Socioeconomic, Demographic, and Environmental Associated with Stunting among Children under Five Years old in Ethiopia: Evidence from Ethiopian Demographic and Health Survey, 2016

DOI: https://doi.org/10.21203/rs.3.rs-16521/v1

Abstract

Background : Stunting is one of the most serious but least addressed health problems in the world. Adequate nutrition is essential for children’s health and development. Globally it is estimated that, directly or indirectly, for at least 35% of deaths in children less than five years of age. Under nutrition is also a major cause of disability preventing children who survive from reaching their full development potential. Methods: Statistical models that can treat the categorical response variable like binary logistic regression model will be employed. Beside this study will include Socio –economic and demographic factors; Sex and age of child, age of mother, Educational status, occupation, health status, religion, sex of household head, number of children under five years, Household income, family size, land ownership and time of cultivation, income source of household, wealth index as independent variables. Empty model, random intercept and fixed slope with random coefficient are the method of analyzing the dataset. Result: The prevalence of stunting among children ages under five years old were about 49.3%. Months of breastfeeding, educational level, and wealth index, currently pregnant and child food nutrient are significantly associated with stunting presence. The odds of stunting status of child from women who are pregnant is more likely to be stunted 4.157 compared to non-pregnant women controlling for other variables in the model and random effects at level two. Women who feed nutrient food to their child are 1.239 more likely to be stunted (OR=1.239) than women who didn’t feed nutrient food controlling for other variables in the model and random effects at level two. Conclusions : Age of child, breast feeding, sex, pregnant status, and food nutrient were found to be significantly associated with stunting in multilevel modeling of random coefficient model. Finally random coefficient model best fit the EDHS 2016 dataset. Therefore, interventions that focus on breast feeding, period of next pregnancy, food nutrient taken by children are required for improving child stunting in Ethiopia.

1. Background

Globally, an estimated 171 million children are stunted, including 167 million children in low- and middle-income countries (Black et al. 2013). Globally, the percentage of children under age 5 who are stunted has decreased, from 40% in 1990 to 28% in 2010, with an anticipated further drop to 22% (142 million) by 2020 [1]. In Africa, however, prevalence of stunting among children under age 5 was 36% compared with 27% in Asia, estimated in 2011. It is projected that by 2020, Asia and Africa will have almost similar numbers of stunted children (68 million and 60 million, respectively). These levels are much higher than the number of children stunted in Latin America, at 7 million in 2010 [2].

The higher prevalence of child stunting in Africa and Asia is a public health problem that has often gone unrecognized. Child stunting reflects a failure to receive adequate nutrition over a long period of time and may be affected by intrauterine growth retardation, poor feeding practices, and frequent exposure to infections [3]. When stunting spans generations, it results in grave consequences that include poor quality of life, morbidity, and mortality [4,5]. The 2014 Demographic and Health Surveys (DHS surveys) for Kenya and Cambodia showed that the prevalence of stunting among children under age 5 was 22% and 25% respectively. The prevalence of stunting in children under age 5 in Kenya and Cambodia was higher, at 32% and 26% respectively [6]. Researchers have found that poverty, poor health and nutrition, and social factors are associated with risks to child growth. These factors have prevented over 200 million children in developing countries from attaining their full potential [7]. In developing countries, where mostly women are denied a voice in household decisions, they are most likely to be undernourished themselves and less likely to have access to resources that can be directed toward children’s nutrition [8].

In Ethiopia 40% of children under age five were stunted and 18% of children were severely stunted with regional variation such as in South Nation Nationality Peoples 44.3%, Afar 49.2%, Tigray 44.4%, Amhara National Region State 42.4% children under five were stunted [9]. Stunting is affected by many factors such as: poverty, low parental education, lack of sanitation, low food intake, poor feeding practices, inadequate breastfeeding, repeated infections, family size and birth interval [5].

Stunting remains one of the most common causes of morbidity and mortality among children throughout the world. It has been responsible, directly or indirectly, for 60% of the 10.9 million deaths annually among children under five. Over two-thirds of these deaths, which are often associated with inappropriate feeding practices, occur during the first year of life. Malnutrition is one of the leading causes of morbidity and mortality in children under the age of five in developing countries. Ethiopia being one of these countries malnutrition is an important public health problem. There is no information available on the stated problem. This study is, therefore, aimed at assessing associated factors of stunting children under five years old.

