Determinants of Under-five Child Mortality in the East End of Freetown,Sierra Leone: A Hurdle Negative Binomial Modelling Approach

Abstract

Objective

To identify the main determinants of under-five child mortality in the eastern region of Sierra Leone’s capital using the most appropriate count regression modeling approach.

Introduction

Sierra Leone has seen rising under-five mortality, especially in densely populated areas like the eastern part of its capital. Understanding the main factors associated with such under-five mortality is vital for guiding healthcare policies and promoting appropriate interventions to reduce its risk.

Methods

In this research, 755 observations were randomly collected from the residents of the study area through interviews and questionnaires. This paper fitted several count models: Poisson and Generalized Poisson regressions, Zero-inflated Poisson regression, Negative binomial regression, and the Hurdle Negative Binomial regression. To compare the models based on how well they fit the count data at hand, this research used the Vuong non-nested test, the Akaike Information Criterion, the Bayesian Information Criterion, and a graphical method called the hanging rootogram.

Results

The hurdle negative binomial regression model is identified as the preferred model that best fits the data used in this study. The best-fitting model showed that the mother’s age, mosquito net use, family income, and child feeding practices are the main determinants.

Conclusion

This study revealed that a younger maternal age, a reduction in family income, a decline in both the frequency and quality of child feeding, and a decrease in the number of times a child sleeps under a mosquito net were each associated with a heightened risk of mortality among children under five in the study area.

Keywords

Africa child mortality Freetown regression risk Sierra Leone under-five mortality vuong non-nested test

Introduction

In Sierra Leone and across Africa, children play a dual role. They not only care for their parents in old age but also represent the future leaders of their communities.¹ Losing a child affects not just the parents but the whole country as well. Reference ². stated that the under-five mortality rate is a vital measure of a population’s health. It is closely linked to economic status and social well-being. Child and infant mortality are indicators of a nation’s healthcare system and its level of socio-economic development.³

Unfortunately, Sierra Leone continues to struggle with a high under-five mortality rate, which needs better policies to reduce it.⁴ Although under-five mortality rates have declined globally.⁵ many children in Sierra Leone still do not live past age five.

In Africa, as a whole, the infant and child mortality rates are 15 times higher than in high-income regions.⁶ Each year, about 8.8 million children under five die before reaching their fifth birthday.⁷

Like other developing countries in Africa, Sierra Leone has witnessed rising childhood mortality rates, especially in densely populated areas like the east end of the capital, which saw a population increase after the decade-long civil war. Due to the civil conflict (also called the rebel war), many people moved from rural areas to the capital seeking food and safety, and most decided to stay after the conflict.

Sierra Leone’s under-five child mortality rate stands at 122 per 1,000 live births, making it one of the highest in the world.⁸ Many children in Sierra Leone and across Africa die before they can explore their potential and dreams. Tragically, many of these deaths are from preventable or treatable causes. In Sierra Leone, treatable diseases such as malaria are significant contributors to deaths among children under five. The country faces one of the highest rates of malaria in the world.⁹

Due to the rising under-five mortality rates in the east end of the capital, the research aimed to identify the primary factors behind this issue (under-five child mortality). Potential factors included personal elements (such as the mother’s age) and socio-economic factors (like family income and maternal education).

The child’s feeding status, including frequency and quality, was also examined as a potential factor in under-five mortality in this area. Malnutrition among children under five in Sierra Leone is prevalent during the rainy season, as many families struggle to afford nutritious food. In low-income households, these children often eat more carbohydrates but have limited access to the essential nutrients required for healthy growth and immunity.¹⁰ This lack of nutrition can weaken immunity, making children more vulnerable to treatable diseases, ultimately leading to the deaths of many malnourished children.

The age of the mother was considered another possible factor in under-five mortality. Research indicates that children born to mothers aged 40 and older often have shorter lifespans compared to those born to mothers younger than 25 years.^11-14 Reference¹⁵ also discovered that children born to mothers under 25 or over 35 frequently have higher mortality rates.

The mother’s education level was seen as another potential influence on under-five child mortality. Greater education for women has led to increased awareness among mothers about health and hygiene for their young children, helping to reduce mortality rates for children under five.¹⁶ Studies show that a mother’s education level affects child mortality rates for those under five.¹⁷ However, a substantial decrease in mortality rates among children under five was particularly noted among those with mothers who had no formal education.¹⁶

Finally, family income level was also examined as a potential factor impacting under-five child mortality in the study area. Mortality rates among children under five tend to be higher in low-income households compared to wealthier ones in developing countries.¹⁸ Reference¹⁹. state that many deaths in children under five result from treatable or preventable diseases, especially in low- and middle-income countries.

Understanding the main factors associated with under-five mortality is vital for guiding healthcare policies, allocating resources effectively, and promoting appropriate interventions to reduce childhood mortality in this part of Sierra Leone. To achieve this, the research used count regression modeling, specifically a hurdle model, to identify the key factors contributing to under-five mortality and their effects on children living in the eastern part of Sierra Leone’s capital.

Data Descriptions

Study Area

This study was carried out in the eastern part of Sierra Leone’s capital city, Freetown. The eastern part of the capital city became overpopulated during the past Sierra Leone’s civil war (commonly referred to as Sierra Leone’s Rebel War). This is as a result of people moving from the provinces to the capital city, in search of refuge, food and shelter during the war. Most of these provincial migrants that settled in the eastern part of Sierra Leone’s capital city were subsistence farmers and local petty traders.

Population, Sample, and Data Collection

The target population consisted of all women of childbearing age living in the east end of Sierra Leone’s capital city, Freetown. The research used primary data obtained through interviews and well-structured questionnaires administered to 755 women of childbearing age, who were randomly selected from the study area.

Questions relating to the number of under-five children that died after the rebel war, the child feeding status in terms of frequency and quality, parents’ socio-economic status, and demographic factors like mothers’ age, mothers’ education, birth spacing, and the availability of preventive measures like mosquito nets were included in the questionnaire.

