# The Causes and Factors Associated with Infant Mortality Rate in Ethiopia: The Application of Structural Equation Modelling

^{*}

## Abstract

**:**

## 1. Introduction

**H1.**

**H2.**

**H3.**

**H4.**

**H5.**

**H6.**

## 2. Materials and Methods

#### 2.1. Statistical Model

#### 2.1.1. Path Analysis

_{1}… y

_{n}and there was a directed edge from y

_{i}to y

_{j}if the coefficient of y

_{i}in the equation for y

_{j}was distinct from zero [57]. Moreover, there was a mediation where one variable (exogenous) caused variation in another variable (endogenous), and the mediator hypothesis was supported if the variables BCGI, MMR, FR, and GGHE-D were significant.

#### 2.1.2. Structural Equation Model (SEM)

_{p×p}gives the regression coefficients of endogenous (y) variables on other endogenous variables (it is the matrix of $\beta $′ regression path coefficients between endogenous to endogenous), $\gamma $

_{p×q}gives the regression coefficients of the exogenous variables (x) on endogenous variables (y) whose ith row indicates the endogenous variable and the jth column indicates the exogenous variable, and ${\varsigma}_{px1}$ is the vector of errors in the equations (i.e., regression residuals) as a vector of the model errors associated with each endogenous variable. The variances and covariances of the endogenous variables are modelled as a function of the exogenous variables. Then, the general form of a SEM path analysis model is expressed in the matrix equation:

^{−1}γx + (I − β)

^{−1}ς′)]

_{x}, ∑

_{x}); y $~N(\mu $

_{y}, ∑

_{y}); the stochastic error has a multivariate Gaussian distribution which has for the mean a zero vector and for the covariance matrix a diagonal matrix where the diagonal elements are $\psi 11,$ $\psi 22,\psi 33,\psi 44,$and $\psi 55$ (i.e., $\varsigma $ $~N(0,$ $\psi i$). Furthermore, the variance–covariance of exogenous variables was determined outside of our model. The causality of infant mortality based on our variables expressed as a single matrix is:

_{1}and x

_{2}and the error terms of the error variances are free parameters, but the covariances of error variances are fixed to zero.

## 3. Results

#### 3.1. Descriptive Statistics

#### 3.2. Model Identification

#### 3.3. Path Analysis

#### 3.4. Structural Equation Model

#### 3.5. Assessment of the Overall Goodness of Fit

^{2}goodness of fit criterion is very sensitive to the sample size, often other descriptive measures of fit are used in addition to the absolute χ

^{2}test and there should be a combination of at least two goodness of fits [41,68]. The overall model fit for the structural equation model was adequate to good in terms of the CFI (0.932) and TLI (0.961).

GHE = −0.683 GDP + 0.5349707, R^{2} = 46.6% |

FR = 0.256 GGHE-D + −0.786 GDP + 0.0450516, R^{2} = 95.5% |

BCG = −0.639 GGHE-D + 0.327 OOP + 0.2451441, R^{2} = 75.5% |

MMR = 0.961FR + −0.071 OOP + 0.0075514, R^{2} = 99.3% |

IMR = +1.03FR + 0.156MMR + 0.192GDP + 0.0005578, R^{2} = 99.5% |

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The path diagram: the path standardised coefficients of the risk factors on IMR (2000–2019).

S. N | Observed Variables | Abbreviation | Definition |
---|---|---|---|

1 | GDP per capita | GDP | Gross domestic product, the monitory wealth of the nation of one country’ goods and services over a given period, usually in one year. |

2 | Out-of-pocket expenditure on health. | OOP | Households or individual direct expenses to health institutions or health service providers (it does not include taxes and health insurances). |

3 | Domestic general government health expenditure on health (as % GDP) | GGHE-D | The share of current domestic government resources used to refund public health expenditure as a share of the economy, and it is measured by GDP. |

4 | Fertility rate | FR | The number of children born to a woman in her childbearing-age years and bearing children in accordance with the age-specific fertility rates of the specified year. |

5 | BCG immunization (% of one year-old children) | BCGI | A vaccine given to a one-year old who has received one dose of bacilli Calmette-Guerin expressed in a percentage. |

6 | Maternal mortality ratio | MMR | Annual number of female deaths per 100,000 live births from any cases (cases related to pregnancy). |

7 | Infant mortality rate | IMR | The probability of dying between birth and exactly one year of age per 1000 births. |

**Table 2.**The descriptive statistics of the association of infant mortality in Ethiopia, the application of structural equation modelling path analysis (from year 2000 to year 2019).

