# Segmentation Effect on the Transferability of International Safety Performance Functions for Rural Roads in Egypt

^{*}

## Abstract

**:**

^{2}statistic, and Z-score parameters are used to evaluate the performance of the transferred models. The overdispersion parameter (k) for each transferred model and each segmentation approach is recalibrated using the local data by the maximum likelihood method. Before estimating the transferability calibration factor (Cr), three methods were used to adjust the local crash prediction of the transferred models, namely: (1) the HSM default crash modification factors (CMFs); (2) local CMFs; and (3) recalibrating the constant term of the transferred model. The latter method is found to outperform the first two methods. Besides, the results show that the segmentation method would affect the performance of the transferability process. Moreover, the Italian SPFs based on the S1 segmentation method outperforms the HSM and all of the investigated international SPFs for transferring their models to the Egyptian rural roads.

## 1. Introduction

#### HSM Transferability Procedure

- (1)
- Choosing the suitable SPF according to the highway facility under specific base conditions,
- (2)
- Adjusting the base conditions using CMFs if the cross-section of the road deviates from the base condition, and
- (3)
- Finally, the calibration factor (Cr) is estimated to calibrate the predictive model to local conditions as follows:

_{obs,i}= observed crashes on segment i; N

_{pred,i}= predicted crashes on segment i and K

_{i}= overdispersion parameter of the prediction model at site i.

## 2. Materials and Methods

#### 2.1. Data Description

- (1)
- Sections with constant length, specifically, a length of one-kilometer (S1). This length was chosen as the crash data reported by GARBLT was available only for every kilometer;
- (2)
- Homogenous sections (S2): in this method, the highway length was divided into homogenous segments, as suggested by HSM [17] with respect to AADT and some geometric characteristics (e.g., number of lanes, median widths, shoulder width, etc.);
- (3)
- Segmentation based on curvature (S3): the highway was divided into two types of segments based on the presence of curves, as follows: (a) segments with curves, and (b) segments with no curves. It is worth mentioning that, as the crash data is reported every kilometer, the consecutive segments that contain curves are taken as one section and the consecutive one-kilometer sections with no curves are taken as one segment. This is done with respect to the AADT and other geometric characteristics; and
- (4)
- Segmentation based on curvature and U-turns (S4): the segments were categorized according to the presence of both curves and U-turns, as in S3. The consecutive segments with curves or U-turns were merged into one segment, and the consecutive sections without curves or U-turns were merged into one segment.

#### 2.2. Investigated SPFs

#### 2.3. Adjusting the Base Conditions

#### 2.3.1. Default CMFs from the HSM

- (a)
- Lane width (LW): 12 ft. (3.65 m),
- (b)
- Right shoulder width: 8 ft. (2.44 m),
- (c)
- Median width: 30 ft. (9.14 m),
- (d)
- Lighting: None, and
- (e)
- Automated speed enforcement: None.

#### 2.3.2. Locally Derived CMFs Values

_{i}= Time trend effect (t

_{2008}, t

_{2009}, t

_{2010}, t

_{2011}); SW = Shoulder width (m); PW = Pavement width in each direction (m); Accesses = Number of side accesses per section and HL = Categorized variable, yes if the section contains a horizontal curve, and No otherwise.

_{x,i}= CMF specific to variable i with value of x; β

_{i}= estimated coefficient for variable i; X = value of variable i, such as lane width, median width, shoulder width and X

_{0,i}= base condition defined for variable i. 12ft (3.65 m) for lane width, 30ft (9.14 m) for median width, 8ft (2.44 m) for shoulder width, and zero for the presence of HL curve and accesses.

#### 2.3.3. Recalibrating the Constant Term and the Over-Dispersion Parameter of the Transferred SPF

#### 2.4. Recalibrating the Over-Dispersion Parameter

#### 2.4.1. Constant Over-Dispersion Parameter

_{i}= observed crashes on segment i; pred

_{i}= predicted crashes on segment i; β

_{0}, β1, …, b = parameter estimates of the model coefficients; b = inverse of the overdispersion parameter (shape parameter or b =1/k); and k = overdispersion parameter.

#### 2.4.2. Over-Dispersion Parameter as a Function of the Segment Length

_{i}= segment length i.

#### 2.5. Goodness-of-Fit (GOF) Measures

^{2}statistic; and (5) Z-score.

#### 2.5.1. The Mean Absolute Deviation (MAD)

_{i}= observed crashes for site i.

#### 2.5.2. The Mean Prediction Bias (MPB)

#### 2.5.3. The Mean Absolute Percentage Error (MAPE)

#### 2.5.4. Pearson χ^{2} Statistic

^{2}statistic is given by the following equation:

_{i}= the mean crash frequency at section i during the same time.

^{2}statistic is a measure of the goodness of fit that tests if a definite SPF developed by using certain data set gives a reliable expectation for a different set of data [13]. In addition, if the SPF that is applied to a new data set is correct and the observations in the new data set are independent, then the expected value and the standard deviation of the Pearson χ

^{2}statistics are as follow [58]:

#### 2.5.5. Z-Score

## 3. Results

#### 3.1. Default CMFs from HSM Versus Locally Derived CMFs

#### 3.2. Locally Derived CMFs Versus Recalibrating the Constant of the Transferred Models

_{p}

^{2}, and Z-score values for transferred Italy (2012) SPF by recalibrating the constant are 4.670, −0.440, 0.819, 309.559, and −0.205, respectively, compared to 5.946, 0.630, 1.043, 179.548 and −2.295, for the transferred Italy (2012) SPF using the locally derived CMFs. Moreover, the MAD, MPB, MAPE, χ

_{p}

^{2}, and Z-score values for transferred Italy (2017) SPF by recalibrating the constant are 4.624, −0.269, 0.811, 312.470, and −0.155, respectively, compared to 5.996, 1.060, 1.052, 166.785 and −2.443, for transferred Italy (2017) SPF using the locally derived CMFs.Thus, it can be concluded that the transfer of the SPFs with recalibrated model constant is superior to the transfer of the SPFs using the local CMFs, and the transferred Italian SPFs using segmentation method S1 predict crashes in Egypt reasonably well based on the GOF results.

