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  • Appendix C. Safety Effectsof Lane-Width and Shoulder-Width Combinations on Rural, Two-Lane Roads (Additional Modeling Results)
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Publication Number:  FHWA-HRT-14-020    Date:  January 2015
Publication Number: FHWA-HRT-14-020
Date: January 2015

 

Factors Influencing Operating Speeds and Safety on Rural and Suburban Roads

Appendix C. Safety Effects of Lane-Width and Shoulder-Width Combinations on Rural, Two-Lane Roads (Additional Modeling Results)

Table 107. Negative binomial regression model estimation results for property damage only crashes (all severities).

Variable

Coefficient

Standard Error

z

P > z

95-Percent Confidence Interval

ln_aadt

0.649

0.061

10.700

< 0.001

0.530

0.768

illinois

1.195

0.108

11.080

< 0.001

0.984

1.407

Lane10

1.047

0.227

4.610

< 0.001

0.602

1.493

Lane11

0.431

0.166

2.610

0.009

0.107

0.756

shoulder

-0.052

0.024

-2.140

0.032

-0.100

-0.004

ln10shld

-0.119

0.060

-1.980

0.048

-0.238

-0.001

ln11shld

-0.037

0.032

-1.160

0.246

-0.099

0.025

barrier

4.346

1.807

2.400

0.016

0.804

7.889

drvwy_den

0.016

0.007

2.340

0.019

0.003

0.029

solid_CL

0.563

0.215

2.620

0.009

0.143

0.984

dash1_CL

0.992

0.334

2.970

0.003

0.338

1.646

curve

0.253

0.076

3.340

0.001

0.105

0.402

_cons

-5.401

0.486

-11.120

< 0.001

-6.352

-4.449

ln(Length)

1

(exposure)

/lnalpha

-0.86727

0.117387

-1.09734

-0.63719

alpha

0.420098

0.049314

0.333757

0.528774

Log likelihood = -1473.751
Number of Observations = 877
LR chi2(12) = 425.44
Prob > chi2 = 0
Pseudo R2 = 0.1261
Likelihood-ratio test of alpha=0: chibar2(01) = 254.30 Prob>=chibar2 = 0.000
— Indicates Not Available

Table 108. Negative binomial regression model estimation results for single-vehicle crashes
(all severities).

sv_all

Coefficient

Standard Error

z

P > z

95-percent Confidence Interval

ln_aadt

0.514

0.059

8.67

< 0.001

0.398

0.631

illinois

1.128

0.103

10.9

< 0.001

0.925

1.331

Lane10

0.896

0.219

4.08

< 0.001

0.466

1.326

Lane11

0.413

0.160

2.58

0.010

0.099

0.727

shoulder

-0.064

0.024

-2.71

0.007

-0.111

-0.018

ln10shld

-0.090

0.058

-1.56

0.120

-0.202

0.023

ln11shld

-0.030

0.031

-0.99

0.323

-0.091

0.030

barrier

3.597

1.760

2.04

0.041

0.147

7.046

drvwy_den

0.017

0.007

2.630

0.009

0.004

0.030

solid_CL

0.478

0.208

2.300

0.022

0.070

0.886

dash1_CL

0.923

0.324

2.850

0.004

0.288

1.559

curve

0.246

0.074

3.330

0.001

0.101

0.391

_cons

-4.174

0.469

-8.890

< 0.001

-5.094

-3.254

ln(Length)

1

(exposure)

/lnalpha

-0.94318

0.120937

-1.180212

-0.7061473

alpha

0.389388

0.047092

0.3072135

0.493542

Log likelihood = -1493.2046
Number of Observations = 877
LR chi2(12) = 408.55
Prob > chi2 = 0
Pseudo R2 = 0.1203
Likelihood-ratio test of alpha=0: chibar2(01) = 229.65 Prob>=chibar2 = 0.000
— Indicates Not Available

Table 109. Negative binomial regression model estimation results for multiple-vehicle crashes (all severities).