Variables Used in the Model

1) Dependent Variable: The dependent variable examined in this research is the count of children who passed away (or died) in the family (or household) following Sierra Leone’s civil war, often referred to as the Rebel War.

2) Independent variables: The independent variables include: the mothers’ age, mothers’ educational level, family income level, availability of mosquito net, post and prenatal visits, Birth Interval, Family size and the child’s feeding status.

The table below (Table 1) provides a summary overview of the dependent and independent variables utilized in this analysis.

Table 1.

Summary of Variables Used in the Analysis

Variable name	Description: Dependent variable(DV)/Independent variable (IV)	Valid range	Variable type
Number of under- five child death	DV	$\geq$ 0	Discrete (count)
Mothers Age	IV	≤ 20 years, ≤ 30 years, $\geq 31$ years	Categorical
Mother’s Educational Level	IV	No Formal Education Primary Education Secondary Education Tertiary Education	Ordinal
Family Income Level	IV	Low Medium High	Ordinal
Birth interval	IV	less than 12 months 12–23 months 24–35 months 36 months and above	Categorical
Family Size	IV	<3 small, =3 normal, >3 big	Categorical
Child’s Feed		Low < 3 Medium ≤ 3 High > 3 times	Ordinal
Pre and post-natal Hospital visit	IV	Regular=always meets Doctor’s appointment Not regular= Never or not always	Categorical
Hospital Type		Private public	Categorical (Dichotomous)
Child sleep under mosquito net		Never Sometimes Always	Categorical

Table 2 present the categorical variable Information. From Table 2, the following findings were noted:

^aA significant portion of the mothers were younger than 30 years old, with approximately 33% being teenagers.

^bNearly 99% of the mothers were classified as either illiterate or as having dropped out of primary or secondary school.

^cAround 34% of the children had never slept under a mosquito net.

^dA majority (61%) of the children under five came from families with low income

Bar Chart of the Number of Under Five Deaths (Dependent Variable)

The bar chart in Figure 1 shows the number of deaths (i.e., the dependent variable) among children under five. The category that indicates zero deaths among under-five children is much higher than the other categories. This points to the need for a count regression model, like hurdle and/or zero-inflated models. The hurdle and zero-inflated models effectively deal with the issues of over-dispersion, under-dispersion, and the high number of zeros often seen in count data (Table 2).

Table 2.

Categorical Variable Information

Factor	Category	N	Percent
Mother’s Age	11-20	248	32.8%
	21-30	201	26.6%
	31 and above	306	40.5%
	Total	755	100.0%
Mother’s Educational Status	Non-formal	306	40.5%
	Primary	192	25.4%
	Secondary	255	33.8%
	Tertiary	2	0.3%
	Total	755	100.0%
Mother’s Occupational Status	Employed	379	50.2%
	Unemployed	376	49.8%
	Total	755	100.0%
Chil’s Family Income Level	Low	460	60.9%
	Medium/Middle	138	18.3%
	High	157	20.8%
	Total	755	100.0%
Frequency of child feeding per day	Low (0-6 times)	345	45.7%
	Medium (7-9 times)	104	13.8%
	High (10-12 times)	306	40.5%
	Total	755	100.0%
Frequency of child sleeping under mosquito net	Low (Never)	260	34.4%
	Medium (Sometimes)	147	19.5%
	High (Always)	348	46.1%
	Total	755	100.0%

Statistical Models

Count Data Regression Models

Data in a count format includes events that occur at a specific frequency. The rate of occurrence can change over time or between observations. When the dependent variable is a numerical count, we can use regression-type analyses with models designed for count data. Using count data as a dependent variable in regression analysis, the first model to consider is the Poisson Regression model. The Poisson regression is part of a group of models called generalized linear models (GLM). This model (Poisson) is normally referred to as the fundamental or baseline model in count regression analysis. However, due to the Poisson regression model’s strict assumption that variance equals the mean, and the different ways count variables can be distributed, the negative binomial, Generalized Poisson (or G-Poisson), zero-inflated and hurdle regression models are sometimes used as alternatives when the Poisson assumption does not hold. These alternative models are applied in cases of overdispersion, meaning when var(Y) is greater than E(Y), under dispersion (i.e., var(Y) less than E(Y)), and excess zeroes.

Moreover, to use count models in regression analysis, it is vital to choose or select the model that best fit the data used in the analysis. Therefore, to compare the Performance of the count models in terms of how best they fit the count data, statistical tests, including, the Voung non-nested test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC) and a graphical method called the hanging Rootogram were employed. The Vuong test²⁰ compares the likelihood functions of two models at a time.

For a more detailed description of the Voung test, AIC BIC, Rootogram and each of the listed count regression models, please see^20-28 and the attached Appendix (Methodologic or Theoretic).

Omnibus Test

Table 3 provides the omnibus test used to determine if the current model, with the included explanatory variables, performs better than the null model. This likelihood ratio chi-square test compares the full model to a null model that includes only the intercept. The results in Table 3 are statistically significant. This indicates that the model, which includes the independent variables used in the count regression analysis, fits significantly better than the null model that only has the intercept.

Table 3.

Omnibus Test

Likelihood ratio chi-square	df	Sig.
859.427	12	.000

The Poisson Regression Model

As already stated, the first regression model to examine in count regression analysis is the Poisson regression model. This model is often regarded as the foundational model in count regression analysis.

Estimated Parameters for the Poisson Regression Model

Table 4 shows the parameter estimates from the Poisson regression analysis. Except for the mother’s occupation (Mom_Occup) and education (Mom_Edu), all other independent variables were statistically significant. Each coefficient was negative, indicating that an increase in any of the independent variables is associated with a significant decrease in the deaths of children under five. However, to ensure the reliability of the results of this analysis, it is crucial that the main assumption of Poisson regression, known as equi-dispersion, is satisfied. Therefore, this assumption needed to be examined.