#### 3.3. Fixed Over-Dispersion Parameter Versus Variable Over-Dispersion Parameter

## 4. Discussion and Conclusions

^{2}statistic, and Z-score.

- The segmentation method was found to affect the performance of the transferred SPF model. The difference between the segmentation approaches and among the investigated international models is statistically significant at the 5% significance level.
- The total crashes calibration factors derived from both HSM default CMFs values and locally derived CMFs are lower than one, meaning that the HSM models are overestimating the crash occurrence on multilane rural divided roads in Egypt. Moreover, the calibrated HSM model using locally derived CMFs with the S2 segmentation method outperformed the calibrated HSM model using HSM default CMFs values;
- The calibrated Italian SPF using both locally derived CMFs and by recalibrating the constant outperformed all other investigated international SPFs, as they performed very well for all segmentation methods, especially, for the S1 segmentation method;
- The recalibration of the constant of the transferred models to allow it to better suit local conditions in Egypt is superior to the SPFs recalibration using the local CMFs;
- Using variable overdispersion parameter for the recalibrated SPFs outperforms the constant overdispersion parameter.

#### Study Limitations

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Selected Rural Roads (Adapted with permission from [4], Springer Nature, 2020).

# | Author | Facility Type | Calibration Factor (Cr) | Transferability Assessment |
---|---|---|---|---|

1 | Sun et al. [36] | Rural two-lane roads in Louisiana State (USA) | Cr = 2.28 for AADT < 10,000vpd Cr = 1.49 for AADT > 10,000vpd | The HSM SPFs underestimate crashes in Louisiana State. |

2 | Fitzpatrick et al. [37] | Rural two-lane roads in Texas State (USA) | Cr = 1.12 | The HSM SPFs slight under-predict crashes in Texas State. |

3 | Martinelli et al. [38] | Rural two-lane roads in Italian Province of Arezzo | Cr = 0.38 | The HSM SPFs overestimate crashes in Arezzo. |

4 | Koorey [39] | Rural two-lane undivided roads in New Zealand | Cr = 0.89 | The HSM SPFs predict New Zealand’s crashes reasonably well. |

5 | Persaud et al. [40] | Rural two-way undivided roads in Ontario (Canada) | Cr = 0.74 | The HSM SPFs overestimate crashes in Ontario. |

6 | Srinivasan et al. [41] | Rural two-lane roads in Arizona (USA) | Cr = 1.079 | The HSM SPFs predict Arizona crashes very well |

7 | Srinivasan et al. [42] | Rural-multilane divided roads in Florida (USA) | Cr =0.664 | The HSM SPFs over estimate crashes in Florida state. |

8 | Brimley et al. [30] | Rural two-lane roads in Utah State (USA) | Cr = 1.16 | The HSM SPFs slight under-predict crashes in Utah State. |

9 | Sacchi et al. [28] | Italian two-lane undivided rural roads | Cr = 0.44 | The HSM SPFs overestimate crashes on Italian roads. |

10 | Dixon et al. [43] | Rural-multilane divided roads in Oregon (USA) | Cr = 0.77 | The HSM SPFs over estimate crashes in Oregon state. |

11 | Sun et al. [26] | Rural-multilane divided roads in Missouri (USA) | Cr = 0.98 | The HSM SPFs predict Missouri crashes very well |

12 | Agostino [19] | Italian rural roads | Cr = 1.26 | The HSM SPFs underestimate crashes on Italian roads. |

13 | Asal & Said [1] | Rural-multilane divided rural roads in Egypt | Cr = 0.48 | The HSM SPFs over estimate crashes in Egypt |

Road Code | Road Name | Length (Km) |
---|---|---|

RD1 | Cairo- Alexandria agriculture road | 50 |

RD2 | Cairo- Alexandria desert road | 108 |

RD3 | Cairo- Suez desert road | 73 |

RD4 | Ismailia-Port Said desert road | 30 |

RD5 | Ismailia-Suez desert road | 61 |

**Table 3.**Crashes and number of sections based on the segmentation approach (Adapted with permission from [4], Springer Nature, 2020).

Road | Total Crashes/Year | Number of Sections | |||
---|---|---|---|---|---|

S1 | S2 | S3 | S4 | ||

RD_{1} | 271.75 | 50 | 16 | 28 | 30 |

RD_{2} | 46.75 | 108 | 21 | 51 | 55 |

RD_{3} | 47.50 | 73 | 31 | 41 | 48 |

RD_{4} | 69.0 | 30 | 13 | 13 | 21 |

RD_{5} | 24.0 | 61 | 34 | 44 | 40 |

Total | 459.0 | 322 | 115 | 177 | 194 |

**Table 4.**Summary statistics of the selected roads geometric elements and AADT (Adapted with permission from [4], © Springer Nature, 2020).

