAPE | • | • | |||||||||||||||||||||

OLS assumption | Linearity of parameters | • | • | • | • | • | • | ||||||||||||||||

Homoscedasticity | • | • | • | • | • | ||||||||||||||||||

Endogeneity | • | • | |||||||||||||||||||||

Multicollinearity | • | • | • | ||||||||||||||||||||

Autocorrelated errors | • | • | |||||||||||||||||||||

Normality of the error distribution | • | • | • |

Functional Form | Original Form | Linearised Form | Notes |
---|---|---|---|

Linear | Y = b_{0} + b_{1}X | Y = b_{0} + b_{1}X | |

Log-log | Y = b_{0}X^{b1} | ln(Y) = B_{0} + b_{1}ln(X) | B_{0} = ln(b_{0}) |

Log-linear exponential | Y = b_{0}b_{1}^{X} | ln(Y) = B_{0} + B_{1}X | B_{0} = ln(b_{0}) and B_{1} = ln(b_{1}) |

Linear-log or logarithm-X | Y = b_{0} + b_{1}ln(X) | ||

Inverse | Y = b_{0} + b_{1}X | Y = b_{0} + b_{1}/X | |

Log-inverse | ln(Y) = b_{0} + b_{1}/X | ||

Reciprocal-Y | 1/Y = b_{0} + b_{1}X | Z = b_{0} + b_{1}X | Z = 1/Y |

Double reciprocal | 1/Y = b_{0} + b_{1}/X | Z = b_{0} + b_{1}W | W = 1/X and Z = 1/Y |

Quadratic | Y = b_{0} + b_{1×1} + b_{2}X_{2} | Y = b_{0} + b_{1}X_{1} + b_{2}W | W = X_{2} |

Variable Transformation | All Data | Capital | Non-Capital Cities | Larger Cities | Medium Cities | Small Cities |
---|---|---|---|---|---|---|

Linear | 4.90 (0.01) ^{NS} | 13.76 (0.00) ^{NS} | 4.016 (0.02) ^{NS} | 3.20 (0.04) ^{NS} | 21.64 (0.00) ^{NS} | 7.04 (0.00) ^{NS} |

Log–log | 0.234 (0.79) | 0.11 (0.89) | 1.06 (0.35) | 1.13 (0.33) | 0.24 (0.79) | 3.15 (0.05) |

Log–linear | 17.34 (0.00) ^{NS} | 3.21 (0.04) ^{NS} | 13.83 (0.00) ^{NS} | 3.76 (0.02) ^{NS} | 3.94 (0.02) ^{NS} | 17.29 (0.00) ^{NS} |

Linear–log | 2.133 (0.12) | 0.93 (0.40) | 2.37 (0.09) | 0.88 (0.42) | 3.86 (0.02) ^{NS} | 7.58 (0.00) ^{NS} |

Inverse | 4.62 (0.01) ^{NS} | 17.68 (0.00) ^{NS} | 5.97 (0.00) ^{NS} | 1.30 (0.28) | 1.06 (0.35) | 20.85 (0.00) |

Log–inverse | 28.03 (0.00) ^{NS} | 45.48 (0.00) ^{NS} | 0.74 (0.07) | 41.50 (0.00) ^{NS} | 3.45 (0.03) ^{NS} | 4.46 (0.01) ^{NS} |

^{NS}Without statistical significance.

Outliers | Model | Sample | Deliveries Per Week | Area | Employees | |||
---|---|---|---|---|---|---|---|---|

Ave. | Sd. | Ave. | Sd. | Ave. | Sd. | |||

With outliers | All data | 860 | 3.23 | 4.57 | 150.35 | 223.01 | 7.08 | 7.62 |

Capital | 374 | 4.12 | 5.81 | 170.40 | 146.74 | 7.00 | 7.38 | |

Non-capital cities | 486 | 2.53 | 3.19 | 134.95 | 201.79 | 7.15 | 7.80 | |

Larger cities | 221 | 7.96 | 5.07 | 150.50 | 192.52 | 4.14 | 8.90 | |

Medium cities | 468 | 3.18 | 4.95 | 154.00 | 230.00 | 6.55 | 6.40 | |

Small cities | 171 | 2.21 | 1.75 | 140.10 | 239.41 | 7.42 | 8.73 | |

Without outliers | All data | 650 | 2.32 | 1.39 | 122.81 | 174.46 | 6.48 | 7.09 |

