Department of Statistics, Jahangirnagar University, Savar, Dhaka, -1342, Bangladesh

Department of Mathematics & Statistics, Bowling Green State University, Bowling Green, OH, 43402, USA

Probationary Senior Officer, Pubali Bank Ltd, Dhaka, Bangladesh

Department of Applied Statistics, University of Malaya, Kuala Lumpur, Malaysia

Department of Agricultural Statistics, Sher-e Bangla Nagar Agricultural University, Sher-e Bangla Nagar, Dhaka, -1207, Bangladesh

Department of Mathematical Sciences, Ball State University, Muncie, IN, 47306, USA

Department of Public Health Medicine, School of Public Health, University of Bielefeld, Bielefeld, Germany

Abstract

Background

Malnutrition is one of the principal causes of child mortality in developing countries including Bangladesh. According to our knowledge, most of the available studies, that addressed the issue of malnutrition among under-five children, considered the categorical (dichotomous/polychotomous) outcome variables and applied logistic regression (binary/multinomial) to find their predictors. In this study malnutrition variable (i.e. outcome) is defined as the number of under-five malnourished children in a family, which is a non-negative count variable. The purposes of the study are (i) to demonstrate the applicability of the generalized Poisson regression (GPR) model as an alternative of other statistical methods and (ii) to find some predictors of this outcome variable.

Methods

The data is extracted from the Bangladesh Demographic and Health Survey (BDHS) 2007. Briefly, this survey employs a nationally representative sample which is based on a two-stage stratified sample of households. A total of 4,460 under-five children is analysed using various statistical techniques namely Chi-square test and GPR model.

Results

The GPR model (as compared to the standard Poisson regression and negative Binomial regression) is found to be justified to study the above-mentioned outcome variable because of its under-dispersion (variance < mean) property**.** Our study also identify several significant predictors of the outcome variable namely mother’s education, father’s education, wealth index, sanitation status, source of drinking water, and total number of children ever born to a woman.

Conclusions

Consistencies of our findings in light of many other studies suggest that the GPR model is an ideal alternative of other statistical models to analyse the number of under-five malnourished children in a family. Strategies based on significant predictors may improve the nutritional status of children in Bangladesh.

Background

Malnutrition among children is a major public health problem in developing countries including Bangladesh

Malnutrition among children is a critical problem because its effects are long lasting and go beyond childhood. It has both short- and long-term consequences

Poverty is found to be strongly associated with child malnutrition

Most of the abovementioned studies, that addressed the topics of child malnutrition, used categorical outcome variables and applied logistic regression (multinomial/binary)

Methods

Data source

The data was extracted from the Bangladesh Demographic and Health Survey (BDHS) conducted in 2007. This survey employs a nationally representative sample which is based on a two-stage stratified sample of households. This type of survey generally provides information on basic national indicators of social development. The BDHS 2007 was a part of the global Demographic and Health Survey (DHS) programme

Dependent variable

Researchers can define nutritional status of children differently. The nutritional status of a child is typically based on several measurements namely height, weight, sex and age of the child. Three commonly used measures for nutritional status are height-for-age, weight-for-height and weight-for-age

Covariates/predictor variables

We consider several covariates (Table

**Predictors**

**n (%)**

**Mean**

**Predictors**

**n (%)**

**Mean**

Place of residence:

Sources of drinking water:

Urban

1590 (35.70)

Piped water

299 (6.70)

Rural

2870 (64.30)

Tube well water

3595 (80.60)

Mother’s education:

Others

566 (12.70)

No education

1136 (25.50)

Religion:

1-5 years education

1371 (30.70)

Islam

4050 (90.81)

6-10 years education

1566 (35.10)

Others

410 (9.19)

11+ years education

385 (8.60)

Access to media:

Father’s education:

Yes

919 (29.10)

No education

1437 (32.20)

No

3127 (70.10)

1-5 years education

1240 (27.80)

