Determinants of the number of children born in Ethiopia, evidenced from 2019 miniEDHS: Using zero-truncated count regression models

doi:10.21203/rs.3.rs-1983782/v1

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Determinants of the number of children born in Ethiopia, evidenced from 2019 miniEDHS: Using zero-truncated count regression models

https://doi.org/10.21203/rs.3.rs-1983782/v1

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Background

In many countries, deferring first births and increasing the interval between births has played an important role in lowering fertility rates. Any country's fertility rate is a key demographic indicator, and it has always been important to closely monitor changes in the pattern of births to determine how many children are being conceived. Any country's fertility rate is a key demographic indicator, and it has always been important to closely monitor changes in the pattern of births to determine how many children are being conceived. The primary goal of this study is to apply zero-truncated regression models to estimate the number of children ever born per mother in Ethiopia from the MiniDHS 2019.

Mothods

The data collection was carried out by the Ethiopian Public Health Institute (EPHI) in collaboration with the Central Statistical Agency (CSA) and the Federal Ministry of Health. Zero truncated count regression models were used to identify the determinant of the number of children ever born from Ethiopian mothers.

Results

The response variable (children ever born) has a range of 1–15. There were 5,753 observations in this study, with the mean and standard deviation of the response variable being 4.04 and 2.48, respectively. According to AIC and BIC model selection criteria and over-dispersed parameter in zero-truncated negative binomial assured the appropriateness of zero-truncated Poisson regression model for this dataset.

Conclusion

The number of children ever born increases with the age group of mothers, but it decreases as mothers' education levels rise. Similarly, region, religion, wealth index, residence area, number of living children, the number of births in the last five years, age at first birth all had a significant impact on the number of children ever born.

Zero truncated Poisson regression

Zero truncated negative binomial regression

Children ever born

Number of children

MiniEDHS 2019

Ethiopia

The number of children which a mother bears is determined by factors like, age at first birth, the interval between births, and fecundity. In many countries, deferring first births and increasing the interval between births has played an important role in lowering fertility rates. Early childbearing is associated with an increased risk of complications during pregnancy and childbirth, as well as higher rates of neonatal mortality. Any country's fertility rate is a key demographic indicator, and it has always been vital to closely monitor changes in the pattern of births to determine how many children are being conceived. The count response variable, which takes into account the reproductive women in the age range (15–19) who have had at least one child, is "child ever born"(Kiser & Hossain, 2019).

In many aspects, public health and medical services are strongly impacted by the average number of children delivered to each woman and the timing of births. For instance, the level of fertility determines the demand for obstetric and child health care and directly affects the rate of maternal mortality. Early adolescent pregnancies and pregnancies after the age of 35 are more dangerous for the mother. Fecundity declines after the age of 35, increasing the need for assisted reproduction(Cleland, 2008). According to a study conducted by (Kiser & Hossain, 2019), the number of children increases with a respondent's age, but the number of children decreases as respondents' and their husbands' education levels rise. The number of children born has also been significantly influenced by factors such as religion affilation, wealth index, and desired last child. Remarkably, the number of children ever born to a mother in rural areas of Bangladesh does not significantly differ from that in urban areas, though there is a slight variation in the number of children ever born to a mother living in seven administrative divisions. Furthermore, the intention to use contraception has no effect on the number of children born to a mother.

Women were more likely than men to have no biological children. The majority of existing research has focused on women, but studying the relationship in men can help distinguish between the biological effects of pregnancy and the social pathways associated with parenthood (Bridger Staatz & Hardy, 2019; Gunther & Harttgen, 2016).

Because of the negative effects of institutionalization on children's developmental outcomes and well-being, countries must aim to reduce the number of children in alternative care (especially institutional care) and, if feasible, reconnect children with their families (Petrowski et al., 2017). There could be over 2.7 million children between the ages of 0 and 17 living in institutional care globally, so accurate estimates of the number of children living in such environments are crucial. However, many countries continue to lack functional administrative procedures for identifying children who are not in the care of their parents. Other research in Ghana and Nigeria revealed that both countries have yet to implement replacement level policies. Therefore, these Sub-Saharan African nations are increasing the average number of children per household, especially in Nigeria, by putting in place every sociodemographic factor that encourages fertility. Governments should take action in the area of mother education because it delays the age at first birth and provides a channel for educating women on family planning measures (YAYA et al., 2018).