The general objective of this study is to empirically investigate the major factors that are associated with stunting among children below five years old in Ethiopia. The specific objectives of the study is to determine the prevalence of stunting among the children aged below five years, to determine the socio-demographic and economic characteristics of households of children aged below five years and to estimate the within-regional and between-regional level of difference for the incidence of stunting among under five-children in Ethiopia.

2. Methods

(see Methods in the Supplementary Files)

3. Results

3.1 Descriptive Statistics

This research utilized the national wide Ethiopia Demographic and Health Survey (EDHS) 2016 collected data on the stunting of children. The analysis presented in the study is based on 11654 under-five children with complete weight-for-age anthropometric index as indicator of a children’s stunting and health status among other indices, since it is an excellent overall indicator of a population’s stunting and health status. Table 2: below, shows that the percentage of the severity status of child’s stunting

As presented in Table 2, the prevalence of stunting found was at 48.74% were female, where males were 49.62%. It shows that 49.82% of urban children were stunted, 48.54% rural of children were stunted and 46.89% of children were stunted their family no education.51.67% of children were stunted their family were primary education, 65.28% of children were stunted their family education were secondary and 75.51% of children were stunted where their family were higher education.

As presented in Table 2, the prevalence of stunting found was 48.85% of children were stunted where their toilet was unsafe and 54.68% of children were stunted where their toilet was safe.40.17% of children were stunted where poorest and 69.90% of children were stunted where richest.

Table 2 shows 46.78% of children were stunted whether currently pregnant or not 68.30% of children were stunted where they were currently pregnant. And 52% of children were stunted where they were not used a soup. 47.26% of children were stunted that they used a soup and 49.28% of children were stunted that they were not found nutrients and 46.05% of children were stunted that they were found nutrients.

Figure1: shows that the Predicted Probability of under five children stunting by predictors vs Region. The Maximum predicted log-odds range is considered as regionally varied variables thus variable duration of breast feeding is regionally varied variables and have high random effects on under-five children stunting compare to the other variables. This variable is used in the random slope model.

3.2 Results of Multilevel Logistic Regression Analysis

In the multilevel analysis, a two-level structure is used with regions as the second-level units and under five children as the first level units. This is basically the analysis of region wise variation of stunting among under-five children. Children were nested in regions with a total of 5732 children included in this study.

3.2.1 Multilevel Logistic Regression Model Comparison

The Maximum predicted log-odds range is considered as regionally varied variables thus variable age and stunting are regionally varied variables and have high random effects on under-five children stunting morbidity compare to the other variables. These variables are used in the random slope model.

The deviance-based chi-square value for the empty model shown in the above Table 3: is the difference in log likelihoods between an empty model of single level logistic regression and empty model of multilevel logistic regression, which is to be compared with the critical value from the chi-squared distribution with 1 degree of freedom. The significance of this test implies that an empty model with random intercept is better than an empty model without random intercept. The significant deviance-based chi-square value and smallest AIC for random intercept model indicates that the random intercept and fixed slope model is a better fit as compared to the empty model. The deviance-based chi-square test of random effects for random coefficient model is not statistically significant and has larger AIC. This implies that as compared to the model with random intercept and fixed slope model, the random coefficients model is not a better fit. Thus, in the above Table 3: shows that among multilevel logistic regression models, the random intercept and fixed slope model fits significantly better than the other multilevel logistic regression models.

3.2.2 Results of Empty Multilevel Logistic Regression Model

The variance of the random factor is significant which indicates that there is regional variation in experiencing stunting among under-five children (Table 4).The intercept βO = -1.18546 is interpreted as the odds of stunting in an average region. That is the intercept informs us that the average probability of incidence of stunting everywhere in Ethiopia is exp (-1.18546) / [1+exp (-1.18546)] = 0.234. The intra-region correlation in intercept only model is 0.049 which is significant at 5% level of significance. This result implied that 4.9% of the variation in the incidence of stunting can be explained by grouping the under-five children in regions (higher level units). The remaining (100-4.9%=95.1% of the variation of incidence of stunting is explained within region-lower level units.

The variance of the regional level residuals errors, symbolized by is estimated to be 0. 140688. This parameter estimate is larger than the corresponding standard errors and calculation of the Z-test shows that it is significant at p<0. 025. The significance of this residual term indicates that there are regional differences in the women unemployment status in Ethiopia.   