Table 4.

Parameter Estimate for the POISSON Model

Variable	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	3.46234	0.19710	17.567	< 2e-16 ***
Mom_Occup	-0.13548	0.09233	-1.467	0.14229
Fam_Incom_lLevel	-0.44852	0.11779	-3.808	0.00014 ***
Mom_Edu	-0.08963	0.04652	-1.927	0.05404
Chi_Sle_und_Mos_Net	-0.55921	0.07258	-7.705	1.31e-14 ***
Chi_Feed_Status	-0.65800	0.10964	-6.001	1.96e-09 ***
Mom_Age	-0.49186	0.07386	-6.659	2.76e-11 ***

Goodness of Fit for Poisson Regression Model

The goodness-of-fit test statistics for the Poisson regression model are shown in Table 5. For a well-fitting model, the deviance ratio to the degrees of freedom (found in Table 5) should be as close to 1 as possible. A value significantly below one points to under-dispersion, above one indicates over-dispersion, and a value equal to one means equi-dispersion. The ratio of deviance to degrees of freedom (=.331), as seen in Table 5, is significantly below 1. This indicates a clear violation of the key assumption of equi-dispersion in Poisson regression. As a result, it supports the use of alternative count regression models, like zero-inflated, G-Poisson, and hurdle models, which can properly handle the issues of excess zeros and under-dispersion present in the data.

Table 5.

Goodness of Fit

	Value	df	Value/df
Deviance	245.309	742	.331
Scaled Deviance	245.309	742
Pearson Chi-Square	271.088	742	.365
Scaled Pearson Chi-Square	271.088	742
Log Likelihood^b	-581.588
Akaike’s Information Criterion (AIC)	1189.175
Finite Sample Corrected AIC (AICC)	1189.667
Bayesian Information Criterion (BIC)	1249.323
Consistent AIC (CAIC)	1262.323

The Generalized Poison (or G-Poisson) Regression Model

While the standard Poisson regression is the fundamental and the most preferred when the variance equals the mean, in the presence of an excess of zeros backed with over- or under dispersion in a data set, as exhibited in Figure 1, the Poisson (or standard Poisson) regression may not be a good choice model. The study, therefore, extended the use of the poison model to the generalized poison model (see^29,30).

Interpretation of the Estimated Parameters of the G Poisson Regression Model

Table 6 shows the parameter estimates from the Generalized Poisson (G Poisson) regression model. Similar to the Poison regression, except for the mother’s occupation (Mom_Occup) and education (Mom_Edu), all the other independent variables were statistically significant. Each coefficient was negative, indicating that an increase in any of the independent variables is associated with a significant decrease in the deaths of children under five years.

Table 6.

Parameter Estimate for the G POISSON Model

Variable	Estimate	Std. Error	z value	Pr(>\|z\|)
Intercept):1	3.462e+00	1.971e-01	17.567	< 2e-16 ***
(Intercept):2	-3.281e+01	2.700e+04	-0.001	0.99903
Mom_Age	4.919e-01	7.386e-02	-6.659	2.75e-11 ***
Fam_Incom_lLevel	4.485e-01	1.178e-01	-3.808	0.00014 ***
Mom_Occup	-1.355e-01	9.233e-02	-1.467	0.14228
Mom_Edu	-8.963e-02	4.652e-02	-1.927	0.05404
Chi_Sle_und_Mos_Net	-5.592e-01	7.258e-02	-7.705	1.31e-14 ***
Chi_Feed_Status	-6.580e-0	1.096e-01	-6.001	1.96e-09 ***

The Negative Binomial Regression Model

Interpretation of the Estimated Parameters of the Negative Binomial Regression Model

The parameter estimates from the negative binomial regression are presented in Table 7. The table also contains the standard errors, z scores, and p-values for the coefficients. A negative coefficient shows that an increase in the independent variable can result in a decrease in the expected log count of the dependent variable (i.e., number of deaths among children under five). All coefficients in the table are negative. This means that an increase in each independent variable results in a lower expected log count of the dependent variable. According to Table 7, the variable “mother’s age” (Mom_Age) has a coefficient of -0.49185, which is statistically significant. This indicates that for every one-year increase in the mother’s age, the expected log count of under-five child deaths decreases by 0.49185. The family income level (Fam_Incom_Level) also has a statistically significant coefficient of -0.44852. This suggests that an increase in family income lowers the expected log count of under-five child deaths by 0.44852. Additionally, the variable Chi_Feed_Status shows a significant negative coefficient of -0.65801. This indicates that better child feeding status is linked to a notable reduction in the expected log count of under-five child deaths. Furthermore, an increase in the number of times children sleep under mosquito nets leads to a decrease in the expected log count of under-five child deaths by 0.55922.

Table 7.

Parameter Estimate of the Negative Binomialmodel

Variable	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	3.46236	0.19711	17.566	< 2e-16 ***
Mom_Occup	-0.13549	0.09234	-1.467	0.05406
Fam_Incom_lLevel	-0.44852	0.11780	-3.808	0.00014 ***
Mom_Edu	-0.08962	0.04653	-1.926	0.05406
Chi_Sle_und_Mos_Net	-0.55922	0.07258	-7.705	1.31e-14 ***
Chi_Feed_Status	-0.65801	0.10965	-6.001	1.96e-09 ***
Mom_Age	-0.49185	0.07387	-6.659 2	2.76e-11 ***

The Hurdle Models

The Hurdle count regression models consist of two components. The first component handles truncated counts for the positive values and the second component addresses the zero counts. In contrast to zero-inflation models, these models do not differentiate between two sources of zeros; the count component is utilized only when the threshold for modeling the occurrence of zeros is surpassed. Generally, the count component is modeled using either a truncated Poisson or negative binomial regression with a log link function. For the hurdle aspect, a binomial model or a censored count distribution can be used. For this analysis the binomial model was used to model the second (or hurdle part) component. The result of the hurdle part of the model indicates the possibility of obtaining a non-zero (positive) count. In most cases, positive coefficients within the hurdle component suggest that an increase in the predictor variable raises the likelihood of a non-zero count, whiles a negative coefficients within the hurdle component suggest that increase in the predictor variable will lead to a decrease in the likelihood of a non-zero count, or a decrease in the predictor variable raises the likelihood of a non-zero count.