All Asian countries had data on the number of children in residential care, but only one (Sri Lanka) had data on the number of children in foster care. As a result, for 28 of the 39 countries with economic growth, regional rates and the number of children in nature were identified, accounting for 96% of the regional child population. However, some regions did obtain at least 33 percent coverage(Petrowski et al., 2017). In addition, the regions with the second and third highest regional population coverage for foster care were 90 and 61 percent, respectively.

A high birth rate combined with a low mortality rate is essential to ensure a realistic chance that the family will not become extinct(Krishnamoorthy, 1980). A moderate to high birth rate and a low mortality rate are required to ensure that the parents have at least one surviving son in their old age. According to (Krishnamoorthy, 1980), zero population increase is unattainable as long as parents rely on their offspring for old age security. As a result, civilizations aiming to reduce their birth rate to the replacement level must implement alternative old-age security measures(Krishnamoorthy, 1980). Specifically, higher mortality rates were observed for mothers of 1 child (HR, 1.18), mothers of 5 to 9 children (HR, 1.21), and mothers of 10 or more children (HR, 1.49) compared with mothers of 2 to 4 children(Dior et al., 2013).

According to the findings of a study conducted in Sub-Saharan Africa, economic status determine the number of surviving children; in the traditionally agricultural societies of Sub-Saharan Africa, the economic benefit of children far outweighs their costs, which are shared by the extended family and the community at large(Mbacke, 1987).

Furthermore, once the desired number of surviving children is less than that predicted by a natural fertility regime, the availability of family planning services becomes an essential factor in the amount and pace of fertility drop. There was a link between the number of children and the probability of maternal mortality.

The study on children ever born used a variety of statistical methods, including logistic regression, the Poisson regression model, multiple classification analysis, and generalized event count models, which performed better than the Poisson model regardless of under or over dispersion (Dwivedi et al., 2016; Getahun & Dejen, 2020; Haque et al., 2015; Karimuzzaman et al., 2020). (Ahmed & ALI, 2015), on the other hand, compared the Poisson model to the Support Vector Machine to predict children born in Bangladesh, but neither model's prediction power was satisfactory. Aside from that, the support vector machine provides no information about the important factors associated with the birth of children.

The goal of this study is to extract statistically significant demographic variables and estimating the number of children ever born which determine the family size of household and the population projection of the country using zero truncated Poisson (ZTP) and zero truncated negative binomial (ZTNB) regression models in order to provide clear information to policymakers and indicate the distribution of children in various regions of Ethiopia(YAYA et al., 2018).

Data Description

The Ethiopian mini-Demographic and Health Survey (EDHS) 2019 dataset was used for this study, which is the second EMDHS and the fifth national-level demographic and health survey. It was carried out by the Ethiopian Public Health Institute (EPHI) in collaboration with the Central Statistical Agency (CSA) and the Federal Ministry of Health (FMoH), and was monitored by the Technical Working Group (TWG). The data collection period lasted from March to June of 2019 (Ethiopian Public Health Institute et al., 2021; ICF., 2021).

The World Bank, the United States Agency for International Development (USAID), and the United Nations Children's Fund all contributed to the 2019 EMDHS (UNICEF). The DHS Program, a USAID-funded project that provides support and technical assistance in the implementation of population and health surveys in countries around the world, was where ICF provided technical assistance. The survey was carried out from March 21, 2019, to June 28, 2019, using a nationally representative sample to provide estimates at the national and regional levels, as well as for urban and rural areas. From a nationally representative sample of 8,663 households, the survey interviewed 8,855 women of reproductive age (15–49). Respondents' background characteristics, fertility determinants, marriage, awareness and use of family planning methods, child feeding practices, nutritional status of children, childhood mortality, and height and weight of children aged 0 to 59 months were all detailed(ICF., 2021).

Sampling Design

The 2019 Ethiopian Population and Housing Census (EPHC), which was carried out by the Central Statistical Agency, served as the basis for the creation of the sampling frame for the EMDHS (CSA). For the 2019 EMDHS, the sample was created to offer estimates of important indicators for the entire nation, rural and urban areas individually, each of the nine regions, and the two administrative cities (ICF., 2021).

