Table 5 The results of random coefficient with auto covariate predictor NB regression model

Intercept

1.404

4.072

0.436

13.13

0.000

3.300

20.070

Age(15–19)(Ref.)

20–24

0.021

1.021

0.018

1.220

0.223

0.987

1.056

25–29

0.078

1.081

0.020

4.240

0.000

1.043

1.121

30–34

0.116

1.122

0.023

5.750

0.000

1.079

1.168

35–39

0.209

1.232

0.025

10.110

0.000

1.183

1.283

40–44

0.265

1.303

0.029

11.780

0.000

1.247

1.362

45–49

0.281

1.323

0.032

11.690

0.000

1.263

1.388

Place(urban)(Ref.)

Rural

0.057

1.058

0.029

2.070

0.039

1.003

1.116

Region(Tigray)(Ref.)

Afar

-0.052

0.949

0.065

-0.760

0.446

0.830

1.086

Amhara

-0.181

0.834

0.023

-6.430

0.000

0.790

0.887

Oromia

-0.268

0.766

0.023

-9.090

0.000

0.722

0.810

Somali

0.543

1.722

0.071

13.100

0.000

1.587

1.868

Benishan

-0.011

0.989

0.058

-0.180

0.855

0.882

1.109

SNNPR

-0.094

0.911

0.029

-2.960

0.003

0.856

0.969

Gambela

-0.084

0.920

0.020

-0.770

0.440

0.743

1.136

Harari

-0.201

0.818

0.103

-1.590

0.112

0.640

1.048

Addis Ababa

-0.190

0.827

0.037

-4.220

0.000

0.758

0.903

Dire Daw

0.060

1.062

0.088

0.730

0.468

0.903

1.249

Sex of Household head(male)(Ref.)

Female

0.006

1.006

0.019

0.330

0.738

1.045

1.055

Women Work(No)(Ref.)

Yes

-0.023

0.978

0.013

-1.690

0.091

0.952

1.004

Wealth index(poorest)(Ref.)

Poorer

0.001

1.000

0.019

0.020

0.982

0.963

1.038

Middle

-0.027

0.973

0.019

-1.390

0.164

0.937

1.011

Richer

-0.021

0.979

0.020

-1.040

0.298

0.941

1.019

Richest

-0.003

0.997

0.026

-0.130

0.894

0.947

1.049

Women’s Education( No education)(Ref.)

Primary

-0.067

0.935

0.014

-4.540

0.000

0.908

0.963

Secondary

-0.114

0.892

0.027

3.770

0.000

0.840

0.946

Higher

-0.109

0.897

0.035

2.810

0.005

0.831

0.968

Marital(single)(Ref.)

Married

0.082

1.086

0.059

1.500

0.133

1.208

1.086

Separated

0.045

1.046

0.022

2.130

0.033

1.004

1.090

Family size

0.040

1.041

0.013

3.160

0.002

1 0.015

1.068

Religion(orthodox)(Ref.)

Catholic

-0.117

0.890

0.070

-1.480

0.140

0.762

1.039

Protestant

0.057

1.059

0.022

2.770

0.006

1.017

1.103

Muslim

0.089

1.093

0.020

4.870

0.000

1.055

1.133

Traditional

0.091

1.096

0.076

1.310

0.189

0.956

1.256

Other

0.312

1.366

0.084

5.040

0.000

1.210

1.541

Contraception(Not using)(Ref.)

Using

-0.083

0.920

0.012

-6.350

0.000

0.897

0.944

Husband’s work(No)(Ref.)

Yes

-0.001

0.999

0.022

-0.060

0.950

0.956

1.043

Don’t know

0.0146606

1.015

0.069

0.220

0.829

0.888

1.159

Age at first birth (yrs)

-0.011

0.989

0.002

6.380

0.000

0.985

0.992

spatial auto covariate (Si)

0.035

1.035

0.027

1.320

0.007

1.003

1.090

Family size

-0.007

0.993

0.004

-1.670

0.004

0.984

0.998

α

2.760

-2.760

0.003

-2.903

-2.616

Zone

Variance

Rate ratio Std Dev.

95%confidenc interval

\({{\delta }}_{\text{u}0}^{2}\) (_cons)

0.004

0.004

0.002

0.0014

0.012

\({{\delta }}_{\text{u}1}^{2}\) (Family size)

0.0002

0.0002

0.00007

0.0001

0.0004