mv_all

Coefficient

Standard Error

z

P > z

95-Percent Confidence Interval

ln_aadt

1.482

0.110

13.430

< 0.001

1.266

1.698

illinois

0.628

0.171

3.680

< 0.001

0.294

0.962

Lane10

0.769

0.470

1.640

0.102

-0.153

1.690

Lane11

0.199

0.306

0.650

0.515

-0.400

0.798

shoulder

0.007

0.040

0.160

0.872

-0.073

0.086

ln10shld

-0.223

0.132

-1.690

0.092

-0.481

0.036

ln11shld

-0.006

0.053

-0.110

0.910

-0.110

0.098

barrier

5.690

2.653

2.150

0.032

0.491

10.889

drvwy_den

-0.002

0.012

-0.160

0.875

-0.024

0.021

solid_CL

0.422

0.343

1.230

0.218

-0.250

1.094

dash1_CL

0.641

0.542

1.180

0.237

-0.421

1.703

curve

-0.013

0.126

-0.100

0.921

-0.259

0.234

_cons

-13.401

0.909

-14.750

< 0.001

-15.182

-11.620

ln(Length)

1

(exposure)

/lnalpha

-1.1353

0.372991

-1.866348

-0.4042488

alpha

0.321326

0.119852

0.1546876

0.667478

Log likelihood = -649.6117
Number of Observations = 877
LR chi2(12) = 213.52
Prob > chi2 = 0
Pseudo R2 = 0.1411
Likelihood-ratio test of alpha=0: chibar2(01) = 12.89 Prob>=chibar2 = 0.000
— Indicates Not Available

Table 110. Negative binomial regression model estimation results for key lane width/shoulder width crashes (all severities).

key_kabco

Coefficient

Standard Error

z

P > z

95-Percent Confidence Interval

ln_aadt

0.606

0.059

10.27

< 0.001

0.490

0.721

illinois

1.083

0.099

10.98

< 0.001

0.890

1.277

Lane10

0.903

0.223

4.04

< 0.001

0.465

1.341

Lane11

0.519

0.161

3.23

0.001

0.205

0.834

shoulder

-0.052

0.023

-2.26

0.024

-0.097

-0.007

ln10shld

-0.076

0.056

-1.37

0.172

-0.185

0.033

ln11shld

-0.060

0.030

-1.97

0.049

-0.119

0.000

barrier

4.305

1.888

2.28

0.023

0.604

8.006

drvwy_den

0.012

0.007

1.88

0.060

-0.001

0.025

solid_CL

0.471

0.209

2.26

0.024

0.062

0.880

dash1_CL

0.800

0.323

2.47

0.013

0.166

1.433

curve

0.231

0.074

3.14

0.002

0.087

0.376

_cons

-4.613

0.466

-9.9

<0.001

-5.527

-3.700

ln(Length)

1

(exposure)

/lnalpha

-0.72081

0.102919

-0.92253

-0.5191

alpha

0.486356

0.050055

0.397512

0.595057

Log likelihood = -1684.8577
Number of Observations = 877
LR chi2(12) = 395.990
Prob > chi2 = 0.000
Pseudo R2 = 0.105
Likelihood-ratio test of alpha=0: chibar2(01) = 395.21 Prob>=chibar2 = 0.000
— Indicates Not Available

Table 111. Negative binomial regression model estimation results for single-vehicle crashes (fatal-plus-injury).

sv_fi

Coefficient

Standard. Error

z

P > z

95-Percent Confidence Interval

ln_aadt

0.562

0.112

5.01

< 0.001

0.342

0.783

illinois

0.427

0.189

2.26

0.024

0.057

0.798

Lane10

-0.035

0.428

-0.08

0.935

-0.874

0.804

Lane11

0.193

0.305

0.63

0.528

-0.406

0.791

shoulder

-0.116

0.045

-2.58

0.010

-0.203

-0.028

ln10shld

0.063

0.106

0.6

0.551

-0.144

0.271

ln11shld

-0.023

0.061

-0.39

0.699

-0.142

0.095

barrier

0.576

3.244

0.18

0.859

-5.783

6.934

drvwy_den

0.007

0.013

0.590

0.553

-0.017

0.032

solid_CL

0.530

0.369

1.440

0.151

-0.194

1.253

dash1_CL

0.345

0.615

0.560

0.575

-0.860

1.550

curve

0.081

0.141

0.580

0.563

-0.194

0.357

_cons

-5.385

0.882

-6.100

<0.001

-7.114

-3.656

ln(Length)