The sample for the 2019 EMDHS was stratified and chosen in two stages. Each region was divided into urban and rural areas, resulting in 21 different sampling strata. In the first stage, 305 EAs were chosen (93 in urban areas and 212 in rural areas) with a probability proportional to EA size (based on the 2019 EPHC frame) and with independent selection in each sampling stratum. In the second stage of selection, a fixed number of 30 households per cluster were chosen at random from the newly created household listing with an equal probability. All women between the ages of 15 and 49 who were either permanent residents or visitors who slept in the selected households the night before the survey were eligible to be interviewed(Ethiopian Public Health Institute et al., 2021).

The number of children born is the most important variable in our study, which was gathered through a questionnaire distributed to ever-married women aged 15 to 49 who had given birth during their lifetime, along with other variables. In our study, the number of children ever born to a mothers ranges from one to fifteen.

Data Analysis Methods

Zero truncated Poisson regression ZTPR model

The Poisson regression model, however, failed due to the lack of a zero in the dataset of all children ever born. This issue shifts to the use of alternative models such as truncated models (zero truncated models). As the number of children ever born is a count response variable with all observations greater than zero, the goal of this study was to build regression models using zero-truncated Poisson and zero-truncated negative binomial models. Let be a count random variable with non-zero response count variable. Then the zero truncated Poisson distribution with probability mass function given by

$$P\left({y}_{i}|{\mu }_{i}\right)=\frac{{e}^{-{\mu }_{i}}{{\mu }_{i}}^{{y}_{i}}}{{y}_{i}!}, {y}_{i}=1, 2, 3,\dots$$

where, represents the expected number of occurrences over a specific time period The Zero truncated Poisson regression ZTPR model's mean is as follows:

$$\text{E}\left({\text{y}}_{\text{i}}\right)={\mu }_{i}$$

Let be $n\times p$ matrix of explanatory variables. The relationship between${y}_{i}$ and ${i}^{th}$ row vector of ${x}_{i}$, linked by $g\left({\mu }_{i}\right)$is given by:

$\text{l}og\left({\mu }_{i }\right)= {\eta }_{i} = {x}_{i}^{T}\beta$ , $i=1, 2, \dots , p$,

In order to find the maximum likelihood function of${\mu }_{i }=E\left({y}_{i}\right)={exp}\left({x}_{i}^{T}\beta \right)$, we define the likelihood function as follows:

$$\mathcal{L}=\mathcal{l}\left({\mu }_{i}, \beta \right)=\prod _{i=1}^{n}\frac{{e}^{{-\mu }_{i}}{{\mu }_{i}}^{{y}_{i}}}{{y}_{i}!}=\prod _{i=1}^{n}\frac{{e}^{{-e}^{{{x}_{i}}^{T}\beta }}{\left({e}^{{{x}_{i}}^{T}\beta }\right)}^{{y}_{i}}}{{y}_{i}!}$$

As a result, the log-likelihood function of the Poisson regression model is nonlinear in beta, ${\beta }$ allowing an iterative algorithm to be used to obtain it. Newton-Raphson or Fisher scoring are the most commonly used iterative algorithms. is the solution to the estimating equations obtained by differentiating the log likelihood in terms of and equating them to zero. As a result, would be determined by maximizing using a numerical iterative method (McCullagh & Nelder, 1989).

Overdispersion

The fundamental property of the Poisson model is equi-dispersion. In practice, it is often found that the data exhibit overdispersion because of the existence of heterogeneity in the population and an excess of zeroes (Loan & Bhat, 2022; Payne et al., 2017). According to research by (Loan & Bhat, 2022) and (Payne et al., 2017), heterogeneity is seen when the population can be divided into a large number of homogeneous subgroups, and an excess of zeroes is seen when the observed zeroes are significantly higher than the number of zeroes generated by the fitted Poisson distribution.

However, the application of Poisson regression model works well for count data, but it is constrained by the assumption of equality of variance and mean. When the variance of count data exceeds the mean,However, the application of Poisson regression model works well for count data, but it is constrained by the assumption of equality of variance and mean. When the variance of count data exceeds the mean, $Var\left[{y}_{i}\right]> E\left[{y}_{i}\right],i=1, 2, 3, \dots , n$ a feature of overdispersion will occur. When overdispersion occurs, the Poisson maximum likelihood estimator obtained will be incorrect (Ismail & Zamani, 2013).