Capital | 285 | 2.67 | 1.73 | 130.85 | 155.81 | 6.03 | 6.32 | |

Non-capital cities | 361 | 2.11 | 1.26 | 119.79 | 191.79 | 6.98 | 8.02 | |

Larger cities | 160 | 2.51 | 1.64 | 131.03 | 163.29 | 7.16 | 7.29 | |

Medium cities | 373 | 2.26 | 1.32 | 112.72 | 142.24 | 5.44 | 5.12 | |

Small cities | 124 | 2.44 | 1.66 | 132.87 | 195.72 | 7.93 | 8.62 |

Model | Variables | Estimated Parameters | T-Value | F-Statistics | R^{2} | AIC | BIC |
---|---|---|---|---|---|---|---|

All data | Intercept | −0.22 | −2.53 ** | 182.6 *** | 0.46 | 844.15 | 862.06 |

Area | 0.07 | 2.70 ** | |||||

Employees | 0.39 | 12.88 *** | |||||

Capital | Intercept | −0.18 | −1.02 | 61.81 *** | 0.52 | 441.96 | 456.57 |

Area | 0.08 | 1.78 | |||||

Employees | 0.41 | 8.53 *** | |||||

Non-capital cities | Intercept | −0.20 | −2.18 * | 156.1 *** | 0.40 | 369.47 | 385.02 |

Area | 0.02 | 0.80 | |||||

Employees | 0.44 | 11.39 *** | |||||

Larger cities | Intercept | 0.69 | 2.88 *** | 35.59 *** | 0.51 | 243.25 | 255.55 |

Area | −0.19 | −3.03 *** | |||||

Employees | 0.56 | 8.03 *** | |||||

Medium cities | Intercept | −0.42 | −3.96 *** | 90.79 *** | 0.47 | 492.57 | 508.26 |

Area | 0.17 | 5.50 *** | |||||

Employees | 0.26 | 6.39 *** | |||||

Small cities | Intercept | 0.59 | 2.69 *** | 116.4 *** | 0.41 | 133.39 | 144.68 |

Area | −0.40 | −5.46 *** | |||||

Employees | 1.06 | 12.40 *** |

**Table 6.**Analysis of the OLS assumption (DW = Durbin–Watson; GQ = Goldfeld–Quandt; BP = Breusch–Pagan; KS = Kolmogorov–Smirnov; SW = Shapiro–Wilk).

Model | Variables | Endogeneity | Multicol. | Linearity | Autocorr. Errors | Homoscedasticity | Normality of Errors |
---|---|---|---|---|---|---|---|

Hauss. Test | VIF | RESET | DW Test | GQ Test | BP Test | ||

All data | Area | 166 (0.00) | 1.68 | 0.11 (0.89) | 1.62 (0.00) | 1.09 (0.22) | 0.28 (0.87) |

Employees | 7.28 (0.01) | 1.68 | |||||

Capital | Area | 72.76 (0.00) | 1.35 | 0.33 (0.72) | 0.99 (0.00) | 1.07 (0.34) | 1.10 (0.58) |

Employees | 3.15 (0.08) ^{NS} | 1.35 | |||||

Non-capital cities | Area | 129.7 (0.00) | 2.17 | 0.58 (0.56) | 1.80 (0.03) | 1.20 (0.10) | 0.38 (0.82) |

Employees | 0.64 (0.42) ^{NS} | 2.17 | |||||

Larger cities | Area | 64.53 (0.00) | 1.65 | 0.06 (0.94) | 0.84 (0.00) | 1.04 (0.44) | 0.97 (0.61) |

Employees | 9.16 (0.00) | 1.65 | |||||

Medium cities | Area | 40.81 (0.00) | 1.59 | 1.12 (0.33) | 1.55 (0.00) | 1.10 (0.25) | 1.26 (0.53) |

Employees | 30.24 (0.00) | 1.59 | |||||

Small cities | Area | 153.8 (0.00) | 3.30 | 0.14 (0.87) | 1.73 (0.06) | 0.67 (0.94) | 3.62 (0.16) |

Employees | 166 (0.00) | 1.68 |

^{NS}Without statistical significance.