The deviance-based Chi-square (deviance = 521.19) indicated in table below is the difference in deviance between an empty model without random effect (deviance = 15,764.71) and an empty model with random effect (deviance =15,243.52). This value is compared to chi-square distribution with 1 degree of freedom. The significant of it (X2 = 521.19, P-value < 0.0001) implies that an empty model with random intercept is better than an empty model without random intercept. The deviance reported in the above Table is a measure of model misfit; when we add explanatory variables to the model, the deviance is expected to go down.

3.2.3 Results of Random Intercept and Fixed Slope Logistic Regression Model

The random intercept and fixed slope logistic regression model is a multilevel model which has random intercept and fixed coefficient of predictors. As can be seen from Table 5: the analysis of multilevel logistic regression revealed that incidence of stunting in under-five children varied among regions. The value of  is the estimated variance of the intercept in random intercept and fixed coefficients model. The result displayed that the region-wise difference in the incidence of childhood stunting was statistically significant. In addition, age of child, maternal working status, duration of breastfeeding, stunting, wasting, and underweight were also found to be significant determinants of incidence of stunting among the regions.

The deviance-based Chi-square (deviance = 928.61) taken from single logistic regression analysis is the difference in deviance between the empty model with random intercept (deviance = 15,243.52) and fixed slope model with random intercept (deviance = 14,314.91). The significant of it (X2 =928.61, DF = 15, P-value < 0.0001) implies that fixed slope model with random intercept model is better than empty model with random intercept. Therefore, this model is a better fit as compared to the empty model with random intercept.  

Moreover, the AIC and BIC value for fixed slope model with random intercept (AIC=14,751.85, and BIC=14,762.01) are less than those for the empty model with random intercept (AIC = 15,247.52 and BIC = 15,248.31). This indicates that fixed slope model with random intercept is a better fit as compared to the empty model with random intercept model.

3.2.4 Results of Random Coefficient Multilevel Logistic Regression Model

Table 6: reveals the effect of the intercept on region j is estimated to be -1.4765 (0.3124) + U0j and their variance 0.024 (Standard error 0.070). The intercept variance of 0.024 (Standard error 0.070) is interpreted as the between-region variance when all other variables are held constant (i.e. equal to zero). Their mean is -1.4765 (standard error 0. 3124) and their variance is 0.024 (standard error 0.070). The between-region variance of slope of Breast feeding status is estimated to be 0.004 (standard error 0.002). Likewise individual region slopes of Breast feeding status vary about with a variance 0.004 (standard error 0.002). The negative covariance estimate of -0.001 (standard error 0.004) between intercept and slopes of Breast feeding status, suggest that regions with a high intercept (above-average) tends to have a flatter-than-average slope.

The quantities AIC and BIC can be used to make an overall comparison of this more complicated model with the random intercept model with fixed slope model. We see that from Table 6: the value of fit statistics for random coefficient model (AIC = 14720.79 and BIC = 14731.35) is less than random intercept model (AIC=14,751.85 and BIC=14,762.01. This indicates that the random coefficient model is a better fit as compared to the random intercept and fixed effect model. 

The odds of stunting of child’s from mothers who have still breast feeding were 0.601 (OR=0.601) times higher than the odds of stunting of child’s from mothers who never breasted controlling other variables in the model and random effects at level two. Women who live in rural households are 0.647 more likely to be stunted (OR=0.647) than women who reside in urban households controlling for other variables in the model and random effects at level two. The odds of stunting status of child from women who are pregnant is more likely to be stunted 4.157 compared to non-pregnant women controlling for other variables in the model and random effects at level two. Women who feed nutrient food to their child are 1.239 more likely to be stunted (OR=1.239) than women who didn’t feed nutrient food controlling for other variables in the model and random effects at level two.

3.3 Discussion

This study analysed the Ethiopian Demographic and Health Survey 2016 dataset, exploring the effect of underlying socioeconomic, demographic, and cultural factors on under-five mortalities in Ethiopia. Under-five children whose mothers had work were 27.8% more likely to experience stunting than under-five children whose mothers had not work. These findings contradict those found in Egypt where stunting was significantly higher among children having mothers not working. This might have the implication that mothers working status affect length of breastfeeding (yilak M. 2014).