N | Minimum | Maximum | Mean | Std. Deviation | Assessment of Normality | ||||
---|---|---|---|---|---|---|---|---|---|

Skewness | Critical Ratio | Kurtosis | Critical Ratio | ||||||

Fertility rate | 20 | 4.15 | 6.54 | 5.26 | 0.75 | 0.180 | 0.328 | −1.186 | −1.082 |

Out-of-pocket expenditure | 20 | 31.34 | 46.54 | 37.81 | 0.607 | 1.108 | −0.028 | −0.026 | 0.607 |

Maternal Mortality ratio | 20 | 354.00 | 1030.00 | 663.35 | 231.94 | 0.281 | 0.513 | −1.380 | −1.259 |

Infant mortality ratio | 20 | 36.60 | 87.20 | 58.16 | 16.09 | 0.347 | 0.634 | −1.134 | −1.035 |

BCG Immunization | 20 | 56.00 | 80.00 | 67.80 | 6.79 | −0.332 | −0.606 | −832 | −0.759 |

Gov.t expenditure on health | 20 | 0.38 | 2.28 | 1.18 | 0.54 | 0.672 | 1.227 | −0.606 | −0.553 |

GDP per capita | 20 | 111.93 | 855.76 | 395.23 | 251.41 | 0.447 | 0.815 | −1.160 | −1.059 |

Valid N (listwise) | 20 | ||||||||

Multivariate | −0.960 | −0.191 |

**Table 3.**The standardised paths for the direct, indirect, and total effects of each factor of the association of infant mortality in Ethiopia, (2000–2019).

Indexes/Pathway | Relation with Standardised Coefficients | |||
---|---|---|---|---|

To | From | Direct | Indirect | Total |

MMR <- OOP | −0.071 (*) | - | −0.071 (*) | |

MMR <- FR | 0.96 (**) | - | 0.96 (**) | |

MMR <- GGHE-D | 0.246 (p = 0.386) | 0.032 (**) | 0.278 (**) | |

MMR <- GDP | - | −0.861 (**) | −0.861 (**) | |

BCGI <- OOP | 0.327 (*) | - | 0.327 (*) | |

BCGI <- GDP | 0.188 (0.260) | 0.437 (*) | 0.625 (**) | |

BCGI <- GGHE-D | −0.640 (**) | - | −0.640 (**) | |

FR <- GGHE-D | 0.256 (**) | - | 0.256 (**) | |

FR <- GDP | −0.784 (**) | −0.175 (*) | −0.959 (**) | |

GGHE-D <- GDP | −0.683(**) | - | −0.683(**) | |

IMR <- MMR | 0.156 (*) | - | 0.156 (*) | |

IMR <- BCGI | −0.0041 (0.774) | - | −0.0041 (0.774) | |

IMR <- FR | 1.032 (**) | 0.136 (*) | 1.168 (*) | |

IMR <- GGHE-D | −0.0012 (0.915) | 0.308 (**) | 0.306 (*) | |

IMR <- GDP | 0.191 (**) | −1.126 (**) | −0.941 (**) | |

IMR <- OOP | - | −0.012 (*) | −0.012 (**) |

**Table 4.**The fitted covariances of observed variables (standardised) for each factor of the causality of infant mortality in Ethiopia, (2000–2019).

MMR | BCGI | IMR | GGHE-D | FR | OOP | GDP | |
---|---|---|---|---|---|---|---|

MMR | 1 | ||||||

BCGI | −0.75 | 1 | |||||

IMR | 0.99 | −0.73 | 1 | ||||

GGHE-D | 0.79 | −0.79 | 0.81 | 1 | |||

FR | 0.99 | −0.72 | 0.99 | 0.80 | 1 | ||

OOP | −0.17 | 0.39 | −0.11 | −0.07 | −0.09 | 1 | |

GDP | −0.96 | 0.66 | −0.95 | −0.69 | −0.96 | 0.09 | 1 |

**Table 5.**The equation-level goodness of fit for the causality of infant mortality in Ethiopia with unstandardised residuals, (2000–2019).

Observed Variables | Variance | R-Squared | mc | mc2 | ||
---|---|---|---|---|---|---|

Fitted | Predicted | Residual | ||||

MMR | 49,877.49 | 49,500.85 | 376.65 | 0.993 | 0.996 | 0.993 |

BCGI | 36.63 | 27.65 | 8.98 | 0.755 | 0.869 | 0.755 |

IMR | 244.65 | 244.51 | 0.14 | 0.999 | 0.996 | 0.999 |

GGHE-D | 0.276 | 0.13 | 0.15 | 0.466 | 0.682 | 0.466 |

FR | 0.544 | 0.52 | 0.025 | 0.955 | 0.978 | 0.955 |

Overall | 0.995 |

^{2}is the Bentler-Raykov squared multiple correlation coefficient.

**Table 6.**The covariance residuals for each factor of the association of infant mortality in Ethiopia, (2000–2019).

MMR | BCGI | IMR | GGHE-D | FR | OOP | GDP | |
---|---|---|---|---|---|---|---|

MMR | 0.076 | ||||||

BCGI | 0.446 | 0.515 | |||||

IMR | 0.047 | −0.445 | 0.016 | ||||

GGHE-D | 0.113 | −0.472 | 0.020 | 0.000 | |||

FR | 0.037 | −0.370 | 0.007 | 0.000 | 0.000 | ||

OOP | 0.731 | 1.034 | −0.818 | −1.841 | −0.716 | 0.000 | |

GDP | 0.022 | 0.000 | −0.003 | −0.000 | −0.000 | 0.000 | 0.000 |

**Table 7.**The finalized and accepted structural equation model for the infant mortality rate in Ethiopia (from 2000–2019).