The negative binomial regression model is transformed into a Poisson regression model when the overdispersion parameter is existing and it can tested how well the negative binomial model performs compared to the Poisson regression model:

${H}_{o}: \delta =0$(The Poisson model can be fitted well the data)$,$ versus

${H}_{o}: \delta >0$ (The data would be better fitted by the negative binomial regression)

The likelihood-ratio test is given by:

$$LRT=2\left(\mathcal{L}-{\mathcal{L}}_{o}\right),$$

where $\mathcal{L}$ and ${\mathcal{L}}_{\text{o}}$ are the log-likelihood of models under the null and alternative hypothesis, respectively. Under the null hypothesis LRT follows a chi-square distribution with degree of freedom one (Lambert, 1992).

Zero Truncated Negative Binomial Regression (Ztnbr) Model

Negative binomial model allows extra variation, $\delta ,$ relative to the standard Poisson model. Specifically, zero truncated negative binomial regression model is more appropriate for count data because the zero truncated Poisson regression model may not be reliable if some of its assumptions are broken. A random variable ${Y}_{i}, i=1, 2, 3, \dots , n$ is outfit a negative binomial distributed count with parameter $\mu and \delta$the probability density function is expressed as follows:

with mean and variance, respectively, given by:

$E\left({Y}_{i}\right) = {\mu }_{i} = exp\left({x}_{i}^{T}\beta \right),$ and $Var\left({Y}_{i}\right) = {\mu }_{i}\left(1 + \delta {\mu }_{i}\right)$

The term $\delta$(read as delta) is called the dispersion parameter and assumed not to depend on a covariate. If the dispersion parameter${\delta }$ approaches to zero then the Zero Truncated negative binomial regression (ZTNBR) model reduces to the classical Poisson model (Getahun & Dejen, 2020). The log-likelihood function is

$$\mathcal{L}=log\mathcal{ }\mathcal{ }\mathcal{l}\left({\mu }_{i},\delta ;{y}_{i}\right)$$

$$=\sum _{i=1}^{n}\left\{-\text{l}\text{o}\text{g}\left({y}_{i}!\right)+\text{l}\text{o}\text{g} \left(\frac{\varGamma \left({y}_{i}+\frac{1}{\delta }\right)}{\varGamma \left(\frac{1}{\delta }\right)}\right)-\frac{1}{\delta }\text{l}\text{o}\text{g}\left(1 + \delta {\mu }_{i}\right)-{y}_{i}\text{l}\text{o}\text{g}\left(1+\frac{1}{\delta {\mu }_{i}}\right)\right\}$$

The likelihood equations to estimate $\beta$ and 𝛿 are obtained by taking the partial derivatives of the log-likelihood function, and setting them equal to zero as follows:

$$\frac{\partial \mathcal{L}}{\partial \beta }=\frac{\partial \mathcal{L}}{\partial \mu }\frac{\partial \mu }{\partial \beta }= \sum _{i=1}^{n}\left[\frac{{y}_{i}-{\mu }_{i}}{1+\delta {\mu }_{i}}\right]{x}_{i},$$

$$\frac{\partial \mathcal{L}}{\partial \delta }=\sum _{i=1}^{n}\left\{{-\delta }^{-2}\sum _{k=0}^{n-1}\frac{1}{(k+\frac{1}{\delta })}+{\delta }^{-2}\text{log}\left(1+\delta {\mu }_{i}\right)+\frac{{y}_{i}-{\mu }_{i}}{\delta (1+\delta {\mu }_{i})}\right\}$$

The likelihood equation are non-linear in parameters $\beta$ and $\delta$. The above equations were solved simultaneously by using iterative algorithm. The iterative algorithm commonly used is either Newton–Raphson or Fisher Scoring (McCullagh & Nelder, 1989).

In this study, we took into account nine predictor variables: age group (5 years), education level of the respondent, husband's education level, wealth index, religion, residence type, desired last child, region, and contraceptive method, which were found to have significant effects on the dependent variable. The dependent variable was the ever-born child of Ethiopian women aged 15–49. This variable had 15 categories (1–15) in the main dataset. The data recorded the number of children born to women between the ages of 15 and 49 who contributed to the population by giving birth, with the lowest possible outcome being one child. Implies, there are no zero count observations, and the data characteristics indicate that this is a count data that is truncated at zero.

The average number of children per mother was 4.04, with a standard deviation of 2.48, indicating that the zero-truncated Poison regression, ZTPR model was inefficient in analyzing this data and that it was forwarded to another model called zero-truncated negative binomial regression, ZTNBR, which was used to treat the dataset well.