The study revealed that incidence of stunting was significantly associated with durations of breastfeeding. Under-five children who had ever been breast fed but not currently were 44.8% less likely to experience stunting as compared to under-five children who were never breasted. Under-five children who are still breastfeeding were 36.4% less likely to experience stunting as compared to under-five children who never breast fed. This present findings is in agreement with a study done in Ghana which found that infants that were either fully breastfed or mixed-fed (fed both breast milk and other foods or liquids) had a lower incidence of stunting than non-breastfed infants [5]. This finding also had confirmed with a study done in Bangladesh which showed than infants who were partially or not breastfed had a high risk of stunting death than exclusively breastfed infants [7]. Not breastfeeding resulted in high exposure of stunting morbidity in comparison to exclusive breastfeeding among infants 0-5 months of age (RR: 10.52) [17] which is also consistent with our study. This might be due to the fact that breast feeding provides vitamins and nutrients that help children develop important antibodies that reduce stunting disease.

This study found that incidence of stunting was significantly associated with nutritional status of under-five children. The prevalence of stunting was higher in stunting under-five children. The odds of having stunting in chronic malnutrition under-five children were 22.6% higher as compared to under-five children who had no chronic malnutrition. This finding is supported by a study done in Zimbabwe and Bangladesh that showed severely stunted children were more likely to have stunting than children of normal height and which had not severe malnutrition [18].

Under-five children who were wasting (acute malnutrition) were 49.2% more likely to experience stunting than under-five children who were not wasted. This present findings is in agreement with a study done in Uganda, which showed that being wasted increases the probability of occurrence of stunting by 14% compared to well-nourished counterparts. The study revealed that incidence of stunting was significantly associated with underweight. Under-five children who were underweight (have low weight-for age) were 54.8% more likely to experience stunting than children who were not underweight. This is consistent with a study in Ghana which showed that stunting was significantly higher for those children who were underweight (yilak M. 2014).

The finding in this study is the identification of variable at the regional level that explains the variation in stunting between the regions of Ethiopia. There are no studies involving multilevel modeling of stunting in Ethiopia that included variables at higher levels. The present study also identified socio-economic indicators of the region as predictors of unemployment. This is the exposure of stunting in different regions of Ethiopia. According to the final model, this level-two variable explains all of the regional-level variation in stunting found in the data.

4. Conclusions

The purpose of this study has been to identify demographic, socio-economic, environmental and nutrition related determinants and to assess regional variation of incidence of childhood stunting in Ethiopia. The descriptive results showed that 15.6% of under-five children have experienced stunting in the two weeks prior to the time of survey (EDHS 2016).

In multilevel logistic regression analysis, under-five children are considered as nested within the various regions in Ethiopia. As a first step in the multilevel approach, non-parametric statistical methods were applied to see if there were differences in the prevalence of stunting in under-five children among the regions. The non-parametric approach based on the chi-square test suggests that prevalence of stunting in under-five children varies among regions. Among the three multilevel logistic regressions models, the random intercept and fixed coefficients model provided the best fit for the data under consideration. It showed that the prevalence of childhood stunting was varying among regions. The significant determinants of prevalence of stunting among regions were age of child, maternal working status, duration of breast fed, stunting, wasting, and underweight.

The main objective of this study is to empirically investigate the major factors that are associated with stunting among children below five years old in Ethiopia. Using the EDHS 2016 data and examines the change in risk factors associated with stunting across the different EDHS years. Age of child, breast feeding, sex, pregnant status, and food nutrient were found to be significantly associated with stunting.

The odds of stunting of child’s from mothers who have still breast feeding were 0.601 (OR=0.601) times higher than the odds of stunting of child’s from mothers who never breasted controlling other variables in the model and random effects at level two. Women who live in rural households are 0.647 more likely to be stunted (OR=0.647) than women who reside in urban households controlling for other variables in the model and random effects at level two. The odds of stunting status of child from women who are pregnant is more likely to be stunted 4.157 compared to non-pregnant women controlling for other variables in the model and random effects at level two. Women who feed nutrient food to their child are 1.239 more likely to be stunted (OR=1.239) than women who didn’t feed nutrient food controlling for other variables in the model and random effects at level two.

Abbreviations

CSA: Central Statistical Agency; DHS: Demographic Health Survey; SE: Standard Error; SNNPR: South Nations Nationalities of Peoples Region; UNICEF: United Nations International Children’s Emergency Fund; WHO: World Health Organization

Declarations

Ethics approval and consent to participate:

Ethics approval for this study was not required since the data is secondary and is available in the public domain.