Geometric Element | Maximum | Minimum | Mean | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Segmentation Method | Segmentation Method | Segmentation Method | ||||||||||

S1 | S2 | S3 | S4 | S1 | S2 | S3 | S4 | S1 | S2 | S3 | S4 | |

L (km) ^{a} | 1.00 | 12.00 | 7.00 | 6.0 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 2.78 | 1.81 | 1.65 |

Accesses ^{b} | 14 | 50 | 25 | 27 | 0 | 0 | 0 | 0 | 2.19 | 6.12 | 3.97 | 4.00 |

Uturn ^{c} | 2.00 | 7.00 | 4.00 | 7.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 1.04 | 0.69 | 1.00 |

NHL ^{d} | 2.00 | 5.00 | 5.00 | 5.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.95 | 0.61 | 1.00 |

AADT ^{e} | 107,947 | 14,101 | 32,212 | |||||||||

PW ^{f} | 13 | 5.50 | 9.52 | |||||||||

SW ^{g} | 5.00 | 1.69 | 3.24 | |||||||||

MW ^{h} | 44.32 | 1.60 | 8.73 | |||||||||

Nlanes ^{i} | 4 | 2 | 3.05 |

^{a}L = Section length.

^{b}Accesses = Number of side access points.

^{c}Uturn = Number of U-turns.

^{d}NHL = Number of horizontal curves per section.

^{e}AADT = Average annual daily traffic (veh/day).

^{f}PW = Pavement width in each direction in meters.

^{g}SW = Shoulder width in meters.

^{h}MW = Median width in meters.

^{i}Nlanes = Number of lanes in each direction.

Model | SPF | Reference |
---|---|---|

HSM | $\mathrm{Ln}\left(\mathrm{N}\right)=-9.025+1.049\times \mathrm{Ln}\left(\mathrm{AADT}\right)+\mathrm{Ln}\left(\mathrm{L}\right)$ | AASHTO [17] |

Virginia | $\mathrm{Ln}\left(\mathrm{N}\right)=-7.47+0.88\times \mathrm{ln}(\mathrm{AAADT})+\mathrm{ln}(\mathrm{L})$ | Kweon et al. [44] |

North-Carolina | $\mathrm{Ln}(\mathrm{N})=-5.89+0.76\times \mathrm{ln}(\mathrm{AADT})+\mathrm{ln}(0.6214\times \mathrm{L})$ | Srinivasan and Carter [45] |

Alabama | $\mathrm{Ln}\left(\mathrm{N}\right)=-6.16+0.74\times \mathrm{ln}(\mathrm{AADT})+0.35\times \mathrm{ln}(0.6214\times \mathrm{L})$ | Mehta & Lou [21] |

Ohio | $\mathrm{Ln}\left(\mathrm{N}\right)=-9.709+1.125\times \mathrm{ln}(\mathrm{AADT})+\mathrm{ln}(0.6214\times \mathrm{L})-0.074\times \mathrm{SW}$ | Farid et al. [46] |

Italy (2012) | $\mathrm{Ln}(\mathrm{N})=-18.52+1.17\times \mathrm{ln}(\mathrm{AADT})+\mathrm{ln}(\mathrm{L})$ | Cafiso et al. [47] |

Italy (2017) | $\mathrm{Ln}\left(\mathrm{N}\right)=-19.19+1.24\times \mathrm{ln}(\mathrm{AADT})+\mathrm{ln}\left({\scriptscriptstyle \frac{\mathrm{L}}{1000}}\right)$ | Cafiso et al. [24] |

Netherlands | $\mathrm{Ln}\left(\mathrm{N}\right)=-10.1934+0.4967\times \mathrm{ln}(\mathrm{AADT})+0.9647\times \mathrm{ln}(L)$ | Reurings & Janssen [48] |

Czech Rep. | $\begin{array}{ll}\mathrm{Ln}(\mathrm{N})=& -13.6468+0.9307\times \mathrm{ln}(\mathrm{AADT})+0.9499\times \mathrm{ln}(\mathrm{L})\\ & +0.42\times \mathrm{LES}+0.0004\times \mathrm{Curvature}\end{array}$ | Šenk et al. [49] |

Korea | $\mathrm{Ln}(\mathrm{N})=-15.245+\mathrm{ln}(\mathrm{AADT})+\mathrm{ln}(\mathrm{L})$ | Choi et al. [50] |

Ghana | $\mathrm{Ln}\left(\mathrm{N}\right)=-1.92+0.37\times \mathrm{ln}(\mathrm{AADT})+0.36\times \mathrm{ln}(\mathrm{L})$ | Ackaah & Salifu [51] |

CMFi | Value |
---|---|

CMF_{SW} | ${e}^{-0.22\times \left(\mathrm{SW}-2.44\right)}$ |

CMF_{PW} | ${e}^{-0.21\times (\mathrm{PW}-\mathrm{N}*3.65)}$ |

CMF_{Accesses} | ${e}^{-0.08\times (\mathrm{Accesses})}$ |

CMF_{HL} | ${e}^{-0.44\times (\mathrm{HL})}$ |

**Table 7.**Recalibrated overdispersion parameters and Calibration factors for the HSM model using HSM default CMFs and locally derived CMFs.