1

(exposure)

/lnalpha

-1.10368

0.491638

-2.06727

-0.1400852

alpha

0.331649

0.163051

0.1265307

0.8692842

Log likelihood = -579.36383
Number of Observations = 877
LR chi2(12) = 64.28
Prob > chi2 = 0
Pseudo R2 = 0.0526
Likelihood-ratio test of alpha=0: chibar2(01) = 6.35 Prob>=chibar2 = 0.006
— Indicates Not Available

Table 112. Negative binomial regression model estimation results for multiple-vehicle crashes (fatal-plus-injury).

mv_fi

Coefficient

Standard Error

z

P > z

95-percent Confidence Interval

ln_aadt

1.142

0.162

7.060

< 0.001

0.825

1.459

illinois

0.557

0.248

2.240

0.025

0.071

1.043

Lane10

0.427

0.992

0.430

0.667

-1.517

2.371

Lane11

0.762

0.481

1.580

0.114

-0.182

1.705

shoulder

0.146

0.059

2.470

0.013

0.030

0.262

ln10shld

-0.185

0.219

-0.840

0.398

-0.613

0.244

ln11shld

-0.100

0.078

-1.290

0.196

-0.252

0.052

barrier

5.476

4.069

1.350

0.178

-2.498

13.450

drvwy_den

-0.011

0.019

-0.570

0.570

-0.048

0.026

solid_CL

0.129

0.559

0.230

0.817

-0.966

1.225

dash1_CL

0.533

0.836

0.640

0.524

-1.106

2.173

curve

0.126

0.186

0.680

0.498

-0.238

0.490

_cons

-12.279

1.343

-9.140

<0.001

-14.911

-9.646

ln(Length)

1

(exposure)

/lnalpha

-1.18079

0.886305

-2.917915

0.5563366

alpha

0.307036

0.272128

0.0540463

1.744271

Log likelihood = -374.64352
Number of Observations = 877
LR chi2(12) = 79.46
Prob > chi2 = 0
Pseudo R2 = 0.0959
Likelihood-ratio test of alpha=0: chibar2(01) = 1.73 Prob>=chibar2 = 0.094
— Indicates Not Available

Table 113. Negative binomial regression model estimation results for key lane-width/shoulder-width crashes (fatal-plus-injury).

key_kabc

Coefficient

Standard Error

z

P > z

95-Percent Confidence Interval

ln_aadt

0.598

0.114

5.27

< 0.001

0.376

0.821

illinois

0.523

0.180

2.9

0.004

0.170

0.875

Lane10

0.080

0.458

0.17

0.862

-0.819

0.978

Lane11

0.552

0.319

1.73

0.084

-0.073

1.178

shoulder

-0.070

0.044

-1.6

0.109

-0.155

0.015

ln10shld

0.068

0.105

0.65

0.518

-0.138

0.274

ln11shld

-0.093

0.060

-1.55

0.121

-0.211

0.025

barrier

0.314

3.738

0.08

0.933

-7.014

7.641

drvwy_den

0.009

0.013

0.67

0.501

-0.017

0.034

solid_CL

0.288

0.397

0.72

0.469

-0.490

1.066

dash1_CL

0.416

0.629

0.66

0.508

-0.815

1.648

curve

0.034

0.147

0.23

0.818

-0.255

0.322

_cons

-5.392

0.888

-6.07

<0.001

-7.132

-3.651

ln(Length)

1

(exposure)

/lnalpha

0.481668

0.153744

 

0.180335

0.783001

alpha

1.618773

0.248877

1.197619

2.18803

Log likelihood = -817.20472
Number of Observations = 877
LR chi2(12) = 66
Prob > chi2 = 0.0000
Pseudo R2 = 0.0388
Likelihood-ratio test of alpha=0: chibar2(01) = 144.74 Prob>=chibar2 = 0.000
— Indicates Not Available

Table 114. Negative binomial regression model estimation results for single-vehicle crashes (PDO).