Interpretation of the Parameter Estimates of the Hurdle Negative Binomialmodel

From Table 8, we can see that all the significant predictor variables (Mom_Age, Chi_Sle_und_Mos_Net and Chi_Feed_Status presented in the hurdle (or second) component are negative, this means that increase in each of the significant predictor variables will lead to a decrease in the likelihood of a non-zero count of under five child mortality or decrease in the predictor variable raises the likelihood of a non-zero count of the under-five child mortality in the study area. This implies that a decrease in the mother’s age, a decrease in the number of times a child sleeps under a mosquito net (Chi_Sle_und_Mos_Net) and a decrease in the child’s feeding status (Chi_Feed_Status) can result to an increase in the likelihood of under-five child mortality in the study area.

Table 8.

Parameter Estimates of Hurdle Negative Binomial Model

Count model coefficients (truncated negbin with log link)
Variable	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	6.5208	0.8179	-1.012	< 2e-16 ***
Mom_Occup	-0.2077	0.2052	-3.878	0.000105 ***
Fam_Incom_lLevel	-2.3487	0.6057	-2.712	0.006680 **
Mom_Edu	-0.2817	0.1039	-3.698	0.000217 ***
Chi_Sle_und_Mos_Net	-0.5925	0.1602	-2.259	0.023868 *
Chi_Feed_Status	-0.8830	0.3908	-6.641	3.12e-11 ***
Mom_Age	-1.4515	0.2186	0.586	0.558174

Zero hurdle model coefficients (binomial with logit link)
Variable	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	18.2923	2.1457	8.525	< 2e-16 ***
Mom_Occup	-0.9768	0.5234	-1.866	0.06200
Fam_Incom_lLevel	-0.6121	0.3670	-1.668	0.09533
Mom_Edu	-0.3860	0.3283	-1.176	0.23973
Chi_Sle_und_Mos_Net	-3.8987	0.4805	-8.114	4.91e-16 ***
Chi_Feed_Status	-2.0418	0.3899	-5.237	1.64e-07 ***
Mom_Age	-0.9911	0.3431	-2.889	0.00387 **

Interpretation of Exponentiated Coefficients for the Hurdle Negative Binomial Model

From, Table 9, the ‘Zero-hurdle model’ column shows that the baseline odds of having a positive count vs zero is 8.794753e+07. This odd is decreased by 3.711584e-01 times by a unit (year) increase in mothers’ age (Mom_Age). Increase in family income level decreases it by 5.422272e-01 times, and increase in the child feeding status in terms of frequency and quality decreases it by 1.297928e-01 times. Also, increase in child sleeping under mosquito net decreases it by 2.026906e-02 times However, both the mothers’ education (Mom_Edu) and mothers’ occupation (Mom_Occup) have no significant effect.

Table 9.

Exponentiated Coefficients for the Hurdle Negative Binomial Model

Variables	Count_model	Zero_inflation_model
(Intercept)	6.790913e+02	8.794753e+07
Mom_Occup	8.124867e-01	3.765215e-01
Fam_Incom_lLevel	9.549281e-02	5.422272e-01
Mom_Edu	7.544702e-01	6.797939e-01
Chi_Sle_und_Mos_Net	5.529705e-01	2.026906e-02
Chi_Feed_Status	4.135448e-01	1.297928e-01
Mom_Age	2.342154e-01	3.711584e-01

According to the “positive count model” column in Table 9, the average count of under-five child mortality among those with positive counts is 6.790913e+02. A unit increase (in years) in mothers’ age decreases the average count by 2.342154e-01 among those who have positive counts. An increase in family income level decreases the average count of under-five child mortality by 9.549281e-02 times, and an increase in child feeding status in terms of frequency and quality decreases it by 4.135448e-01 times. Also, an increase in children sleeping under mosquito nets decreases it by 5.529705e-01 times.

The Zero-Inflated Model

The result of the zero-inflated model shown in Table 10 is divided into two sections. The first section includes the truncated Poisson regression coefficients for all variables, along with their standard errors, z-scores, and p-values.

Table 10.

Zero-Inflated Model

Count model coefficients (Poisson with log link)
Variable	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	2.51118	0.22685	11.070	< 2e-16 ***
Mom_Occup	-0.10401	0.09159	-1.136	0.25615
Fam_Incom_lLevel	-0.34897	0.12109	-2.882	0.00395 **
Mom_Edu	-0.09086	0.04675	-1.944	0.05195
Chi_Sle_und_Mos_Net	-0.30676	0.07324	-4.188	.81e-05 ***
Chi_Feed_Status	-0.22724	0.11603	-1.959	0.05016
Mom_Age	-0.46029	0.07359	-6.254	3.99e-10 ***

Zero-inflation model coefficients (binomial with logit link)
Variable	Estimate	Std. Error	z value	Pr(>\|z\|)
(Intercept)	-446.8642	1746.1721	-0.256	0.798
Mom_Occup	19.0366	125.0846	0.152	0.879
Fam_Incom_lLevel	8.7689	55.0891	0.159	0.874
Mom_Edu	45.2327	187.1228	0.242	0.809
Chi_Sle_und_Mos_Net	95.0041	355.7984	0.267	0.789
Chi_Feed_Status	34.0521	158.2334	0.215	0.830
Mom_Age	-0.9882	45.3339	-0.022	0.983

The second section corresponds to the inflation model. This section includes the logit coefficients for predicting excess zeros along with their standard errors, z-scores, and p-values. Three of the predictors, mother’s age, child sleeping under a mosquito net, and family income level, are each negative and statistically significant in the count model section (first block) of the model. This implies that an increase in each of these variables will lead to a decrease in the count of under-five child mortality in the study area.

