Table 6 Bivariable and multivariable inverse-Weibull gamma shared frailty model on predictors of age at first birth among reproductive-age women in Ethiopia, EDHS, 2016

Log-likelihood

− 1036.84

5907.45

Effect size

Gave

Not gave

CHR

AHR

Region

 Most urban

474

568

1

1

 Northern

3224

1603

1.08 (1.01–1.18)**

1.08 (0.97–1.19)

 Oromia

4130

1552

1.07 (0.98–1.18)*

1.18 (1.06–1.30)***

 SNNP

2192

1090

0.98 (0.90–1.18)

1.19 (1.06–1.33)***

 Eastern

424

161

1.00 (0.92–1.09)

1.16 (105–1.28)***

 Western

144

60

1.12 (1.03–1.22)**

1.37 (1.24–1.52)***

Residence

 Urban

1769

1678

1

1

 Rural

8818

3357

0.96 (0.91–1.02)

1.09 (0.98–1.19)

Education

 No education

6785

684

1

1

 Primary

2865

2610

1.72 (1.64–1.82)***

1.12 (1.05–1.19)

 Secondary

593

1209

0.83 (0.76–0.87)***

0.86 (0.78–0.96)***

 Higher

344

524

0.72 (0.65-.80)***

0.75 (0.65–0.85)***

Occupation

 Not working

5243

2556

1.18 (1.13–1.24)***

0.98 (0.92–1.04)

 Agriculture

2522

726

0.98 (0.93–1.04)

0.94 (0.88–1.02)

 Nonagriculture

2822

1754

1

1

Wealth index

 Poorest

2060

570

1

1

 Poorer

2122

681

1.03 (0.96–1.10)

0.98 (0.91–1.05)

 Middle

2128

840

1.12 (1.05–1.21)***

1.00 (0.93–1.09)

 Richer

2089

1001

1.12 (1.05–1.21)***

1.10 (1.01–1.19)*

 Richest

2190

1941

1.12 (1.05–1.21)***

1.08 (0.97–1.15)

Spousal age diffe

 < 5 years

2984

342

1

1

 ≥ 5 years

6366

501

1.26 (1.21–1.33)***

1.11 (1.05–1.16)***

Contraceptive

 Ever not use

4617

4278

1

1

 Ever use

5970

757

0.50 (0.48–0.52)***

0.91 (0.86–0.97)***

Media exposure

 No

8342

3166

1

1

 Yes

2245

1870

1.10 (1.04–1.15)***

1.01 (0.94–1.08)

Age at first marriage

 < 15 years

2915

129

9.10 (8.83–9.86)***

1.26 (0.87–1.82)

 15–17 years

3890

366

3.47 (3.30–3.64)***

2.33 (2.08–2.63)***

 ≥ 18 years

3689

611

1

1

Age at first sex

 < 15 years

2860

167

1.89 (1.78–1.99)***

27.78 (23.26–32.26)***

 15—17 years

4576

486

0.68 (0.65–0.71)***

2.60 (2.07–2.63)***

 ≥ 18 years

3151

4395

1

1

Husband education

 No Edu-

4516

234

1

1

 Primary

3454

311

0.99 (0.94–104)

1.03 (0.97–1.09)

 Secondary

808

163

0.88 (0.81–0.95)***

1.05 (0.96–1.15)

 Higher

573

134

0.68 (0.63–0.74)***

1.03 (0.93–1.14)

Husband occupation

 Not working

740

62

1.14 (1.05–1.23)***

0.98 (0.91–1.o6)

 Agriculture

5930

393

1.13 (1.08–1.19)***

0.96 (0.91–1.02)

 Non agriculture

2681

397

1

1

Religion

 Orthodox

4371

2391

1

1

 Muslim

3593

1288

1.02 (0.97–108)

1.10 (1.03–1.19)***

 protestant

2367

1295

0.99 (0.92–1.05)

1.01 (0.92–1.10)

 Others

255

75

0.90 (0.77–1.06)

1.03 (0.87–1.22)

> 18intercourse and marriage

1

< 15marriege < 15 intercourse

1.32 (0.62–2.89)

< 15 marriage 15-17intercourse

0.86 (0.62–1.23)

15–17 intercourse < 15marriage

4.55 (2.13–10.02)***

15–17 intercourse 15–17 marriage

2.63 (2.01–3.45)***

Theta

0.05 (0.04–0.06)

0.025 (0.016–0.039)***

MHR

1.24 (1.21–1.27)

1.16 (1.13–1.20)***

LR test of theta = 0

 Chibar2(1)

126.23

35.40

 Prob-hibar2

 < 0.001

 < 0.001