Variable | Segmentation Method | |||
---|---|---|---|---|

S1 | S2 | S3 | S4 | |

Recalibrated overdispersion parameter (k) | 2809 | 2579 | 2.965 | 2.713 |

Observed crashes | 1836 | |||

Predicted crashes using HSM default CMFs | 5695 | 5676 | 5678 | 5675 |

Calibration factor using HSM default CMFs (Cr) | 0.322 ^{a,b,c,g}(0.066) * | 0.323 ^{a,d,e,g}(0.127) | 0.323 ^{b,d,g}(0.115) | 0.323 ^{c,e,g}(0.102) |

Predicted crashes using Local CMFs | 4692 | 2488 | 3706 | 3823 |

Calibration factor using Local CMFs | 0.391 ^{a,b,c,g}(0.081) | 0.738 ^{a,g}(0.289) | 0.495 ^{b,g}(0.176) | 0.480 ^{c,g}(0.151) |

^{a}The difference between S1 and S2 segmentation methods is statistically significant at the 5% SL.

^{b}The difference between S1 and S3 segmentation methods is statistically significant at the 5% SL.

^{c}The difference between S1 and S4 segmentation methods SPF is statistically significant at the 5% SL.

^{d}The difference between S2 and S3 segmentation methods SPF is statistically significant at the 5% SL.

^{e}The difference between S2 and S4 segmentation methods SPF is statistically significant at the 5% SL.

^{f}The difference between S3 and S4 segmentation methods SPF is statistically significant at the 5% SL.

^{g}The difference between the two methods for the same segmentation method is statistically significant at the 5% SL.

Model | N_{obs.} | S1 | S2 | S3 | S4 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

k | N_{pred.} | Cr | k | N_{pred.} | Cr | k | N_{pred.} | Cr | k | N_{pred.} | Cr | ||

HSM | 1836 | 2.809 | 4692 | 0.391 ^{a,b,c}(0.081) * | 2.580 | 2488 | 0.738 ^{a}(0.289) | 2.966 | 3706 | 0.495 ^{b}(0.176) | 2.713 | 3823 | 0.480 ^{c}(0.151) |

Virginia | 2.551 | 3760 | 0.488 ^{a,b,c}(0.096) | 2.379 | 1997 | 0.919 ^{a}(0.346) | 2.714 | 2965 | 0.619 ^{b}(0.210) | 2.475 | 3055 | 0.601 ^{c}(0.181) | |

N. Carolina | 3.210 | 5506 | 0.333 ^{a,b,c}(0.073) | 3.004 | 2931 | 0.626 ^{a}(0.265) | 3.537 | 4338 | 0.423 ^{b}(0.164) | 3.099 | 4467 | 0.411 ^{c}(0.138) | |

Alabama | 2.972 | 5636 | 0.326 ^{a,b,c}(0.069) | 2.229 | 1305 | 1.406 ^{a,d,e}(0.516) | 3.499 | 2487 | 0.738 ^{b,d}(0.284) | 2.564 | 2792 | 0.658 ^{c,e}(0.201) | |

Ohio | 1.812 | 2436 | 0.754 ^{a,b,c}(0.125) | 1.675 | 1302 | 1.410 ^{a} (0.446) | 1.934 | 1945 | 0.944 ^{b}(0.271) | 1.784 | 1996 | 0.920 ^{c}(0.235) | |

Italy (2012) | 1.657 | 2039 | 0.901 ^{a,b,c}(0.143) | 1.611 | 1082 | 1.697 ^{a}(0.526) | 1.800 | 1613 | 1.138 ^{b}(0.315) | 1.741 | 1665 | 1.103 ^{c}(0.278) | |

Italy (2017) | 1.752 | 2177 | 0.843 ^{a,b,c}(0.138) | 1.634 | 1156 | 1.588 ^{a}(0.496) | 1.838 | 1725 | 1.065 ^{b}(0.298) | 1.775 | 1781 | 1.031 ^{c}(0.263) | |

Netherlands | 1.966 | 1914 | 0.959 ^{a,b,c}(0.166) | 1.852 | 990 | 1.854 ^{a}(0.616) | 2.050 | 1469 | 1.250 ^{b}(0.369) | 1.892 | 1519 | 1.209 ^{c}(0.318) | |

Czech | 2.987 | 5045 | 0.364 ^{a,b,c}(0.077) | 2.708 | 2527 | 0.727 ^{a}(0.292) | 3.122 | 3834 | 0.479 ^{b}(0.174) | 2.854 | 3982 | 0.461 ^{c}(0.149) | |

Korea | 3.921 | 8958 | 0.205 ^{a,b,c}(0.050) | 3.606 | 4752 | 0.386 ^{a}(0.179) | 4.083 | 7072 | 0.260 ^{b}(0.108) | 3.764 | 7292 | 0.252 ^{c}(0.093) | |

Ghana | 2.323 | 2593 | 0.708 ^{a}(0.133) | 2.188 | 761 | 2.413 ^{a,d,e}(0.871) | 2.440 | 1388 | 1.323 ^{d}(0.426) | 2.148 | 1554 | 1.181 ^{e}(0.331) |

^{a}The Difference between S1 and S2 methods for the same transferred SPF is statistically significant at the 5% SL.

^{b}The difference between S1 and S3 methods for the same transferred SPF is statistically significant at the 5% SL.

^{c}The difference between S1 and S4 methods for the same transferred SPF is statistically significant at the 5% significance level.

^{d}The difference between S2 and S3 methods for the same transferred SPF is statistically significant at the 5% SL.

^{e}The Difference between S2 and S4 methods for the same transferred SPF is statistically significant at the 5% SL.

^{f}The Difference between S3 and S4 methods for the same transferred SPF is statistically significant at the 5% SL.