sv_o

Coefficient

Standard Error

z

P > z

95-Percent Confidence Interval

ln_aadt

0.515

0.065

7.9

< 0.001

0.387

0.643

illinois

1.307

0.117

11.17

< 0.001

1.077

1.536

Lane10

1.029

0.240

4.3

< 0.001

0.560

1.499

Lane11

0.427

0.175

2.44

0.015

0.083

0.770

shoulder

-0.054

0.026

-2.04

0.041

-0.105

-0.002

ln10shld

-0.113

0.064

-1.77

0.077

-0.238

0.012

ln11shld

-0.031

0.034

-0.9

0.370

-0.097

0.036

barrier

4.386

1.928

2.27

0.023

0.606

8.166

drvwy_den

0.018

0.007

2.490

0.013

0.004

0.032

solid_CL

0.499

0.230

2.170

0.030

0.048

0.951

dash1_CL

1.031

0.356

2.900

0.004

0.333

1.728

curve

0.288

0.081

3.570

<0.001

0.130

0.447

_cons

-4.589

0.519

-8.840

<0.001

-5.606

-3.572

ln(Length)

1

(exposure)

/lnalpha

-0.76859

0.121186

-1.006113

-0.5310743

alpha

0.463665

0.05619

0.3656375

0.587973

Log likelihood = -1390.4041
Number of Observations = 877
LR chi2(12) = 397.58
Prob > chi2 = 0
Pseudo R2 = 0.1251
Likelihood-ratio test of alpha=0: chibar2(01) = 239.28 Prob>=chibar2 = 0.000
— Indicates Not Available

Table 115. Negative binomial regression model estimation results for multiple-vehicle crashes (PDO).

mv_o

Coefficient

Standard Error

z

P > z

95-Percent Confidence Interval

ln_aadt

1.727

0.144

12.010

< 0.001

1.445

2.009

illinois

0.671

0.222

3.020

0.003

0.236

1.105

Lane10

0.686

0.542

1.270

0.206

-0.376

1.749

Lane11

-0.198

0.383

-0.520

0.605

-0.948

0.552

shoulder

-0.095

0.052

-1.810

0.071

-0.197

0.008

ln10shld

-0.186

0.167

-1.120

0.264

-0.514

0.141

ln11shld

0.068

0.070

0.980

0.329

-0.069

0.205

barrier

5.742

3.298

1.740

0.082

-0.722

12.207

drvwy_den

0.004

0.014

0.290

0.775

-0.024

0.032

solid_CL

0.568

0.420

1.350

0.176

-0.254

1.391

dash1_CL

0.653

0.682

0.960

0.338

-0.684

1.991

curve

-0.096

0.161

-0.590

0.552

-0.412

0.220

_cons

-15.436

1.179

-13.090

<0.001

-17.747

-13.124

ln(Length)

1

(exposure)

/lnalpha

-0.79447

0.433001

-1.643133

0.0542011

alpha

0.451823

0.19564

0.1933733

1.055697

Log likelihood = -469.42118
Number of Observations = 877
LR chi2(12) = 178.04
Prob > chi2 = 0
Pseudo R2 = 0.1594
Likelihood-ratio test of alpha=0: chibar2(01) = 9.54 Prob>=chibar2 = 0.001
— Indicates Not Available

Table 116. Negative binomial regression model estimation results for key lane-width/shoulder-width crashes (PDO).

key_o

Coefficient

Standard Error

z

P > z

95-Percent Confidence Interval

ln_aadt

0.615

0.066

9.37

< 0.001

0.486

0.743

illinois

1.276

0.113

11.25

< 0.001

1.054

1.498

Lane10

1.059

0.245

4.33

< 0.001

0.579

1.539

Lane11

0.494

0.177

2.8

0.005

0.148

0.841

shoulder

-0.046

0.026

-1.8

0.072

-0.097

0.004

ln10shld

-0.104

0.063

-1.67

0.096

-0.227

0.018

ln11shld

-0.049

0.034

-1.45

0.147

-0.115

0.017

barrier

5.253

2.057

2.55

0.011

1.221

9.286

drvwy_den

0.013

0.007

1.85

0.065

-0.001

0.028

solid_CL

0.544

0.232

2.35

0.019

0.090

0.999

dash1_CL

0.913

0.358

2.55

0.011

0.211

1.614

curve

0.292

0.081

3.6

< 0.001

0.133

0.451

_cons

-5.167

0.523

-9.88

< 0.001

-6.192

-4.141

ln(Length)

1

(exposure)

/lnalpha

-0.5778

0.107196

-0.7879

-0.3677

alpha

0.561129

0.060151

0.454797

0.692322

Log likelihood = -1524.6018
Number of Observations = 877
LR chi2(12) = 391.03
Prob > chi2 = 0
Pseudo R2 = 0.1137
Likelihood-ratio test of alpha=0: chibar2(01) = 363.82 Prob>=chibar2 = 0.000
— Indicates Not Available

Table 117. Multinomial logit model estimation results for total crashes (all types and severities)—base outcome: PDO.