Descriptive Statistics Of Response Variable

The summary statistics of the response variable (children ever born) is present in Table 1.The Table 1 shows the summary statistics for the response variable (children ever born). The response variable (children ever born) has a range of 1–15. There were 5753 observations in this study, with the mean and standard deviation of the response variable being 4.04 and 2.48, respectively. The smallest number of children was one, and the largest number of children was fifteen. Furthermore, the summary statistic in Table 1 indicates an overdispersion in the number of children ever born. As a result, this overdispersion property demonstrates the suitability of zero-truncated negative binomial regression models (Mohebbi et al., 2014).

Table 1

Summary statistics for response Variable( Number children ever born)
Variable	Obs	Mean	Std.	Min	Max
NuCEB	5753	4.04	2.48	1	15

Figure 1 shows that the number of children born is consistent with a zero-truncated negative binomial distribution. Thus, rather than using the zero-truncated Poisson regression model, the number of children ever born dataset is estimated by over-dispersed existing models such as the zero-truncated negative binomial regression model.

Table 2

Frequency distribution of response variable (number of children ever born,NuCEB)
Total children ever born, NuCEB *
	age in 5-year groups	N	%	Mean	Std	Min	Max
age in 5-year groups	15–19	296	5.15	1.42	0.66	1	4
	20–24	1143	19.87	2.09	1.05	1	6
	25–29	1858	32.30	3.42	1.70	1	10
	30–34	1239	21.54	4.95	2.06	1	11
	35–39	765	13.30	5.91	2.33	1	14
	40–44	339	5.89	7.27	2.29	1	15
	45–49	113	1.96	8.41	2.84	2	14
Region where mothers live	tigray	454	7.89	3.59	2.23	1	11
	afar	652	11.33	4.07	2.35	1	13
	amhara	511	8.88	3.75	2.32	1	12
	oromia	719	12.50	4.41	2.74	1	14
	somali	637	11.07	5.23	2.62	1	15
	benishangul	530	9.21	4.25	2.53	1	12
	snnpr	660	11.47	4.18	2.29	1	12
	gambela	450	7.82	3.76	2.30	1	11
	harari	447	7.77	3.75	2.32	1	15
	addis adaba	291	5.06	2.20	1.22	1	8
	dire dawa	402	6.99	3.73	2.62	1	14
Type of place of residence	urban	1328	23.08	3.18	2.25	1	13
Type of place of residence	rural	4425	76.92	4.29	2.49	1	15
highest educational level of mothers	no education	3149	54.74	4.98	2.49	1	15
	primary	1823	31.69	3.16	2.08	1	12
	secondary	480	8.34	2.33	1.46	1	9
	higher	301	5.23	2.17	1.12	1	8
religion	orthodox	1612	28.02	3.45	2.22	1	12
	catholic	32	0.56	3.25	1.87	1	7
	protestant	1053	18.30	3.92	2.46	1	14
	muslim	2974	51.69	4.39	2.57	1	15
	traditional	62	1.08	4.48	2.13	1	11
	other	20	0.35	4.85	2.50	1	9
sex of household head	male	4598	79.92	4.09	2.47	1	15
sex of household head	female	1155	20.08	3.84	2.52	1	15
wealth index combined	poorest	1964	34.14	4.69	2.50	1	15
	poorer	994	17.28	4.42	2.56	1	13
	middle	805	13.99	4.08	2.42	1	12
	richer	738	12.83	3.72	2.38	1	15
	richest	1252	21.76	2.87	1.99	1	13
	Total	5753	100.00	4.04	2.48	1	15

Table 2 displays the total number of children born by sociodemographic variables, including counts, percentages, means, standard deviations, minimums, and maximums. It is truly the case that the number of children increases as the age of the mother increases. Mothers in the first age group, 15–19, had the lowest mean number of children ever born (1.46), the highest number of children born (4), and a standard deviation is 0.69. Apart from having the highest mean number of children (7.76, which is higher than the aggregate mean), mothers in the last age group (44–49) have a standard deviation of 2.71, and the maximum number of children ever born is 14. In terms of regional distribution, Somalia (6.67) and Oromia (6.33) had the highest mean number of children born, with standard deviations of 2.78 and 2.85, respectively. Furthermore, Addis Abeba city administration mothers had the lowest mean number of children (2.96) and the lowest standard deviation (1.64).