Test for Multicollinearity

Multicollinearity arises when a regression model includes several independent variables that are correlated with one another. With highly correlated independent variables in a statistical model, it becomes increasingly difficult to pinpoint the separate effects of these independent variables. Additionally, if the problem of multicollinearity is not addressed, any statistical conclusions drawn from the data may lack reliability. The VIF is a standard statistical tool used to check for multicollinearity^31,32. It (VIF) measures how much the variance of a regression coefficient is amplified due to the presence of multicollinearity among the independent variables. The VIF test is typically employed to check for any multicollinearity that might exist among the independent variables in the analysis. Therefore, this research utilized the VIF test to evaluate the existence of multicollinearity in the set of predictor variables used in the count regression analysis.

In testing for multicollinearity using the variance inflation factor (VIF), a VIF value greater than 5 implies that the independent variables are correlated (i.e., multicollinearity exists).³³ From the result presented in Table 11, all the VIF values are below 2. Hence, multicollinearity is not a problem here. Therefore, the assumption of ‘no multicollinearity’ is satisfied.

Table 11.

Variance Inflation Factor (VIF) Test Results: Testing for Multicollinearity

Mom_Age	Fam_Incom_Level	Mom_Occup	Chi_Sle_und_Mos_Net	Chi_Feed_Status
1.216634	1.146624	1.056361	1.196892	1.479412

Model Comparison for the Hurdle, g. Poisson, Negative Binomial, and the Zero-Inflated Models

To determine the appropriate model, the Vuong non-nested test.³⁴ was employed to compare the count models utilized in this research. The null hypothesis for the test is that the two models are indistinguishable. A positive value of the Vuong z-statistic suggests that the first model in the test (called model 1) is superior, while a negative Vuong z-statistic shows that the second model (model 2) in the Vuong non-nested test is the preferred model. Based on the test result presented in Table 12, the hurdle negative binomial model was the most preferred model.

Table 12.

Vuong Test for Comparing Count Models

Vuong non-nested hypothesis test-statistic
Model 1 is hurdle negative binomial and model 2 is ziro-inflated model				Outstanding model
	Vuong z-statistic	H_A	p-value	Hurdle Negative Binomial
Raw	9.705287	model1 > model	2.22e-16
AIC-corrected	9.705287	model1 > model2	2.22e-16
BIC-corrected	9.705287	model1 > model2	2.22e-16
Model 1 is ziro-inflated model and model 2 is the Generaized Poisson model
	Vuong z-statistic	H_A	p-value	Ziro-inflated
Raw	8.983371	model1 > model	7.4901e-06
AIC-corrected	7.578354	model1 > model2	1.7542e-14
BIC-corrected	4.328979	model1 > model2	5.7732e-13
Model 1 is Negative Binomial and model 2 is Hurdle Negative Binomial
	Vuong z-statistic	H_A	p-value	Hurdle Negative Binomial
Raw	-12.48758	model1 > model	2.22e-16
AIC-corrected	-12.04447	model1 > model2	2.22e-16
BIC-corrected	-11.01970	model1 > model2	2.22e-16
Model 1 is Generalized Poison and model2 is negatve Binomial
	Vuong z-statistic	H_A	p-value	Generalized Poison
Raw	6.228605	model1 > model	2.353e-10
AIC-corrected	6.228605	model1 > model2	2.353e-10
BIC-corrected	6.228605	model1 > model2	2.353e-10

Assessment of the Fit of Count Regression Models Using the Hanging Rootogram

In addition to the Vuong non-nested test used for choosing the most appropriate count regression model for this research, a graphical tool called the hanging rootogram was also utilized for assessing the fit of all the count regression models used in the analysis. The rootogram has been identified as an effective graphical tool for identifying and addressing problems like dispersion and/or an excess of zeros in models dealing with count data.^26,27

In using the hanging rootogram, the square root of the empirical frequencies is graphically compared with the expected frequencies from the count model. The count outcome is on the horizontal axis, also called the x-axis, while the square root of the frequencies is on the y-axis, called the vertical axis. The red line in the rootogram displays the predicted (or expected) counts of the model, and the hanging bars extending from the red line depict the observed counts. The zero line in the rootogram is called the reference line because, at zero, the model fits perfectly well as expected. More specifically, the model’s predicted count and the actual count agree if a bar touches the line at the point 0. Any bar that hangs above the line at 0 indicates that the model is overpredicting; that counts as the projected count is larger than the observed count. In the same way, any bar that hangs below the line at 0 indicates that the model is underpredicting; that counts because the anticipated or expected count is lower than the observed count.

In line with the Vuong non-nested test result presented in Table 11, the graphs of the hanging rootograms presented in Figure 2 show that the hurdle negative binomial model is the most appropriate count regression model for this study. This is because it can be seen that the rootogram plot for the hurdle negative binomial model presented in Figure 2 fits the data much better than the rootograms for all the other count regression models used in the analysis. In particular, the resulting rootogram plot of the Hurdle negative binomial model accommodates the inflated zeros effectively, as illustrated by the first bar representing the zero occurrence perfectly touching the horizontal line. The model also gradually accommodates the dispersion present in the count data, as most bars are either close to the zero line or are within the dotted lines that represent the confidence interval. Based on the rootogram, the hurdle negative binomial regression model is the only model that perfectly addresses the issue of the inflated zeros present in the data and is, therefore, considered the most preferred model for modeling the count data used in this research.