Severity

Variable

Coefficient

Standard Error

z

P > z

95-Percent Confidence Interval

0

(base outcome)

1

ln_aadt

0.103

0.190

0.540

0.588

-0.270

0.476

illinois

-2.615

0.301

-8.700

0.000

-3.205

-2.026

Lane10

-0.993

0.914

-1.090

0.277

-2.784

0.797

Lane11

-0.125

0.546

-0.230

0.819

-1.195

0.945

shoulder

-0.079

0.071

-1.110

0.267

-0.218

0.060

ln10shld

0.216

0.173

1.250

0.211

-0.123

0.555

ln11shld

0.023

0.088

0.260

0.797

-0.150

0.195

barrier

-5.154

7.644

-0.670

0.500

-20.137

9.829

drvway_den

-0.008

0.025

-0.330

0.739

-0.058

0.041

solid_CL

-0.905

0.767

-1.180

0.238

-2.409

0.599

dash1_CL

0.857

1.031

0.830

0.406

-1.163

2.877

curve

-0.377

0.237

-1.590

0.111

-0.842

0.087

_cons

-1.450

1.448

-1.000

0.316

-4.288

1.387

2

ln_aadt

0.038

0.134

0.280

0.780

-0.226

0.301

illinois

-0.007

0.257

-0.030

0.980

-0.511

0.498

Lane10

-1.107

0.630

-1.760

0.079

-2.341

0.127

Lane11

-0.172

0.368

-0.470

0.641

-0.893

0.550

shoulder

0.082

0.053

1.540

0.124

-0.023

0.186

ln10shld

0.133

0.152

0.880

0.380

-0.164

0.431

ln11shld

-0.032

0.070

-0.450

0.650

-0.170

0.106

barrier

1.097

4.403

0.250

0.803

-7.532

9.726

drvway_den

-0.022

0.017

-1.300

0.192

-0.054

0.011

solid_CL

-0.331

0.495

-0.670

0.504

-1.301

0.639

dash1_CL

-0.595

0.771

-0.770

0.441

-2.107

0.917

curve

-0.218

0.168

-1.300

0.194

-0.547

0.111

_cons

-2.529

1.099

-2.300

0.021

-4.683

-0.375

3

ln_aadt

0.257

0.168

1.530

0.126

-0.073

0.587

illinois

0.613

0.393

1.560

0.119

-0.157

1.383

Lane10

-0.057

0.693

-0.080

0.934

-1.416

1.302

Lane11

0.443

0.481

0.920

0.357

-0.500

1.386

shoulder

0.085

0.073

1.160

0.248

-0.059

0.229

ln10shld

-0.069

0.215

-0.320

0.747

-0.491

0.352

ln11shld

-0.097

0.096

-1.010

0.312

-0.284

0.091

barrier

-1.734

5.888

-0.290

0.768

-13.273

9.806

drvway_den

-0.022

0.019

-1.130

0.258

-0.060

0.016

solid_CL

0.884

0.485

1.820

0.068

-0.067

1.836

dash1_CL

-1.950

1.012

-1.930

0.054

-3.934

0.034

curve

0.179

0.205

0.870

0.382

-0.222

0.580

_cons

-5.679

1.441

-3.940

0.000

-8.503

-2.855

4

ln_aadt

0.228

0.351

0.650

0.516

-0.460

0.917

illinois

-0.130

0.700

-0.190

0.853

-1.501

1.242

Lane10

1.177

1.687

0.700

0.485

-2.129

4.484

Lane11

1.441

1.082

1.330

0.183

-0.681

3.562

shoulder

0.207

0.156

1.320

0.186

-0.099

0.513

ln10shld

-0.671

0.962

-0.700

0.486

-2.557

1.216

ln11shld

-0.211

0.189

-1.110

0.265

-0.581

0.160

barrier

-3.203

12.442

-0.260

0.797

-27.589

21.183

drvway_den

-0.054

0.050

-1.090

0.276

-0.152

0.043

solid_CL

0.672

1.006

0.670

0.504

-1.300

2.644

dash1_CL

0.528

1.968

0.270

0.788