^{g}The Difference between the HSM-The Netherlands models for the S1 method is statistically significant at the 5% SL.

^{h}The difference between the Alabama-Virginia models for the S2 method is statistically significant at the 5% SL.

^{i}The Difference between the Korea-Ohio models for the S3 method is statistically significant at the 5% SL.

^{j}The Difference between the Czech-Italy (2017) models for the S4 method is statistically significant at the 5% SL.

Model | S1 | S2 | S3 | S4 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

New Constant | k | Cr | New Constant | k | Cr | New Constant | k | Cr | New Constant | k | Cr | |

HSM | −10.202 | 1.605 | 1.134 ^{a,b,c} | −10.17 | 1.593 | 1.102 ^{a,d,e} | −10.306 | 1.628 | 1.263 ^{b,d} | −10.146 | 1.694 | 1.076 ^{c,e} |

(0.177) * | (0.334) | (0.332) | (0.265) | |||||||||

Virginia | −8.458 | 1.642 | 1.184 ^{a,b,c} | −8.455 | 1.561 | 1.185 ^{a,d,e} | −8.575 | 1.65 | 1.335 ^{b,d} | −8.423 | 1.687 | 1.147 ^{c,e} |

(0.187) | (0.362) | (0.354) | (0.282) | |||||||||

N. Carolina | −7.278 | 1.688 | 1.202 ^{a,b,c} | −7.295 | 1.593 | 1.228 ^{a,d,e} | −7.426 | 1.691 | 1.4 ^{b,d} | −7.256 | 1.788 | 1.181 ^{c,e} |

(0.193) | (0.379) | (0.375) | (0.138) | |||||||||

Alabama | −7.394 | 1.697 | 1.204 ^{a,b,c} | −9.41 | 1.564 | 1.141 ^{a,d,e} | −7.094 | 2.078 | 1.4 ^{b,d} | −7.091 | 1.799 | 1.308 ^{c,e} |

(0.194) | (0.346) | (0.416) | (0.335 | |||||||||

Ohio | −10.219 | 1.581 | 1.154 ^{a,b,c} | −10. 191 | 1.642 | 1.130 ^{a,d,e} | −10.323 | 1.538 | 1.285 ^{b,d} | −10. 172 | 1.546 | 1.104 ^{c,e} |

(0.176) | (0.331) | (0.329) | (0.263) | |||||||||

Italy (2012) | −18.826 | 1.568 | 1.084 ^{a,b,c} | −18.774 | 1.542 | 1.031 ^{a,d,e} | −18.937 | 1.62 | 1.214 ^{b,d} | −18.757 | 1.669 | 1.014 ^{c,e} |

(0.168) | (0.313) | (0.319) | (0.251) | |||||||||

Italy (2017) | −19.545 | 1.605 | 1.05 ^{a,b,c} | −19.481 | 1.549 | 0.987 ^{a,d,e} | −19.639 | 1.627 | 1.156 ^{b,d} | −19.467 | 1.685 | 0.974 ^{c,e} |

(0.164) | (0.3) | (0.304) | (0.242) | |||||||||

Netherlands | −10.5 | 1.865 | 1.195 ^{a,b,c} | −10.531 | 1.741 | 1.296 ^{a,d,e} | −10.621 | 1.861 | 1.393 ^{b,d} | −10.498 | 1.792 | 1.227 ^{c,e} |

(0.201) | (0.418) | (0.392) | (0.314) | |||||||||

Czech | −14.921 | 1.627 | 1.172 ^{a,b,c} | −14.867 | 1.556 | 1.19 ^{a,d,e} | −15.006 | 1.653 | 1.333 ^{b,d} | −14.861 | 1.699 | 1.147 ^{c,e} |

(0.184) | (0.363) | (0.353) | (0.282) | |||||||||

Korea | −17.081 | 1.612 | 1.157 ^{a,b,c} | −17.057 | 1.553 | 1.128 ^{a,d,e} | −17.189 | 1.629 | 1.287 ^{b,d} | −17.031 | 1.691 | 1.099 ^{c,e} |

(0.18) | (0.342) | (0.338) | (0.27) | |||||||||

Ghana | −2.51 | 1.979 | 1.166 ^{a,b,c} | −1.933 | 2.188 | 1.372 ^{a,d,e} | −2.23 | 2.348 | 1.359 ^{b,d} | −2.234 | 2.053 | 1.279 ^{c,e} |

(0.202) | (0.495) | (0.429) | (0.35) |

^{a}The difference between S1 and S2 methods for the same transferred SPF is statistically significant at the 5% SL.

^{b}The difference between S1 and S3 methods for the same transferred SPF is statistically significant at the 5% SL.

^{c}The difference between S1 and S4 methods for the same transferred SPF is statistically significant at the 5% SL.

^{d}The difference between S2 and S3 methods for the same transferred SPF is statistically significant at the 5% SL.

^{e}The difference between S2 and S4 methods for the same transferred SPF is statistically significant at the 5% SL.

^{f}The difference between S3 and S4 methods for the same transferred SPF is statistically significant at the 5% SL.

^{g}The difference between the Netherlands-Italy (2017) models for the S1 method is statistically significant at the 5% SL.

^{h}The difference between the Ghana-Italy (2017) models for the S2 method is statistically significant at the 5% SL.

^{i}The difference between the Alabama-Italy (2017) models for the S3 method is statistically significant at the 5% SL.

^{j}The difference between the Alabama-Italy (2012) models for the S4 method is statistically significant at the 5% SL.