In terms of place of residence, mothers in the rural area had a higher mean number of children ever born (4.29) than those in the urban area (3.18), with a standard deviation of 2.49 and 2.25, respectively. It is a fact that, as the education level of mothers increases, the number of children born from them decreases. Evidently, mothers with no education level had the largest mean number of children ever born (4.98), whereas mothers with higher education had the smallest mean number of children ever born (2.17), with a corresponding standard deviation of 2.49 and 1.12, respectively. Surprisingly, the maximum number of children ever born from educated mothers is 8; whereas, from no educated mothers, the maximum number of children ever born is 15. The mean number of children ever born (4.09) is high when the sex of the household head is being male as compared to being female (3.84), with a standard deviation of 2.47 and 2.52, respectively.

Besides, the mean number of children ever born from Muslim mothers and traditional believers is 3.39 and 4.48, with a standard deviation of 2.57 and 2.13, respectively. The average number of children born to Protestant and Catholic mothers is 3.92 and 3.25, with standard deviations of 2.46 and 1.87, respectively. Regarding the wealth index, the average number of children born decreases as the wealth index rises from the poorest to the richest level. The mean number of children born when the mother's wealth index is the lowest(poorest) is 4.69, and the mean number of children born when the mother's wealth index is the highest(richest) is 2.87, with standard deviations of 2.50 and 1.99, respectively.

Estimating The Number Of Children Ever Born Using Ztpr And Ztnbr Models

Table 3 reveald the output of the ZTPR and ZTRNB regression models, estimated using Newton-Rapson iteration methods, is shown in Table 4 for the number of children ever born per woman. As a result of these analyses, the log number of children is expected to increase or decrease by approximately the corresponding coefficient in the column of coefficients in the ZTPR model for every one unit change in a unit of the significant predictors (coef.). In this model, variables with p-values less than 0.05 were considered statistically significant. We use incidence rate ratios (to interpret categorical data, which is important for explaining the change in percentage ) of significant predictors.

The childbearing tendency increases for Ethiopian mothers from the lower age group of 20–24 to 45–49. The mothers in the age groups of 20–24 and 25–29 had approximately 1.13 and 2.3 times more children than mothers in the age group of 15–19, respectively. Similarly, mothers aged 30–34 had 3.1 times more children, 35–39 had 3.67 times more children, 40–44 had 4.1 times more children, and 44–49 had 4.87 times more children than the reference age group of mothers. In terms of the regional distribution of the number of children ever born, mothers in Addis Abeba had 13%. In terms of religious affiliation, Protestant and Muslim mothers had 8% and 7% more children, respectively, than Orthodox mothers. Regarding the wealth index of mothers, the richest mothers had a 6% lower number of children ever born than the poorest mothers. fewer children than the Tigray reference group.

It is obvious that as mothers' education levels rise, the number of children born decreases. The result of zero truncated Poisson regression model support revealed that mothers with primary, secondary, and higher education levels had 5%, 15%, and 17% fewer children than mothers without education, respectively. In terms of religious affiliation, Protestant and Muslim mothers had 8% and 7% more children, respectively, than Orthodox mothers. Regarding the wealth index of mothers, the richest mothers had a 4% lower number of children ever born than the poorest mothers.

The number of children ever born increases as the number of living children increases and the number of births within the last five years increases, whereas the number of children ever born decreases as mothers' age at first birth decreases.