-3.330

4.386

curve

0.403

0.425

0.950

0.343

-0.430

1.236

_cons

-7.442

3.027

-2.460

0.014

-13.376

-1.508

Log likelihood = -1543.1747
Number of observation = 2397
LR chi2(48) = 198.440
Prob > chi2 = 0.000
Pseudo R2 = 0.060
— Indicates Not Available

Table 118. Multinomial logit model estimation results for fatal-plus-injury crashes (all types)—base outcome: possible injury.

severity_rev

Variable

Coefficient

Standard Error

z

P > z

95-Percent Confidence Interval

1

(base outcome)

2

ln_aadt

-0.273

0.231

-1.180

0.237

-0.726

0.180

illinois

2.531

0.388

6.530

<0.001

1.771

3.290

Lane10

0.011

1.163

0.010

0.992

-2.267

2.290

Lane11

0.044

0.689

0.060

0.949

-1.305

1.394

shoulder

0.163

0.091

1.780

0.075

-0.016

0.342

ln10shld

-0.191

0.250

-0.770

0.444

-0.682

0.299

ln11shld

-0.063

0.118

-0.530

0.594

-0.294

0.168

barrier

10.549

9.177

1.150

0.250

-7.438

28.537

drvway_den

-0.006

0.031

-0.200

0.840

-0.067

0.054

solid_CL

0.618

0.866

0.710

0.475

-1.079

2.316

dash1_CL

-1.659

1.326

-1.250

0.211

-4.258

0.940

curve

0.147

0.304

0.490

0.627

-0.448

0.742

_cons

0.604

1.785

0.340

0.735

-2.895

4.103

3

ln_aadt

-0.057

0.263

-0.220

0.829

-0.572

0.459

illinois

3.230

0.505

6.400

<0.001

2.240

4.220

Lane10

1.030

1.226

0.840

0.401

-1.372

3.432

Lane11

0.758

0.781

0.970

0.332

-0.773

2.289

shoulder

0.184

0.111

1.660

0.096

-0.033

0.401

ln10shld

-0.389

0.299

-1.300

0.192

-0.974

0.196

ln11shld

-0.155

0.141

-1.100

0.273

-0.432

0.122

barrier

7.135

10.398

0.690

0.493

-13.245

27.514

drvway_den

-0.005

0.033

-0.150

0.884

-0.069

0.059

solid_CL

1.739

0.882

1.970

0.049

0.010

3.468

dash1_CL

-3.028

1.529

-1.980

0.048

-6.025

-0.030

curve

0.542

0.336

1.610

0.107

-0.116

1.199

_cons

-2.654

2.127

-1.250

0.212

-6.823

1.515

4

ln_aadt

-0.047

0.406

-0.120

0.907

-0.843

0.748

illinois

2.492

0.779

3.200

0.001

0.966

4.017

Lane10

2.603

2.183

1.190

0.233

-1.676

6.882

Lane11

1.840

1.247

1.480

0.140

-0.604

4.284

shoulder

0.310

0.178

1.740

0.082

-0.039

0.660

ln10shld

-1.145

1.307

-0.880

0.381

-3.707

1.417

ln11shld

-0.289

0.217

-1.330

0.183

-0.715

0.137

barrier

4.281

15.898

0.270

0.788

-26.879

35.442

drvway_den

-0.041

0.057

-0.720

0.472

-0.152

0.070

solid_CL

1.370

1.227

1.120

0.264

-1.035

3.775

dash1_CL

-0.305

2.244

-0.140

0.892

-4.702

4.092

curve

0.757

0.496

1.530

0.127

-0.216

1.730

_cons

-4.744

3.408

-1.390

0.164

-11.423

1.936

Log likelihood = -464.69741
Number of Observations = 426
LR chi2(36) = 112.18
Prob > chi2 = 0
Pseudo R2 = 0.1077
— Indicates Not Available

 

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