Consent for publication:

Not applicable

Availability of data and materials:

The datasets used and/ or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests:

The authors declare that they have no competing interests.

Funding:

The authors have no support or funding to report.

Authors' contributions:

GB involved in the inception to design, analysis and interpretation and revises critically the manuscript and edit the manuscript for the final submission, YB involved from the inception to design, acquisition of data, analysis and interpretation, drafting the manuscript. Both authors read and approved the final manuscript.

Author details

1 Department of Statistics, College of Natural Sciences, Wollo University, Dessie, Ethiopia        

2 Department of Statistics, College of Natural and Computational Sciences, Salale University, Fiche, Ethiopia

Acknowledgments

The authors are grateful to ICF macro (Calverton, USA) for providing the 2016 DHS data of Ethiopia.

References

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Tables

Table 1: Variables in the Study

No.

Variable Description 

Code (If any)

  1.  

Breast feeding status

0=never breastfed;       1=inconsistent

  1.  

Sex of child

0=female;                   1=male

  1.  

Age of child

0->29 months;         1-<30 months

  1.  

Residence of child

0=urban;             1=rural

  1.  

Level of education of Mother

0=no education; 1=primary; 2=secondary   3=higher

  1.  

Use of toilet

0=unsafe;          1=safe

  1.  

Pregnant status 

0=no;                1=yes

  1.  

Food nutrient status 

0=no;                  1=yes

  1.  

 

Region

Addis Ababa = 0(ref), Tigray = 1, Afar = 2, Amhara = 3, 

Oromya = 4, Somali = 5, Benishangul-Gumuz = 6, SNNP = 7, Gambella = 8, Harari = 9, Dire Dawa = 10



Table 2: Descriptive Statistics of Variables

Characteristics 

Category 

Not Stunted 

 Stunted

Total

Count

%

Count

%

Count 

%

Sex of child

Female

2973

51.26

2827

48.74

5800

49.77

Male

2949

50.38

2905

49.62

5854

50.23

Residence

Urban

2933

50.18

2912

49.82

5845

50.15

Rural

2989

51.45

2820

48.54

5809

49.85

 

Educational level

No education

4324

53.10

3818

46.89

8142

69.86

Primary

1416

48.33

1514

51.67

2930

25.14

Secondary

134

34.72

252

65.28

386

3.31

Higher

48

24.49

148

75.51

196

1.68

Toilet

Not Safe

5610

51.14

5358

48.85

10968

5.87

Safe

310

45.32

374

54.68

684

5.87

Currently pregnant

No 

5509

53.22

4842

46.78

10351

88.82

Yes

413

31.70

890

68.30

1303

11.18

Child age in months

<29 months

648

32.63

1338

67.37

1986

17.04

> 30 months

5922

61.32

4394

45.46

9658

82.87

Months of breast feeding

 

Ever breastfed, not currently breastfed

754

62.72

448

37.27

1202

10.31

Never breastfed

591

69.45

260

30.55

851

7.30

Inconsistent

288

43.70

371

56.30

659

5.65

Food nutrient status

No

5711

50.72

5548

49.28

11259

96.61

Yes

205

66.56

175

46.05

380

3.26



 Table 3: Multilevel Logistic Regression Model for Stunting and their Deviance Based Chi-square Test Statistics.

 

Empty model

Random intercept model

Random coefficient model

-2*log likelihood 

7254.4834

6802.2541

6802.544

Deviance based chi-square test

84.1252

245.213

2.1569

P-value

0.0000*

0.0000*

0.6099

Model Fit Diagnostics

AIC

7295.012

6950.034

6972.0152

BIC

7312.187

7015.312

7096.182

*significant at 5% level



Table4: Results for Multilevel Logistic Regression Model without Explanatory Variables

Fixed part

Coefficients

S.E.

t-value

P-value

 

-1.18546

0.019

-62.4

0.000**

Random part                                                      

Estimate

S.E.

Z-value

P-value

 

0.140688

0.0235

5.987

0.011*

Rho (ρ)

0.048546

0.0204

2.38

0.025*

Deviance= 15,243.52,                                   AIC = 15,247.52,                        BIC = 15,248.31,  Deviance-based Chi-square = 521.19

**significant at 1% level,                               *significant at 5% level




Table 5: Results of Random Intercept and Fixed Coefficient Logistic Regression Model

Fixed part

Fixed effect

 

S.E.