Coef. | Std. Err. | z | p > |z| | [95% Conf. Interval] | ||
---|---|---|---|---|---|---|

GGHE-D <- | ||||||

GDP | −0.6819305 | 0.1196231 | −5.70 | 0.000 | −0.9163875 | −0.4474736 |

_cons | 3.343989 | 0.4232345 | 7.90 | 0.000 | 2.514464 | 4.173513 |

FR <- | ||||||

GGHE-D | 0.2547491 | 0.071664 | 3.55 | 0.000 | 0.1142903 | 0.3952079 |

GDP | −0.7855652 | 0.0623844 | −12.59 | 0.000 | −0.9078363 | −0.663294 |

_cons | 7.893804 | 1.260267 | 6.26 | 0.000 | 5.423727 | 10.36388 |

BCGI <- | ||||||

GGHE-D | −0.6394371 | 0.1900197 | −3.37 | 0.001 | −1.011869 | −0.2670054 |

OOP | 0.3266416 | 0.1577665 | 2.07 | 0.038 | 0.0174249 | 0.6358584 |

GDP | 0.1888563 | 0.1671475 | 1.13 | 0.259 | −0.1387468 | 0.5164595 |

_cons | 8.858733 | 2.392873 | 3.70 | 0.000 | 4.168789 | 13.54868 |

MMR <- | ||||||

GGHE-D | 0.246499 | 0.0531217 | 0.62 | 0.385 | −0.0710667 | 0.1371665 |

FR | 0.9609476 | 0.0323262 | 29.73 | 0.000 | 0.8975893 | 1.024306 |

OOP | −0.0707044 | 0.0289071 | −2.45 | 0.014 | −0.1273614 | −0.0140475 |

_cons | −3.269208 | 0.5745308 | −5.69 | 0.000 | 4.395268 | −2.143148 |

IMR <- | ||||||

MMR | 0.1454458 | 0.0593495 | 2.62 | 0.009 | 0.0391229 | 0.2717687 |

BCGI | −0.0071356 | 0.0144006 | −0.29 | 0.774 | −0.0323602 | 0.024089 |

GGHE-D | −0.002406 | 0.0420536 | −0.03 | 0.976 | −0.0836643 | 0.081183 |

FR | 1.025088 | 0.0543037 | 18.88 | 0.000 | 0.9186548 | 1.131521 |

GDP | 0.1912811 | 0.0313778 | 6.10 | 0.000 | 0.1297818 | 0.2527805 |

_cons | −4.382065 | 0.7871316 | −5.57 | 0.000 | −5.924815 | −2.839315 |

mean (OOP) | 10.6367 | 1.696609 | 6.27 | 0.000 | 7.311404 | 13.96199 |

mean(GDP) | 1.612898 | 0.3391696 | 4.76 | 0.000 | 0.9481377 | 2.277658 |

var(e. GGHE-D) | 0.5349707 | 0.1631493 | 0.2942661 | 0.9725676 | ||

var(e.FR) | 0.0450516 | 0.0196886 | 0.01913 | 0.1060976 | ||

var(e.BCGI) | 0.2451441 | 0.0921224 | 0.1173679 | 0.5120277 | ||

var(e.MMR) | 0.0076 | 0.0033638 | ||||

var(e.IMR) | 0.0005578 | 0.0002494 | 0.0002322 | 0.0013399 | ||

var (OOP) | 1 | |||||

var (GDP) | 1 | |||||

cov(OOP,GDP) | 0.095317 | 0.2215753 | 0.43 | 0.667 | −0.3389626 | 0.5295965 |

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## Share and Cite

**MDPI and ACS Style**

Derso, E.A.; Campolo, M.G.; Alibrandi, A.
The Causes and Factors Associated with Infant Mortality Rate in Ethiopia: The Application of Structural Equation Modelling. *Children* **2023**, *10*, 397.
https://doi.org/10.3390/children10020397

**AMA Style**

Derso EA, Campolo MG, Alibrandi A.
The Causes and Factors Associated with Infant Mortality Rate in Ethiopia: The Application of Structural Equation Modelling. *Children*. 2023; 10(2):397.
https://doi.org/10.3390/children10020397

**Chicago/Turabian Style**

Derso, Endeshaw Assefa, Maria Gabriella Campolo, and Angela Alibrandi.
2023. "The Causes and Factors Associated with Infant Mortality Rate in Ethiopia: The Application of Structural Equation Modelling" *Children* 10, no. 2: 397.
https://doi.org/10.3390/children10020397