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Modelling road traffic safety indices by means of regression with panel data

Katarzyna Brzozowska-Rup
Katarzyna Brzozowska-Rup
 and 
Marzena Nowakowska
Marzena Nowakowska
   | Dec 31, 2020
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Published Online: Dec 31, 2020
Page range: 40 - 51
Received: Jul 30, 2020
Accepted: Dec 01, 2020
DOI: https://doi.org/10.2478/emj-2020-0026
Keywords
© 2020 Katarzyna Brzozowska-Rup et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Fig. 1

The dynamics of road traffic accidents (left) and the accident fatalities (right) per voivodeship in Poland in 2012–2018Source: authors’ own elaboration
The dynamics of road traffic accidents (left) and the accident fatalities (right) per voivodeship in Poland in 2012–2018Source: authors’ own elaboration

Fig. 2

Illustration of the goodness of fit for the panel data models for the variables: RA100 (a), RAF100 (b), RAI100 (c)Source: authors’ own elaboration
Illustration of the goodness of fit for the panel data models for the variables: RA100 (a), RAF100 (b), RAI100 (c)Source: authors’ own elaboration

Fig. 3

Illustration of the goodness of fit for the panel data models for the variables: RA100 (a), RAF100 (b), RAI100 (c)Source: authors’ own elaboration
Illustration of the goodness of fit for the panel data models for the variables: RA100 (a), RAF100 (b), RAI100 (c)Source: authors’ own elaboration

i, tindices denoting the object (subject, group, unit, section element) i = 1, ..., N, and time period t = 1, ... T, respectively;
α,structural parameters (constant coefficients)
βas in the classic multiple linear regression model, the β vector (vector of slopes) determines the effect of the exogenous variables Xk on the endogenous variable Y;
xkitthe k-th explanatory variable;
Kthe number of exogenous variables;
μiindividual effect resulting from the observation belonging to the i-th group also referred to as group effect;
θttime-specific effect;
vitthe random component of the model, vit∼IID(0,σv2){v_{it}}\sim IID(0,\sigma _v^2)

Characteristics of Polish public road categories

Road categoryRoad classRoad ownerRoad manager (administrator)
National roadsMotorway, expressway, main road of accelerated trafficThe TreasuryGeneral Director of National Roads and Motorways, Concessionaire
Voivodeship roadsMain road of accelerated traffic, main roadVoivodeship self-governmentVoivodeship Board
County roadsMain road of accelerated traffic, main road, collector roadCounty self-governmentCounty Board
Communal roadsMain road of accelerated traffic, main road, collector road, local road, local access roadCommunal self-governmentHead of the Commune (Mayor, Mayor of the City)

Estimation results of the panel data models for the three road traffic safety measures (endogenous variables)