Z-Value

p-value

Breast feeding status (Never breasted=ref.cat) 

Ever breasted, not currently

-.6010689   

.2131114

-2.82   

0.005*     

Still breast feeding

-.4555433  

.2165306    

-2.10   

0.035*

Sex of child (female =ref.cat)

Male

0.7458415   

0.14482

5.15

0.002*

Age of child (less than or equals to 29 months =ref.cat)

Greater than 29 months

0.2452757   

0.0639085     

3.84

0.000*

Residence of child (urban =ref.cat)

Rural 

0.2021277   

0.0778864     

2.60   

0.009*

Level of education of Mother (no education =ref.cat)

primary

0.4378549    

0.080129     

5.46

0.000*

secondary

0.5244647    

0.045434     

11.54

0.004*

Higher 

0.6000154    

0.064524     

9.30

0.001*

Use of toilet (unsafe =ref.cat)

Safe   

0.400427   

0.0910844     

4.40

0.000*

Pregnant status (no =ref.cat)

Yes

0.345115   

0.0542164     

6.37

0.005*

Food nutrient status (no =ref.cat)

Yes 

0.822101   

0.061005     

13.48

0.003*

Constant

-.8856897   

.2500704    

-3.54

0.000*

Random part   

Estimate

S.E.

Z-value

P-value

 

0.13432

0.06651

2.02

0.0217*

Intra-region correlation (rho) 

.0392259   

.0178844

2.1933

0.0141*

Deviance based chi-square

928.61

0.000*

Deviance =14,314.91,                                          AIC = 14,751.85,                       BIC = 14,762.01

*significant at 5% level, (ref) = reference category, ICC: Intra-region correlation 


Table 6: Results of Random Coefficient Multilevel Logistic Regression Model

Solutions for Fixed Effects

Odds Ratio Estimates  

Effect 

Level

Estimate 

S.E

DF

t-value

Pr>|t| 

Estimate

95% Confidence
 Limits

LCL

UCL

Intercept

 

-1.4765

0.3124

58

-4.73

<.0001*

.

.

.

Age of child

 

>29 months

0

.

.

.

.

.

.

.

<30 months

0.3513

0.1396

2797

2.52

0.0119*

0.219

0.164

0.293

 

 

Breast feeding status 

 

Never breasted

0

.

.

.

.

.

.

.

Ever breasted not currently

-0.0124

0.1282

2797

-0.10

0.9227

0.222

0.164

0.300

Still breast feeding

0.5095

0.1053

2797

4.84

<.0001*

0.601

0.489

0.739

Sex 

Female

0

.

.

.

.

.

.

.

Male

-0.4514

0.1722

2797

-2.62

0.0088*

1.388

0.283

0.533

Residence of child

Urban

0

.

.

.

.

.

.

.

Rural

0.4356

0.1277

2797

3.41

0.0007*

0.647

0.504

0.831

Level of education of Mother 

no education

0

.

.

.

.

.

.

.

Primary

0.01740

0.00668

2797

2.61

0.7451

1.033

1.004

1.031

Secondary

0.4950

0.1769

2797

2.80

0.2721

 1.117

0.431

0.862

Higher

0.7325

0.1449

2797

5.06

0.0862

1.223

0.984

1.634

Use of toilet

Unsafe

0

.

.

.

.

.

.

.

Safe

-2.3357

1.6853

2797

-1.39

0.1659

0.097

0.004

2.635

Pregnant status

No

0

.

.

.

.

.

.

.

Yes

1.4249

0.5159

2797

2.76

0.0058*

4.157

1.512

11.433

Food nutrient status

Yes

0

.

.

.

.

.

.

.

No 

-0.45

0.17

28

4.06 

0.0006* 

1.239

0.28

0.53

Random effect

B

S.E

Z-value

P- Value

 

Var(u0j) = σ2

 

0.070 

2.12

0.0255

 

Var(u2j) = σ22

0.004

0.002

2.42

0.0041

 

Cov(u0j, u2j)

-0.001 

0.004 

-2.34

0.0039

 

Deviance = 14281.85,                               AIC= 14720.79,                   BIC = 14731.35, 

Deviance based chi-square=25.11