Aic and Bic Scores for Comparing Non-nested Count Regression Models

Alongside the Vuong non-nested test shown in Table 11 and the hanging rootograms illustrated in Figure 2, this research employed the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) to assess the fit of the non-nested count regression models used in the analysis. Generally, in choosing the most suitable model, the AIC and BIC evaluate the count models according to their goodness of fit and parameter simplicity (or parsimony). The model with the minimum value of AIC and/or BIC score(s) is usually chosen as the best-fit model for the data. From the AIC and BIC scores shown in Table 13, the hurdle negative binomial model is the model with the minimum AIC and BIC scores and thus the most appropriate model for the count data used in this study. The next model with respect to fit based on the AIC and BIC values is the generalized Poisson model (G-Poisson model). Numerous empirical investigations also revealed that, unlike the case where there is over-dispersion in the data, the generalization of the Poisson distribution performs better than the negative binomial model when dealing with under-dispersion of count data; see, for example^29,35,36:

Table 13.

AIC and BIC Output for Comparing Non-nested Count Models

Count model	AIC	BIC
Poison (G. Poisson)	1079.492	1111.87
Zero-Inflated NB	1188.561	1244.066
Hurdle NB	894.961	950.4657
Negative Binomial	1255.388	1287.766

Aic, Bic, and Log-likelihood Scores for Comparing Nested Count Regression Models

In the context of nested count regression models, the Poisson model is encompassed (or nested) within the Generalized Poisson (or G. Poisson) model. This is due to the fact that the Generalized Poisson model incorporates a dispersion parameter (λ), which permits either overdispersion (variance > mean) or underdispersion (variance < mean). When this dispersion parameter is set to 1, the Generalized Poisson model simplifies to the Poisson model (or standard Poisson model).

According to the AIC and BIC scores shown in Table 14, the values for the G. Poisson model are lower than those for the Poisson model for both AIC and BIC. This indicates that the G. Poisson model with the extra dispersion parameter performs much better than the standard Poisson model.

Table 14.

AIC, BIC, and Log-likelihood Output for Comparing Nested Count Models

Count model	AIC	BIC	DF	LogLik
Poison	1189.175	1249.323	6	-620.6877
G. Poisson	1079.492	1111.87	7	-607.6497

Since the Poisson model is nested within the G-Poisson model, the log-likelihood score was also used to compare the two models in terms of goodness of fit to the data. The log-likelihood score measures how likely it is that the data used in the analysis (observed data) occurred under the specified model. The value of the log-likelihood score is mostly negative, and a higher value (i.e., a negative value closer to zero) indicates a better fit.

From Table 14, it can be seen that the log-likelihood value for the G Poisson model is the highest. This further confirms that for the two nested models (G Poisson and Poisson), the G Poisson model is a better fit to the data compared to the Poisson (or standard Poisson) model.

Result Discussion

This study aimed to determine the key factors contributing to child mortality in children under five in the eastern part of Freetown, the capital of Sierra Leone. It also sought to highlight the effect of each factor on child mortality in the area being studied.

Due to the count nature of the dependent variable, many count-regression models were utilized in the analysis. However, the presence of excess zeros and the clear violation of the restrictive equi-dispersion requirement of the baseline count regression model led to the use of count regression models, including the hurdle and zero-inflated models, that can effectively handle the instances of excessive zeros and under-dispersion (or over dispersion) in the data. The data analysis using the count regression models suggests that the hurdle negative binomial model outperformed all the other count regression models.

The results of the analysis using the hurdle negative binomial model, along with other count regression models, showed that the mother’s age (Mom_Age), the number of times a child sleeps under a mosquito net (Chi_Sle_und_Mos_Net), family income level (Fam_Incom_Level), and the child’s feeding status (Chi_Feed_Status) were the primary factors influencing under-five child mortality in the eastern part of Freetown. The analysis further revealed that a decrease in the mother’s age can increase the likelihood of under-five child mortality in the study area. This finding is supported by.³⁷ who also observed in their study that the rates of mortality in early childhood were at their peak among under-five children from young teenage mothers. In a similar vein,²³ also discovered in their research that insufficient spousal support, often experienced by mothers aged 17-19, corresponds with an elevated risk of child mortality for those under five years old.

Additionally, a decrease in the frequency of the number of times children sleep under mosquito nets was found to be associated with a higher risk of mortality among children under five in the research area. Research findings presented by⁹ stated that Sierra Leone faces one of the highest rates of malaria in the world. The mosquito is a carrier (or vector) of malaria; therefore, controlling mosquitoes using mosquito nets implies using one of the most effective ways to reduce the incidence of deaths among children under five due to malaria.

Furthermore, a decrease in family income level was found to be associated with an increase in the likelihood of under-five child mortality in the study area. Reference²⁸. also observed in their research that income significantly influences child survival. This finding is supported by,.¹⁰ who revealed in their study that a rise in family income leads to a decrease in malnutrition rates among children under five.

Finally, decrease in the frequency and quality of child feeding was found to be associated with a higher risk of mortality among children under five in the research area. In a similar vein,³⁸ found in their study that malnutrition is responsible for 45% of all childhood fatalities worldwide (also see¹⁵). Reference²² also identified in their research that breastfeeding practices and the mother’s age are significant factors influencing the mortality rate for children under five in Sierra Leone.

Conclusion

This research aimed to use the count regression modeling techniques to identify the main factors influencing child mortality in children under five in the eastern part of Freetown, the capital city of Sierra Leone. It also highlighted how each specific factor impacts under-five child mortality in the study area. Among the count regression models applied in the analysis, the hurdle negative binomial model showed better performance than the other count regression models. The findings from the analysis utilizing the hurdle model along with other count regression models revealed that a younger maternal age, a reduction in family income, a decline in both the frequency and quality of child feeding, and a decrease in the number of times a child sleeps under a mosquito net were each associated with a heightened risk of mortality among children under five in the area studied.