Model nameRA100KMRAF100KMRAI100KM
F test DF(15,85)F = 49.55 (p-value = 0.00)F = 5.91 (p-value = 0.00)F = 43.04 (p-value = 0.00)
B-P testAsymptotic Chi-2 = 161.05 (p-value = 0.00)Asymptotic Chi-2 = 19.56 (p-value = 0.00)Asymptotic Chi-2 = 134.94 (p-value = 0.00)
Hausman testAsymptotic Chi-2 = 47.25 (p-value = 0.00)Asymptotic Chi-2 = 39.61 (p-value = 0.00)Asymptotic Chi-2 = 61.85 (p-value = 0.00)
Panel data model estimation results
Mcodel typeFull*Backward selectionFull*Backward selectionFull*Backward selection
Exogenous variableEstimator (p value)Estimator (p value)Estimator (p value)Estimator (p value)Estimator (p value)Estimator (p value)
Intercept3.89 (0.74)4.28 (0.00)0.1 (0.95)0.49 (0.00)6.54 (0.76)16.94 (0.00)
GDPPC−0.05 (0.32)−0.01 (0.43)−0.01 (0.01)−0.05 (0.36)
RUI−19.97 (0.16)−14.90 (0.00)1.51 (0.59)1.04 (0.00)−27.46 (0.28)−14.45 (0.00)
CMR−0.01 (0.32)−0.01 (0.05)0 (0.59)−0.02 (0.45)−0.04 (0.00)
TMR0.20 (0.00)0.11 (0.00)0.01 (0.38)0.005 (0.00)0.26 (0.04)0.20 (0.00)
MMR0.01 (0.97)0.02 (0.39)0.01 (0.00)−0.03 (0.84)
DCR−0.22 (0.66)−0.02 (0.79)−0.65 (0.25)
RLPC136.40 (0.49)−47.93 (0.05)−53.82 (0.00)296.18 (0.36)
SGTERK0.03 (0.01)0.02 (0.00)0 (0.47)0.03 (0.00)0.03 (0.00)
GDICERK0 (0.65)0 (0.35)0.00004 (0.02)0 (0.09)
GDRRERK0 (0.88)0 (0.89)0 (0.66)
GDCRMERK0 (0.71)0 (0.26)−0.002 (0.02)−0.01 (0.67)
CS16.51 (0.00)4.63 (0.00)−0.11 (0.62)−0.19 (0.00)9.64 (0.01)6.80 (0.00)
CS20.03 (0.99)−0.24 (0.40)−0.28 (0.00)0.50 (0.88)
CS3−3.22 (0.36)−1.73 (0.00)0.08 (0.88)−4.38 (0.37)−1.81 (0.00)
CS41.44 (0.52)1.41 (0.00)−0.26 (0.25)−0.31 (0.00)3.32 (0.31)3.02 (0.00)
CS55.82 (0.00)5.14 (0.00)−0.15 (0.35)−0.20 (0.00)8.14 (0.00)7.46 (0.00)
CS62.54 (0.35)2.83 (0.00)−0.07 (0.88)−0.19 (0.00)3.35 (0.40)3.41 (0.00)
CS71.35 (0.63)1.09 (0.00)0.18 (0.68)2.00 (0.66)3.65 (0.00)
CS8−0.70 (0.88)−0.22 (0.76)−0.30 (0.00)−0.06 (0.99)
CS9−0.94 (0.71)0.01 (0.98)−1.60 (0.66)−1.61 (0.00)
CS107.72 (0.00)6.96 (0.00)−0.25 (0.13)−0.34 (0.00)10.92 (0.00)8.86 (0.00)
CS1112.33 (0.00)9.19 (0.00)−0.35 (0.38)−0.42 (0.00)17.02 (0.01)11.09 (0.00)
CS12−6.48 (0.06)−2.74 (0.00)0.05 (0.93)−9.03 (0.09)−4.66 (0.00)
CS133.33 (0.20)3.45 (0.00)−0.07 (0.80)−0.11 (0.00)4.57 (0.19)3.58 (0.00)
CS14−2.01 (0.38)−1.05 (0.00)−0.19 (0.60)−0.25 (0.00)−2.19 (0.50)
CS153.52 (0.10)3.09 (0.00)−0.35 (0.17)−0.35 (0.00)5.10 (0.14)2.89 (0.00)
Year 20122.80 (0.15)2.71 (0.00)0.15 (0.48)0.16 (0.00)3.25 (0.34)0.51 (0.02)
Year 20132.29 (0.18)2.25 (0.00)0.13 (0.53)0.13 (0.00)2.59 (0.38)0.34 (0.01)
Year 20141.72 (0.25)1.75 (0.00)0.11 (0.55)0.11 (0.00)1.83 (0.48)
Year 20151.32 (0.25)1.34 (0.00)0.04 (0.77)0.05 (0.03)1.39 (0.48)
Year 20161.33 (0.09)1.36 (0.00)0.04 (0.73)0.04 (0.05)1.59 (0.23)0.65 (0.00)
Year 20170.73 (0.10)0.71 (0.00)−0.01 (0.84)0.95 (0.19)0.40 (0.00)
Adjusted R20.97400.97440.77590.79600.97270.9732
AIC133.633124.946−329.891−346.322194.218184.226
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