Table 3

the result of ZTPR and ZTNBR models
	ZTPR				ZTNBR
Children_ever_born	IRR	SE	[95% CI]		IRR	SE	[95% CI]
Mother_age_group (15–19)		REF.
20–24	2.127***	0.189	1.786	2.532	2.127***	0.189	1.786	2.532
25–29	3.314***	0.289	2.794	3.931	3.314***	0.289	2.794	3.931
30–34	4.104***	0.363	3.451	4.882	4.104***	0.363	3.451	4.882
35–39	4.674***	0.423	3.913	5.582	4.674***	0.423	3.913	5.582
40–44	5.106***	0.476	4.253	6.130	5.106***	0.476	4.253	6.130
45–49	5.877***	0.581	4.841	7.134	5.877***	0.581	4.841	7.134
Region (Tigray)	REF.
Afar	0.963	0.042	0.883	1.050	0.963	0.042	0.883	1.050
Amhara	0.955	0.035	0.889	1.026	0.955	0.035	0.889	1.026
Oromia	0.972	0.038	0.900	1.050	0.972	0.038	0.900	1.050
Somali	1.027	0.045	0.943	1.118	1.027	0.045	0.943	1.118
Benishangul	1.030	0.041	0.953	1.114	1.030	0.041	0.953	1.114
SNNPR	1.000	0.040	0.925	1.081	1.000	0.040	0.925	1.081
Gambela	0.999	0.045	0.915	1.090	0.999	0.045	0.915	1.090
Harari	0.998	0.045	0.913	1.091	0.998	0.045	0.913	1.091
Addis Adaba	0.868**	0.053	0.769	0.979	0.868**	0.053	0.769	0.979
Dire Dawa	1.021	0.048	0.931	1.118	1.021	0.048	0.931	1.118
Residence (Urban)	REF.
Rural	1.007	0.026	0.958	1.058	1.007	0.026	0.958	1.058
Morher_Edu_level (No education)		REF.
Primary	0.953***	0.018	0.919	0.989	0.953***	0.018	0.919	0.989
Secondary	0.850***	0.034	0.785	0.920	0.85***	0.034	0.785	0.920
Higher	0.827***	0.045	0.744	0.920	0.827***	0.045	0.744	0.920
Religion(Orthodox)	REF.
Catholic	1.031	0.035	0.964	1.102	1.031	0.035	0.964	1.102
Protestant	1.075***	0.012	1.052	1.100	1.075***	0.012	1.052	1.100
Muslim	1.071***	0.011	1.049	1.094	1.071***	0.011	1.049	1.094
Traditional	1.009	0.029	0.953	1.069	1.009	0.029	0.953	1.069
Other	1.184***	0.055	1.081	1.296	1.184***	0.055	1.081	1.296
Sex_HH(Male)	REF.
Female	1.014	0.020	0.977	1.053	1.014	0.020	0.977	1.053
Wealth(Poorest)	REF.
Poorer	1.011	0.022	0.969	1.054	1.011	0.022	0.969	1.054
Middle	1.002	0.024	0.956	1.050	1.002	0.024	0.956	1.050
Richer	0.973	0.025	0.925	1.023	0.973	0.025	0.925	1.023
Richest	0.935**	0.030	0.877	0.997	0.935**	0.030	0.877	0.997
Living_children	1.142***	0.006	1.130	1.153	1.142***	0.006	1.130	1.153
Birthin_5_year	1.176***	0.012	1.152	1.200	1.176***	0.012	1.152	1.200
Age_at_first_birth	0.962***	0.002	0.958	0.966	0.962***	0.002	0.958	0.966
_cons	0.972	0.081	0.825	1.146	0.972	0.081	0.825	1.146
lnalpha					-17.419	19.409	-55.460	20.622

*** Significant At 0.01, ** Significant At 0.05, *significant At 0.1

Table 4

Model comparison using AIC and BIC
Model	N	ll(null)	ll(model)	df	AIC	BIC
ZTPR	5,753	-13055.1	-8750.103	34	17568.21	17794.56
ZTNBR	5,753	-12596.2	-8750.103	35	17570.21	17803.22

Table 4 displays the values of the well-known model selection criteria AIC, BIC, and log (L). Although both models produced nearly identical results, their standard errors were slightly different(Karimuzzaman et al., 2020). The AICs, BICs, and Log-Likelihoods for both models were computed and compared to determine the best fitted model. For the zero-truncated Poisson and negative binomial models, the AICs were 17568.21 and 17570.21, respectively. For the zero-truncated Poisson and Negative Binomial models, the BICs were 17794.56 and 17803.22, respectively. Based on AIC and BIC criteria, the zero truncated Poisson regression (ZTPR) model is preferable to the candidate model, the zero truncated negative binomial regression (ZTNBR). Furthermore, the overdispersion parameter delta ($\delta$) is not statistically significant, which means overdispersion is not a problem in the dataset. Therefore, this shows that a zero truncated Poisson regression model is appropriate to estimate the numbers of children ever born.

Besides, the number of living children clearly increases the number of children ever born in the family. According to the ZTPR, increasing the number of live children by one increases the number of children ever born by 14%. This indicates that the number of children born increases by reducing child deaths from various causes, according to study results by (Karimuzzaman et al., 2020; Kiser & Hossain, 2019).