Finally, it is worth noting the following:

a. For this research, the test for multicollinearity using the VIF showed that the issue of multicollinearity is not alarming, as the VIF for each of the independent variables is less than 2; (see³³). This shows that the regressors are independent of one another. However, in some cases, this assumption may not hold. In such situations, alternative estimation techniques, such as ridge regression or other regularization methods, may be more appropriate. For further discussion on count data models in the presence of multicollinearity, see^39-43 among others.

b. The findings of this study are limited to the data analyzed in this paper. As the models were developed and evaluated using a specific area in the eastern part of Freetown, the results should not be generalized to other areas of the country without further validation.

Supplemental Material

Supplemental Material - Determinants of Under-five Child Mortality in the East End of Freetown, Sierra Leone: A Hurdle Negative Binomial Modelling Approach

Supplemental material for Determinants of Under-five Child Mortality in the East End of Freetown, Sierra Leone: A Hurdle Negative Binomial Modelling Approach by Regina Baby Sesay, Sheku Seppeh and Kpangay Mohamed in Sage Open Pediatrics.

Footnotes

ORCID iD

Regina Baby Sesay

Ethical Considerations

This study does not need ethical approval because our community (institution) does not require it for reporting individual cases (or series of cases).

Consent to Participate

The participants consented to be interviewed, as they were eager to vent about the circumstances surrounding the death of their children.

Consent for Publication

The subjects/participants (mothers interviewed) consented as they insisted on wanting their voices to be heard so that they could receive help that can prevent them from experiencing the sad event of losing a child.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect tothe research, authorship, and/or publication of this article: More specifically, the authors declare thatthey have no known competing financial interests or personal relationships that could have appeared toinfluence the work reported in this paper.

Data Availability Statement

Data will be made available upon request to the corresponding author.*

Supplemental Material

Supplemental material for this article is available online.

References

Akram

Amin

Afzal

Kibria

BMG

. Lukman estimator for the zero inflated negative binomial regression model: theory, simulation and applications. Communications in Statistics - Simulation and Computation. 2025;54(5):1464-1480. doi:10.1080/03610918.2023.2286436.

Rerimoi

Jasseh

Agbla

Reniers

Roca

Timæus

. Under-five mortality in The Gambia: Comparison of the results of the first demographic and health survey with those from existing inquiries. PLoS One. 2019;14(7):e0219919. doi:10.1371/journal.pone.0219919.

Okobi

Ibanga

Egbujo

Egbuchua

Oranu

Oranika

. Trends and Factors Associated With Mortality Rates of Leading Causes of Infant Death: A CDC Wide-Ranging Online Data for Epidemiologic Research (CDC WONDER) Database Analysis. Cureus. 2023;15(9):e45652. doi:10.7759/cureus.45652.

Koroma

Kabba

Wanda

, et al. Under-five mortality in Sierra Leone and possible associated factors: evidence from the 2019 Demographic and Health Survey. Health Policy Plan. 2022;37(10):1210-1220. doi:10.1093/heapol/czac070.

Argawu

Mekebo

. Risk factors of under-five mortality in Ethiopia using count data regression models. Ann Med Surg. 2022;82:2. doi:10.1016/j.amsu.2022.104764

UNICEF Raising clean hands: Advancing learning, health and participation through WASH in schools [homepage on the Internet; 2010. https://www.unicef.org/wash/schools/files/raisingcleanhands

You

Jones

Hill

Wardlaw

Chopra

. Levels and trends in child mortality, 1990-2009. Lancet. 2010;376(9745):931-933. doi:10.1016/S0140-6736(10)61429-8.

Carshon-Marsh

Aimone

Ansumana

, et al. Child, maternal, and adult mortality in Sierra Leone: nationally representative mortality survey 2018-20. Lancet Glob Health. 2022;10(1):e114-e123. doi:10.1016/S2214-109X(21)00459-9.

Oxner

Vellanki

Myers

, et al. Reducing mortality from severe malaria in Sierra Leonean children by applying the World Health Organization's standard malarial protocol with additional sublingual glucose: A continuous quality improvement report. Int J Infect Dis. 2020;96:61-67. doi:10.1016/j.ijid.2020.04.046.

10.

Sesay

Seppeh

. Application of Adjacent Categories and Continuation Ratio Logit Models in Determining Factors Influencing Malnutrition in Children Living in the Eastern Part of Freetown. Sierra Leone. IJRSI. 2022;9(1):2321-2705. doi:10.51244/ijrsi.2022.9110.

11.

Bock

Jarvis

Corey

Stone

Gribble

. Maternal age alters offspring lifespan, fitness, and lifespan extension under caloric restriction. Sci Rep. 2019;9(1):3138. doi:10.1038/s41598-019-40011-z.

12.

Jalavisto

. Parental Age Effects on Man. In: Wolstenholme

GEW

, ed. Ciba Foundation Symposium - The Lifespan of Animals (Colloquia on Ageing); 1959. doi:10.1002/9780470715253.ch3.

13.

Gavrilov

Gavrilova

. Human longevity and parental age at conception. In: Robine

Kirkwood

TBL

Allard

, eds. Sex and longevity: Sexuality, gender, reproduction, parenthood. Berlin, Heidelberg: Springer-Verlag; 2000:7-31. doi:10.1007/978-3-642-59558-5_2.

14.

Yaya

Bishwajit

Okonofua

Uthman

. Under five mortality patterns and associated maternal risk factors in sub-Saharan Africa: A multi-country analysis. PLoS ONE. 2018;13(10):3. doi:10.1371/journal.pone.0205977

15.

Myrskylä

Fenelon

. Maternal age and offspring adult health: evidence from the health and retirement study. Demography. 2012;49(4):1231-1257. doi:10.1007/s13524-012-0132-x.

16.