S1 Segmentation Method | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

SPF Model | MAD | MBP | MAPE | χ_{p}^{2} | σ(χ_{p}^{2}) | Z−score | ||||||

Local CMFs | New Constant | Local CMFs | New Constant | Local CMFs | New Constant | Local CMFs | New Constant | Local CMFs | New Constant | Local CMFs | New Constant | |

HSM | 10.717 | 4.781 | 8.870 | −0.673 | 1.880 | 0.838 | 71.423 | 293.208 | 77.922 | 61.315 | −3.216 | −0.469 |

Virginia | 9.094 | 5.013 | 5.977 | −1.180 | 1.595 | 0.836 | 76.460 | 285.254 | 74.656 | 61.886 | −3.289 | −0.594 |

N. Carolina | 13.146 | 5.069 | 11.398 | −0.960 | 2.306 | 0.889 | 66.012 | 287.028 | 82.738 | 62.583 | −3.094 | −0.559 |

Alabama | 13.730 | 5.089 | 11.798 | 0.968 | 2.408 | 0.893 | 68.819 | 288.034 | 79.910 | 62.727 | −3.168 | −0.541 |

Ohio | 6.583 | 4.675 | 1.864 | −0.762 | 1.154 | 0.820 | 119.594 | 284.803 | 64.420 | 59.940 | −3.142 | −0.621 |

Italy (1) | 5.946 * | 4.670 ** | 0.630 * | −0.440 ** | 1.043 * | 0.819 ** | 179.548 | 309.559 | 62.083 | 60.756 | −2.295 * | −0.205 ** |

Italy (2) | 5.996 ** | 4.624 * | 1.060 ** | −0.269 * | 1.052 ** | 0.811 * | 166.785 | 312.470 | 63.543 | 61.340 | −2.443 ** | −0.155 * |

Netherlands | 6.604 | 5.363 | 1.243 | −0.930 | 1.158 | 0.940 | 70.159 | 290.670 | 76.888 | 62.895 | −3.275 | −0.498 |

Czech Rep. | 11.708 | 4.902 | 9.965 | −0.837 | 2.053 | 0.860 | 68.558 | 286.699 | 80.092 | 61.657 | −3.164 | −0.573 |

Korea | 22.356 | 4.832 | 22.118 | −0.749 | 3.921 | 0.848 | 60.885 | 289.918 | 90.667 | 61.422 | −2.880 | −0.522 |

Ghana | 7.868 | 5.533 | 2.352 | −0.811 | 1.380 | 0.970 | 122.362 | 348.290 | 71.650 | 66.895 | −2.786 | 0.393 |

S2 Segmentation Method | ||||||||||||

HSM | 12.885 | 9.601 | 4.530 | −1.182 | 1.011 | 0.753 | 26.560 | 93.582 | 44.837 | 44.837 | −1.972 | −0.595 |

Virginia | 12.567 | 9.945 | 1.120 | −1.993 | 1.986 | 0.780 | 27.613 | 90.811 | 43.261 | 43.261 | −2.020 | −0.668 |

N. Carolina | 15.858 | 10.161 | 7.607 | −2.369 | 1.244 | 0.797 | 24.716 | 90.754 | 47.986 | 47.986 | −1.881 | −0.664 |

Alabama | 12.462 | 9.762 | −3.685 | −1.576 | 0.977 | 0.766 | 36.286 | 91.967 | 42.048 | 42.048 | −1.872 | −0.639 |

Ohio | 10.993 | 9.400 | −3.708 | −1.463 | 0.862 | 0.737 | 37.252 | 89.532 | 40.610 | 40.610 | −1.997 | −0.727 |

Italy (1) | 10.689 ** | 9.382 ** | −5.238 ** | −0.389 ** | 0.838 ** | 0.736 ** | 60.680 | 96.620 | 36.662 | 36.662 | −1.482 * | −0.510 ** |

Italy (2) | 10.581 * | 9.270 * | −4.721 * | 0.163 * | 0.830 * | 0.727 * | 58.974 | 98.557 | 36.878 | 36.878 | −1.519 ** | −0.455 * |

Netherlands | 11.458 | 10.648 | −5.871 | −2.915 | 0.899 | 0.835 | 53.716 | 90.094 | 38.844 | 38.844 | −1.578 | −0.714 |

Czech Rep. | 13.701 | 9.782 | 4.802 | −2.036 | 1.075 | 0.767 | 25.797 | 90.919 | 45.812 | 45.812 | −1.947 | −0.666 |

Korea | 22.514 | 9.708 | 20.253 | −1.450 | 1.766 | 0.761 | 23.369 | 92.521 | 52.135 | 52.135 | −1.758 | −0.624 |

Ghana | 11.992 | 11.458 | −7.473 | −3.459 | 0.941 | 0.899 | 47.923 | 93.439 | 36.719 | 36.719 | −1.826 | −0.604 |

S3 Segmentation Method | ||||||||||||

HSM | 15.037 | 7.992 | 10.566 | −2.162 | 1.450 | 0.770 | 37.719 | 149.175 | 59.196 | 45.636 | −2.353 | −0.610 |

Virginia | 13.547 | 8.252 | 6.379 | −2.605 | 1.306 | 0.796 | 39.276 | 144.694 | 56.894 | 45.965 | −2.421 | −0.703 |

N. Carolina | 18.660 | 8.394 | 14.137 | −2.964 | 1.799 | 0.809 | 35.295 | 151.525 | 62.883 | 46.432 | −2.253 | −0.549 |

Alabama | 13.714 | 9.175 | 3.676 | −2.963 | 1.322 | 0.885 | 43.441 | 144.405 | 58.054 | 46.634 | −2.301 | −0.699 |