These models also revealed that Protestant and Muslim mothers in Ethiopia had 8% [IRR = 1.07; CI (1.05, 1.09)] and 7% [IRR = 1.08; CI (1.05, 1.10)] more children than orthodox mothers; this result is consistent with the article conducted by (Karimuzzaman et al., 2020) and (Kiser & Hossain, 2019). Furthermore, the result of this analysis indicated that as mothers' education levels rise, the number of children born decreases, which is noteworthy to study conducted by(Karimuzzaman et al., 2020; Kiser & Hossain, 2019). The rate of 4% [IRR = 0.95; CI (0.92,0.99)] for primary, 15% [IRR = 0.85; CI (0.79, 0.92)] for secondary, and 17% [IRR = 0.83; CI (0.74, 0.92)] for higher levels of education of mothers with respective SE of 0.02, 0.03, and 0.06 had the lowest number of children ever born, with a decreasing rate from lower to higher level when compared to no education level.

According to the wealth index of Ethiopian mothers, those who were rich (richer or richest) had fewer children than those with the lowest wealth index. According to the findings, the recher and richest mothers intended to have fewer children than the poorest mothers, which is consistent with the articles produced by (Karimuzzaman et al., 2020; Kiser & Hossain, 2019). In detail, the results show that richest mothers had about 6% [IRR = 0.94, CI(0.88,1)] with SE (0.03) fewer children than poorest mothers, and the rate of having fewer children increased with the mothers wealth index status.

According to the findings of this study, the age of women is a statistically significant predictor of the number of children born in Ethiopia. The age at first birth, in particular, increases the number of children ever born from particular mothers declined by 4% which is similar result with (Karimuzzaman et al., 2020). Furthermore, the number of children born within the last five years has increased the number of children ever born by 18%.

According to AIC and BIC model selection criteria, candidate models of zero-truncated Poisson and negative binomial models, the zero truncated Poisson regression (ZTPR) model is preferred to estimate the number of children ever born in Ethiopia based on MiniEDHS 2019 data. As a result, the mean number of children ever born is determined by the age group of the mothers; education level of mothers; religious affiliation of mothers; wealth index of mothers; regions; numbers of living children; numbers of births in the last five years; and age at first birth are statistically significant variables based on the ZTPR model.

CSA: Centeral Statistical Authority; CEB: children ever born; AIC: Akakie Information Criterion; BIC: Bayesian information criterion; WHO: World Health Organization; EPHI: Ethiopian Public Health Institute; EMDHS: Ethiopian mini-Demographic and Health Survey; TWG: Technical Working Group;

Ethics approval and consent to participate

I received a letter granting me permission to download data from the Demographic and Health Surveys (DHS) program after registering. The data were taken directly from the DHS website and were used for this study.

Consent for publication

Not Applicable

Availability of data and materials

The dataset used for this study was retrieved from the DHS repository, https://www.dhsprogram.com/customcf/legacy/data/download_dataset.cfm?Filename=ETKR81DT.zip&Tp=1&Ctry_Code=ET&surv_id=551&dm=1&dmode=nm, by registering with my email [email protected] and passwords as user to get download approval.

Competing interests

The authors declare that they have no competing interests

Funding

The authors received no funding.

Acknowledgements

Not applicable

Authors

¹Getachew Tadesse

¹Amsalu Arega,

²Dejen Tesfaw

¹Department of Statistics, Wollo University, Dessie, Ethiopia

²Department of Statistics, Addis Ababa University, Addis Ababa, Ethiopia

Author’s Constitution

Getahun W. designed the study, analyzed the data, and wrote the manuscript. Amsalu A., Dejen T., and Getachew T. assisted with Data cleanup, statistical analysis, and interpretation were all completed. The manuscript was revised by all of the authors. The final manuscript was read and approved by all authors.

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No competing interests reported.

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Determinants of the number of children born in Ethiopia, evidenced from 2019 miniEDHS: Using zero-truncated count regression models

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Introduction

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Zero truncated Poisson regression ZTPR model

Overdispersion

Zero Truncated Negative Binomial Regression (Ztnbr) Model

Results And Discussion

Descriptive Statistics Of Response Variable

Estimating The Number Of Children Ever Born Using Ztpr And Ztnbr Models

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