Model | Variables | Estimated Parameters | z-Value | Residual Standard Error | AIC | BIC |
---|---|---|---|---|---|---|

All data | Intercept | −0.24 | −2.53 ** | 0.51 | 844.47 | 862.38 |

Area | 0.07 | 2.49 ** | ||||

Employees | 0.40 | 12.07 *** | ||||

Capital | Intercept | −0.21 | −1.09 | 0.61 | 441.99 | 456.60 |

Area | 0.08 | 1.76 ‘ | ||||

Employees | 0.42 | 8.17 *** | ||||

Non-capital cities | Intercept | −0.20 | −2.11 * | 0.46 | 369.66 | 385.22 |

Area | 0.02 | 0.63 | ||||

Employees | 0.45 | 11.26 *** | ||||

Larger cities | Intercept | 0.69 | 2.75 ** | 0.58 | 243.26 | 255.56 |

Area | −0.20 | −2.92 *** | ||||

Employees | 0.56 | 7.69 *** | ||||

Medium cities | Intercept | −0.43 | −3.79 *** | 0.54 | 492.82 | 508.51 |

Area | 0.17 | 5.12 *** | ||||

Employees | 0.27 | 6.19 *** | ||||

Small cities | Intercept | 0.57 | 2.43 * | 0.38 | 492.82 | 508.51 |

Area | −0.40 | −5.10 *** | ||||

Employees | 1.06 | 11.67 *** |

Model | Variables | Estimated Parameters | z-Value | Log-Likelihood | AIC | BIC |
---|---|---|---|---|---|---|

All data | Intercept | −0.79 | −6.04 *** | −596.36 | 1200.7 | 1218.6 |

Area | 0.11 | 2.89 *** | ||||

Employees | 0.55 | 12.11 *** | ||||

Capital | Intercept | −0.59 | −2.42 ** | −283.12 | 574.24 | 588.85 |

Area | 0.10 | 1.67 ‘ | ||||

Employees | 0.54 | 8.23 *** | ||||

Non-capital cities | Intercept | −0.79 | −5.34 *** | −292.91 | 593.81 | 609.37 |

Area | 0.05 | 1.05 (0.29) | ||||

Employees | 0.63 | 10.27 *** | ||||

Larger cities | Intercept | 0.52 | 1.62 | −155.27 | 318.54 | 330.84 |

Area | −0.26 | −2.91 *** | ||||

Employees | 0.74 | 7.74 *** | ||||

Medium cities | Intercept | −1.18 | −6.93 *** | −342.81 | 693.62 | 709.31 |

Area | 0.26 | 5.58 *** | ||||

Employees | 0.39 | 6.33 *** | ||||

Small cities | Intercept | 0.52 | 1.72 ‘ | −91.33 | 190.66 | 201.94 |

Area | −0.53 | −5.00 *** | ||||

Employees | 1.34 | 10.23 *** |

Technique | Statistics | All Data | Larger Cities | Medium Cities | Small Cities |
---|---|---|---|---|---|

LOOCV | RMSE | 0.343 | 0.397 | 0.307 | 0.322 |

R-squared | 0.178 | 0.093 | 0.18 | 0.346 | |

MAE | 0.262 | 0.307 | 0.238 | 0.241 | |

K-fold | RMSE | 0.343 | 0.39 | 0.305 | 0.316 |

R-squared | 0.188 | 0.147 | 0.214 | 0.408 | |

MAE | 0.262 | 0.305 | 0.238 | 0.241 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Oliveira, L.K.d.; Araújo, G.G.F.d.; Bertoncini, B.V.; Pedrosa, C.D.; Silva, F.G.F.d.
Modelling Freight Trip Generation Based on Deliveries for Brazilian Municipalities. *Sustainability* **2022**, *14*, 10300.
https://doi.org/10.3390/su141610300

**AMA Style**

Oliveira LKd, Araújo GGFd, Bertoncini BV, Pedrosa CD, Silva FGFd.
Modelling Freight Trip Generation Based on Deliveries for Brazilian Municipalities. *Sustainability*. 2022; 14(16):10300.
https://doi.org/10.3390/su141610300

**Chicago/Turabian Style**

Oliveira, Leise Kelli de, Gracielle Gonçalves Ferreira de Araújo, Bruno Vieira Bertoncini, Carlos David Pedrosa, and Francisco Gildemir Ferreira da Silva.
2022. "Modelling Freight Trip Generation Based on Deliveries for Brazilian Municipalities" *Sustainability* 14, no. 16: 10300.
https://doi.org/10.3390/su141610300