Ohio | 10.445 | 7.882 | 1.615 | −2.301 | 1.007 | 0.760 | 54.672 | 144.180 | 49.097 | 44.680 | −2.492 | −0.735 |

Italy (1) | 9.585 ** | 7.773 ** | −1.259 ** | −1.826 ** | 0.924 ** | 0.749 ** | 75.859 | 158.888 | 47.636 | 45.643 | −2.123 * | −0.397 ** |

Italy (2) | 9.572 * | 7.678 * | −0.629 * | −1.402 * | 0.923 * | 0.740 * | 73.503 | 159.278 | 48.061 | 45.722 | −2.153 ** | −0.388 * |

Netherlands | 10.501 | 8.858 | −2.072 | −2.926 | 1.012 | 0.854 | 66.624 | 157.078 | 52.324 | 48.321 | −2.193 | −0.412 |

Czech Rep. | 16.198 | 8.209 | 11.288 | −2.591 | 1.562 | 0.791 | 36.637 | 145.992 | 60.583 | 46.005 | −2.317 | −0.674 |

Korea | 30.188 | 8.071 | 29.581 | −2.313 | 2.910 | 0.778 | 29.039 | 147.401 | 68.488 | 45.691 | −2.160 | −0.648 |

Ghana | 10.501 | 9.773 | 11.288 | −2.738 | 1.059 | 0.942 | 71.171 | 117.476 | 48.486 | 78.527 | −2.183 | −0.758 |

S4 Segmentation Method | ||||||||||||

HSM | 13.659 | 7.493 | 10.242 | −0.668 | 1.443 | 0.792 | 43.319 | 163.096 | 59.548 | 48.158 | −2.530 | −0.642 |

Virginia | 12.099 | 7.771 | 6.285 | −1.213 | 1.278 | 0.821 | 45.698 | 155.991 | 57.180 | 48.196 | −2.594 | −0.789 |

N. Carolina | 16.968 | 7.951 | 13.562 | −1.454 | 1.793 | 0.840 | 40.068 | 153.741 | 63.209 | 48.439 | −2.435 | −0.831 |

Alabama | 12.681 | 8.063 | 4.928 | −2.228 | 1.340 | 0.852 | 46.082 | 164.059 | 58.077 | 49.858 | −2.547 | −0.601 |

Ohio | 9.405 | 7.436 | 0.924 | −0.890 | 0.994 | 0.776 | 72.072 | 158.497 | 49.672 | 46.845 | −2.455 | −0.758 |

Italy (2012) | 8.748 ** | 7.347 ** | −0.880 ** | −0.130 * | 0.924 ** | 0.776 ** | 109.561 | 169.772 | 49.178 | 48.355 | −1.717 * | −0.501 ** |

Italy (2017) | 8.720 * | 7.263 * | −0.282 * | 0.256 ** | 0.921 * | 0.767 * | 105.363 | 171.620 | 49.583 | 48.547 | −1.788 ** | −0.461 * |

Netherlands | 9.599 | 8.346 | −1.636 | −1.751 | 1.014 | 0.882 | 92.172 | 162.146 | 50.914 | 49.777 | −2.000 | −0.640 |

Czech Rep. | 14.739 | 7.667 | 11.063 | −1.213 | 1.557 | 0.810 | 41.700 | 156.258 | 60.910 | 48.108 | −2.500 | −0.785 |

Korea | 28.439 | 7.572 | 28.126 | −0.850 | 3.005 | 0.800 | 37.504 | 160.706 | 69.064 | 48.130 | −2.266 | −0.690 |

Ghana | 10.024 | 8.566 | −1.453 | −2.065 | 1.059 | 0.905 | 96.587 | 124.462 | 53.758 | 52.720 | −1.812 | −1.319 |

**Table 11.**The Calibration factors estimates using the locally derived CMFs with “fixed” and “variable” over-dispersion parameters.

Model | Segmentation S1 | Segmentation S2 | Segmentation S3 | Segmentation S4 | ||||
---|---|---|---|---|---|---|---|---|

Fixed k | Variable k | Fixed k | Variable k | Fixed k | Variable k | Fixed k | Variable k | |

HSM | 0.391 (0.081) * | 0.391 (0.081) | 0.738 (0.289) | 0.738 (0.266) | 0.495 (0.176) | 0.495 (0.128) | 0.480 (0.151) | 0.480 (0.117) |

Virginia | 0.488 (0.096) | 0.488 (0.096) | 0.919 (0.346) | 0.919 (0.270) | 0.619 (0.210) | 0.619 (0.152) | 0.601 (0.181) | 0.601 (0.139) |

N. Carolina | 0.333 (0.073) | 0.333 (0.073) | 0.626 (0.265) | 0.626 (0.204) | 0.423 (0.164) | 0.423 (0.116) | 0.411 (0.138) | 0.411 (0.106) |

Alabama | 0.326 (0.069) | 0.326 (0.069) | 1.406 (0.516) | 1.406 (0.370) | 0.738 (0.284) | 0.738 (0.178) | 0.658 (0.201) | 0.658 (0.148) |

Ohio | 0.754 (0.125) | 0.754 (0.125) | 1.410 (0.446) | 1.410 (0.365) | 0.944 (0.271) | 0.944 (0.199) | 0.920 (0.235) | 0.920 (0.182) |