Wealth index:

6-10 years education

1184 (26.50)

Lowest quintile

849 (19.00)

11+ years education

594 (13.30)

Second quintile

901 (20.20)

Father’s occupation:

Middle quintile

835 (18.80)

Farmer

1118 (25.53

Fourth quintile

850 (19.00)

Worker

2003 (45.75)

Highest quintile

1025 (23.00)

Professional

201 (4.59)

Business

1056 (24.12)

Total number of children ever born to a woman

2.67

Toilet facility:

Total number of children dead in a family

0.24

Yes

3286 (74.00)

No

1153 (26.00)

GPR model

The generalized Poisson probability function of the number of malnourished children (

The mean and variance of _{
i
}| _{
i
}) = _{
i
} and _{
i
}| _{
i
}) = _{
i
}(1 + _{
i
})^{2}, where the mean of the dependent variable is related to the explanatory variables through the link function _{
i
} = _{
i
}(_{
i
}) = exp(_{
i
}
_{
i
} is a

For selecting the right type of Poisson regression model, it is necessary to check the existence of dispersion problem in the data. The moment estimators of the two parameters in the Poisson distribution given by Consul and Jain

And

Where □ and ^{2} are sample mean and variance respectively. The asymptotic variances of the moment estimators given by Shoukri

And

The adequacy of the GPR model over the PR model is assessed by setting the following hypothesis

Versus

This test of hypothesis determines whether the dispersion parameter is statistically different from zero. The rejection of _{0} recommends the use of the GPR model rather than the standard Poisson regression model. To perform the test, the asymptotically normal Wald type “Z” statistic defined as the ratio of the estimate of

The estimation of regression coefficients

Where

Statistical analysis

Simple summary statistics (either as percentage for the categorical variables or mean for the continuous variables) are shown for selected socioeconomic predictors (Table
_{0} : _{1}) is used which indicates that the value of the dispersion parameter is unequal to zero. Bivariate analyses (based on Pearson Chi-square test) are performed to examine association between dependent variable and each of the selected predictors (Table

**Characteristics**

**
χ
**

**
P
**

Place of residence

55.36^{*}

<0.001

Mother’s education

252.70^{*}

<0.001

Father’s education

241.91^{*}

<0.001

Father’s occupation

123.75^{*}

<0.001

Wealth index

253.21^{*}

<0.001

Sources of drinking water

34.45^{*}

<0.001

Toilet facility

47.48^{*}

<0.001

Religion

0.01

0.925

Access to media

14.49^{*}

<0.001

Total number of children ever-born to a woman

79.55^{*}

<0.001

Total number of children died in a family

30.78^{*}

<0.001

**Predictors**

**Categories**

**Estimated regression coefficient (ß)**

**
χ
**

**P-value**

**Estimated IRR**

**95% CI for IRR**

Notes: ^{(r)} indicates the reference group in each category.

*****

Place of residence:

Urban

0.06

0.44

0.507

1.07

0.88-1.28

Rural^{(r)}

Mother’s education:

No education

0.33*

7.01

0.008

1.39

1.09-1.78

1-5 years education

0.32*

6.81

0.009

1.37

1.08-1.74

6- 10 years education

0.22

3.00

0.083

1.24

0.97-1.59

11+ years education^{(r)}

Father’s education:

No education

0.29*

5.17

0.023

1.33

1.04-1.71

1-5 years education

0.26*

3.92

0.048

1.30

1.00-1.68

6- 10 years education

0.20

2.26

0.133

1.22

0.94-1.58

11+ years education^{(r)}

Father’s occupation:

Farmer

0.39

2.45

0.118

1.48

0.91-2.43

Worker

0.32

2.04

0.153

1.39

0.89-2.17

Professional

0.11

0.14

0.705

1.12

0.63-1.97

Business^{(r)}

Wealth index:

Lowest quintile

0.50*

22.90

<0.001

1.64

1.34-2.01

Second quintile

0.41*

10.38

0.001

1.50

1.17-1.93

Middle quintile

0.33*

12.46

<0.001

1.39

1.16-1.67

Fourth quintile

0.22*

4.46

0.035

1.25

1.02-1.53

Highest quintile^{(r)}

Sources of drinking water:

Piped water

−0.24

3.18

0.075

0.79

0.61-1.02

Tubewell water

−0.34*

16.48

<0.001

0.71

0.60-0.84

Others^{(r)}

Toilet facility:

No

0.36*

56.32

<0.001

1.43

1.30-1.56

Yes^{(r)}

Access to media:

No

0.08

1.41

0.235

1.08

0.95-1.22

Yes^{(r)}

Total number of children ever born to a woman

0.05*

11.04

0.001

1.06

1.02-1.09

Total number of children dead in a family

−0.03

0.16

0.688

0.97

0.83-1.13

Results

The estimated mean
_{
y
}
^{2} = 0.369) of the outcome variable reveal the under-dispersion property of the data. In the total sample, 16.9 percent of the under-five children are malnourished. Table

Table

The estimated value of the dispersion parameter (_{0} :

According to the results of GPR analysis (Table

Discussion

Our study demonstrates that the GPR model is an ideal alternative to study the malnutritional status of children defined as the number of under-five malnourished children in a family. This model is a good alternative because most of the results of this study are found to be consistent with the findings of many other studies

According to the GPR model, the malnutritional status of children is insignificant between rural and urban areas. This finding is both consistent

Many studies suggest that mother education is linked with child health outcomes. The relationship of maternal education with child malnutrition is more demonstrable than paternal education, health service availability, and socioeconomic status

The relationship between economic inequality and children nutritional status is investigated by many studies

Our finding reveals a strong positive association between number of children ever born to a woman and the number of under-five malnourished children in a family. These results are consistent with the findings of other study

In Bangladesh men are generally the main earner of a family, although employment opportunities are increasing for women due to the flourishing garment sectors. Income of the family is strongly associated with the type of father’s occupation. Normally fathers with more prestigious job have higher income than fathers with low level jobs and therefore children from the higher income families should have better nutritional status. However, this is not the case in our study. The insignificant association of father’s occupation with the nutritional status of children can be explained by the lack of proper nutritional knowledge and confounding effect of education of parents. Like father’s occupation, religion does not play any significant role in explaining the nutritional status of the under-five children in Bangladesh.

In our study factors namely source of drinking water and type of toilet also show significant association with child malnutrition. Similar results are reported by Pongou et al

This study has several strengths. The use of nationally representative data is one of the important strengths. Our findings could be reliable because of the large sample. Application of the GPR model as an alternative of other methods is another strength. Inclusion of right predictors into the model based on previous studies also increases the strength of the study. However, this study is not free from limitation. Firstly, all inherent limitations associated with the cross-sectional data are also true here. Another limitation of the study is that the model does not include regional and cultural variables, which are also reported as significant predictors

Conclusions

Our study demonstrates that the GPR model is an appropriate model to identify predictors affecting the nutritional status of children in Bangladesh. Father’s and mother’s education, wealth index, source of drinking water of the household, toilet facility, and total number of children ever born to a woman are significantly associated with child malnutrition in Bangladesh. Various strategies are reported by many studies

Competing interests

The authors have no competing interests arising from the publication of this article.

Authors’ contributions

MI, MA and MAK conceptualized the research topic together with MMHK and drafted the manuscript. MT mainly performed the data analysis. RP significantly contributed to the writing process and interpretation. MB revised the article critically and provided further inputs. MMHK finally structured the manuscript, collected the references and edited extensively before finalization. All authors read and approved the final manuscript.

Acknowledgements

We acknowledge support of the publication fee by Deutsche Forschungsgemeinschaft and the Open Access Publication Funds of Bielefeld University.

Pre-publication history

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