Bado

Sathiya Susuman

. Women's Education and Health Inequalities in Under-Five Mortality in Selected Sub-Saharan African Countries. PLoS One. 2016;11(7):e0159186. doi:10.1371/journal.pone.0159186.

17.

Balaj

York

Sripada

, et al. Parental education and inequalities in child mortality: a global systematic review and meta-analysis. The Lancet. 2021;398(10300):608-620. doi:10.1016/S0140-6736(21)00534-1.

18.

Fagbamigbe

Kandala

Uthman

. Severe acute malnutrition among under-5 children in low- and middle-income countries: A hierarchical analysis of associated risk factors. Nutrition. 2020;3:75-76. doi:10.1016/j.nut.2020.110768.

19.

Birhanu

Yitbarek

Atlantis

Woldie

Bobo

. Trends in social determinants of inequality in child undernutrition from the Ethiopian Demographic and Health Surveys, 2005-2016. PLoS ONE. 2024;19(1):e0295810. doi:10.1371/journal.pone.0295810.

20.

Lambert

. Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics. 1992;34(1):1-14. doi:10.2307/1269547.

21.

Bozdogan

. Model Selection and Akaike’s Information Criterion (AIC): The General Theory and its Analytical Extensions. Psychometrika. 1987;52(3):345-370. doi:10.1007/bf02294361.

22.

Hilbe

. Modeling Count Data. Cambridge: Cambridge University Press; 2014. doi:10.1017/cbo9781139236065.

23.

Min

Agresti

. Random effect models for repeated measures of zero-inflated count data. Statistical Modelling. 2005;5(1):1-19. doi:10.1191/1471082X05st084oa.

24.

Heilbron

. Zero‐altered and other regression models for count data with added zeros. Biometrical J. 1994;36(5):531-547. doi:10.1002/bimj.4710360505.

25.

Kuha

. AIC and BIC: Comparisons of Assumptions and Performance: Comparisons of Assumptions and Performance. Sociological Methods & Research. 2004;33(2):188-229. doi:10.1177/0049124103262065.

26.

Kleiber

Zeileis

. Visualizing Count Data Regressions Using Rootograms. The American Statistician. 2016;70(3):296-303. doi:10.1080/00031305.2016.1173590.

27.

Wainer

. The Suspended Rootogram and Other Visual Displays: An Empirical Validation. The American Statistician. 1974;28(4):143-145. JSTOR . doi:10.2307/2683341. Accessed 10 May 2026.

28.

O'Hare

Makuta

Chiwaula

Bar-Zeev

. Income and child mortality in developing countries: a systematic review and meta-analysis. J R Soc Med. 2013;106(10):408-414. doi:10.1177/0141076813489680.

29.

Consul

Jain

. A Generalization of the Poisson Distribution. Technometrics. 1973;15(4):791-799. doi:10.1080/00401706.1973.10489112.

30.

Consul

Famoye

. Generalized poisson regression model. Communications in Statistics - Theory and Methods. 1992;21(1):89-109. doi:10.1080/03610929208830766.

31.

Nayem

Kibria

BMG

. The Ridge-Hurdle Negative Binomial Regression Model: A Novel Solution for Zero-Inflated Counts in the Presence of Multicollinearity. Stats. 2025;8:102. https://doi.org/10.3390/stats8040102

32.

Schwarz

. Estimating the Dimension of a Model. Annals of Statistics. 1978;6:461-464. https://doi.org/10.1214/aos/1176344136

33.

Zuur

Ieno

Walker

. Mixed Effects Models and Extensions in Ecology with R. Springer; 2009. https://doi.org/10.1007/978-0-387-87458-6

34.

Vuong

. Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses on JSTOR. Econometrica. 1989;57:307. Accessed September 30, 2025.

35.

Efron

. Double exponential families and their use in generalized linear regression. J. Am. Stat. Assoc. 1986;81:709-721. doi:10.1080/01621459.1986.10478327. [Google Scholar].

36.

Wang

Famoye

. Modeling household fertility decisions with generalized Poisson regression. J Popul Econ. 1997;10(3):273-283. doi:10.1007/s001480050043.

37.

Woodall

Driscoll

. Racial and Ethnic Differences in Mortality Rate of Infants Born to Teen Mothers: United States, 2017-2018. NCHS Data Brief. 2020;371:1-8.

38.

Madewell

Keita

Das

, et al. Contribution of malnutrition to infant and child deaths in Sub-Saharan Africa and South Asia. BMJ Glob Health. 2024;9(12):e017262. doi:10.1136/bmjgh-2024-017262. Published 2024 Dec 5.

39.

Nayem

Kibria

BMG

. The Ridge-Hurdle Negative Binomial Regression Model: A Novel Solution for Zero-Inflated Counts in the Presence of Multicollinearity. Stats. 2025;8:102. doi:10.3390/stats8040102.

40.

Kibria

BMG

Alghamdi

Sapkota

Gemeay

Abd-Elmougod

Hammad

. Enhancing a robust Poisson regression estimator for multicollinear and outliered data: Simulation and application. AIP Advances. 2025;15(9):095130. doi:10.1063/5.0290412.

41.

Alghamdi

Hammad

Kibria

Abd-Elmougod

Sapkota

Gemeay

. On Robust and Non-Robust Modified Liu Estimation in Poisson Regression Model with Multicollinearity and Outliers. International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems. 2025;33(6):787. doi:10.1142/S0218488525500266.

42.

Omer

Sjölander

Månsson

Kibria

BMG

. Improved estimators for the zero-inflated Poisson regression model in the presence of multicollinearity: simulation and application of maternal death data. Communications in Statistics: Case Studies, Data Analysis and Applications. 2021;7(3):394-412. doi:10.1080/23737484.2021.1952493.

43.

Hammad

. Enhancing a Robust Poisson Regression Estimator for Multicollinear and Outliers Data: Simulation and Application. AIP Advances. 2025;15:095130. doi:10.1063/5.0290412.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.90 MB