Italy (2012) | 0.901 (0.143) | 0.901 (0.143) | 1.697 (0.526) | 1.697 (0.417) | 1.138 (0.315) | 1.138 (0.234) | 1.103 (0.278) | 1.103 (0.212) |

Italy (2017) | 0.843 (0.138) | 0.843 (0.138) | 1.588 (0.496) | 1.588 (0.343) | 1.065 (0.298) | 1.065 (0.221) | 1.031 (0.263) | 1.031 (0.201) |

Netherlands | 0.959 (0.166) | 0.959 (0.166) | 1.854 (0.616) | 1.854 (0.480) | 1.250 (0.369) | 1.250 (0.272) | 1.209 (0.318) | 1.209 (0.247) |

Czech Rep. | 0.364 (0.077) | 0.364 (0.077) | 0.727 (0.292) | 0.727 (0.226) | 0.479 (0.174) | 0.479 (0.126) | 0.461 (0.149) | 0.461 (0.114) |

Korea | 0.205 (0.050) | 0.205 (0.050) | 0.386 (0.179) | 0.386 (0.139) | 0.260 (0.108) | 0.260 (0.078) | 0.252 (0.093) | 0.252 (0.072) |

Ghana | 0.708 (0.133) | 0.708 (0.133) | 2.413 (0.871) | 2.413 (0.675) | 1.323 (0.426) | 1.323 (0.317) | 1.181 (0.331) | 1.181 (0.255) |

**Table 12.**The Calibration estimates after recalibrating the constant with “fixed” and “variable” over-dispersion parameters.

Model | Segmentation S1 | Segmentation S2 | Segmentation S3 | Segmentation S4 | ||||
---|---|---|---|---|---|---|---|---|

Fixed k | Variable k | Fixed k | Variable k | Fixed k | Variable k | Fixed k | Variable k | |

HSM | 1.134 (0.177) * | 1.134 (0.177) | 1.102 (0.334) | 1.102 (0.263) | 1.263 (0.332) | 1.263 (0.253) | 1.076 (0.265) | 1.076 (0.201) |

Virginia | 1.184 (0.187) | 1.184 (0.187) | 1.185 (0.362) | 1.185 (0.285) | 1.335 (0.354) | 1.335 (0.270) | 1.147 (0.282) | 1.147 (0.216) |

N. Carolina | 1.202 (0.193) | 1.202 (0.193) | 1.228 (0.379) | 1.228 (0.299) | 1.400 (0.375) | 1.4 (0.288) | 1.181 (0.138) | 1.181 (0.226) |

Alabama | 1.204 (0.194) | 1.204 (0.194) | 1.141 (0.346) | 1.141 (0.273) | 1.400 (0.416) | 1.4 (0.327) | 1.308 (0.335) | 1.308 (0.261) |

Ohio | 1.154 (0.176) | 1.154 (0.176) | 1.130 (0.331) | 1.130 (0.262) | 1.285 (0.329) | 1.285 (0.251) | 1.104 (0.263) | 1.104 (0.201) |

Italy (2012) | 1.084 (0.168) | 1.084 (0.168) | 1.031 (0.313) | 1.031 (0.247) | 1.214 (0.319) | 1.214 (0.243) | 1.014 (0.251) | 1.014 (0.190) |

Italy (2017) | 1.050 (0.164) | 1.050 (0.164) | 0.987 (0.300) | 0.987 (0.206) | 1.156 (0.304) | 1.156 (0.232) | 0.974 (0.242) | 0.974 (0.183) |

Netherlands | 1.195 (0.201) | 1.195 (0.201) | 1.296 (0.418) | 1.296 (0.330) | 1.393 (0.392) | 1.393 (0.300) | 1.227 (0.314) | 1.227 (0.245) |

Czech Rep. | 1.172 (0.184) | 1.172 (0.184) | 1.190 (0.363) | 1.190 (0.285) | 1.333 (0.353) | 1.333 (0.271) | 1. 147 (0.282) | 1.147 (0.215) |

Korea | 1.157 (0.180) | 1.157 (0.180) | 1.128 (0.342) | 1.128 (0.270) | 1.287 (0.338) | 1.287 (0.259) | 1.099 (0.270) | 1.099 (0.206) |

Ghana | 1.166 (0.202) | 1.166 (0.202) | 1.372 (0.495) | 1.372 (0.384) | 1.359 (0.429) | 1.359 (0.336) | 1.279 (0.350) | 1.279 (0.279) |

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**MDPI and ACS Style**

Elagamy, S.R.; El-Badawy, S.M.; Shwaly, S.A.; Zidan, Z.M.; Shahdah, U.E.
Segmentation Effect on the Transferability of International Safety Performance Functions for Rural Roads in Egypt. *Safety* **2020**, *6*, 43.
https://doi.org/10.3390/safety6030043

**AMA Style**

Elagamy SR, El-Badawy SM, Shwaly SA, Zidan ZM, Shahdah UE.
Segmentation Effect on the Transferability of International Safety Performance Functions for Rural Roads in Egypt. *Safety*. 2020; 6(3):43.
https://doi.org/10.3390/safety6030043

**Chicago/Turabian Style**

Elagamy, Sania Reyad, Sherif M. El-Badawy, Sayed A. Shwaly, Zaki M. Zidan, and Usama Elrawy Shahdah.
2020. "Segmentation Effect on the Transferability of International Safety Performance Functions for Rural Roads in Egypt" *Safety* 6, no. 3: 43.
https://doi.org/10.3390/safety6030043