Descriptive Results
Figure1, the bar chart depicts the vaccination status distribution among 1900 respondents, divided into three categories: Not vaccinated, partially vaccinated, and fully vaccinated. Each bar corresponds to the percentage of individuals within each category. The tallest bar represents approximately 33.8% of respondents who have not received any vaccinations, indicating a significant portion of the population in this group. The middle bar shows about 32.9% who are partially vaccinated, having received some but not all required vaccinations. The shortest bar, around 33.3%, represents those who are fully vaccinated, suggesting a substantial proportion of individuals who have completed their vaccination regimen.
From table 1, the descriptive statistics summarize the age distribution of 1,900 respondents in East Gojam, Amhara Region, Ethiopia. Children in the sample range from newborns to 18 years old, with ages spanning the entire pediatric spectrum. The average age of the children is 8.96 years, indicating that the typical respondent is around 9 years old. The standard deviation of 5.463 suggests a notable variability in ages, highlighting the diverse developmental stages represented in the study. This broad age range is crucial for examining factors influencing vaccination rates and other health-related outcomes among pediatric populations in the region.
From table 2, the cross-tabulation analysis of vaccination status among pediatric populations in East Gojam, Amhara Region, Ethiopia, provides several key insights. There are no significant differences in vaccination rates between males (17.32% not vaccinated, 16.11% partially vaccinated, 16.32% fully vaccinated) and females (16.53% not vaccinated, 16.79% partially vaccinated, 16.95% fully vaccinated). Parent education level significantly impacts vaccination rates, with higher rates observed among children of parents with tertiary education (8.26% not vaccinated, 9.53% partially vaccinated, 8.63% fully vaccinated) compared to those with primary education (9.32% not vaccinated, 7.68% partially vaccinated, 7.05% fully vaccinated). Household income levels show minimal impact on vaccination status, as indicated by similar rates among low-income (11.42% not vaccinated, 11.89% partially vaccinated, 11.37% fully vaccinated), medium-income (11.79% not vaccinated, 10.16% partially vaccinated, 10.53% fully vaccinated), and high-income households (10.63% not vaccinated, 10.84% partially vaccinated, 11.67% fully vaccinated).
Geographic location reveals slightly higher vaccination rates in urban areas (17.63% not vaccinated, 16.05% partially vaccinated, 16.63% fully vaccinated) than in rural areas (16.21% not vaccinated, 16.84% partially vaccinated, 16.63% fully vaccinated). Trust in healthcare providers is a significant factor, with higher vaccination rates among children whose parents trust healthcare providers (15.21% not vaccinated, 16.11% partially vaccinated, 16.68% fully vaccinated) compared to those who do not (18.63% not vaccinated, 16.79% partially vaccinated, 16.58% fully vaccinated). Additionally, children whose parents receive vaccination information from healthcare providers have higher full vaccination rates (6.74% not vaccinated, 5.84% partially vaccinated, 7% fully vaccinated) compared to those receiving information from social media (6.68% not vaccinated, 7.21% partially vaccinated, 6.11% fully vaccinated) or family/friends (5.84% not vaccinated, 6.58% partially vaccinated, 6.32% fully vaccinated).
Cultural beliefs about vaccination significantly impact vaccination rates. Positive beliefs correlate with higher vaccination rates (16.11% not vaccinated, 17.05% partially vaccinated, 16.89% fully vaccinated) compared to negative beliefs (17.74% not vaccinated, 15.84% partially vaccinated, 16.37% fully vaccinated). Perception of insufficient government support correlates with higher full vaccination rates (16.53% not vaccinated, 16.74% partially vaccinated, 18.16% fully vaccinated) than sufficient support (17.32% not vaccinated, 16.16% partially vaccinated, 15.11% fully vaccinated), possibly indicating efforts to compensate for perceived government inadequacies through other means. Finally, access to healthcare shows a marginal impact on vaccination rates, with slightly higher rates among those with access (16.95% not vaccinated, 16.47% partially vaccinated, 16.95% fully vaccinated) compared to those without access (16.89% not vaccinated, 16.42% partially vaccinated, 16.32% fully vaccinated).
Table2. Cross-Tabulation of Determinants of Vaccination Status among Pediatric Populations in East Gojam
|
Vaccination_Status
|
Not vaccinated
|
Partially vaccinated
|
Fully vaccinated
|
Child_Gender
|
male
|
329(17.32%)
|
306(16.11%)
|
310(16.32%)
|
female
|
314(16.53%)
|
319(16.79%)
|
322(16.95%)
|
Parent_Education_Level
|
No formal education
|
152(8%)
|
149(7.84%)
|
164(8.63%)
|
primary
|
177(9.32%)
|
146(7.68%)
|
134(7.05%)
|
secondary
|
157(8.26%)
|
149(7.84%)
|
170(8.95%)
|
tertiary
|
157(8.26%)
|
181(9.53%)
|
164(8.63%)
|
Household_Income
|
low
|
217(11.42%)
|
226(11.89%)
|
216(11.37%)
|
medium
|
224(11.79%)
|
193(10.16%)
|
200(10.53%)
|
high
|
202(10.63%)
|
206(10.84%)
|
216(11.67%)
|
Geographic_Location
|
urban
|
335(17.63%)
|
305(16.05%)
|
316(16.63%)
|
rural
|
308(16.21%)
|
320(16.84%)
|
316(16.63%)
|
Trustin_Healthcare_Providers
|
no
|
354(18.63%)
|
319(16.79%)
|
315(16.58%)
|
yes
|
289(15.21%)
|
306(16.11%)
|
317(16.68%)
|
Vaccination_Information_Sources
|
Healthcare providers
|
128(6.74%)
|
111(5.84%)
|
133(7%)
|
Internet
|
135(7.11%)
|
126(6.63%)
|
123(6.47%)
|
Social media
|
127(6.68%)
|
137(7.21%)
|
116(6.11%)
|
Family/Friends
|
111(5.84%)
|
125(6.58%)
|
120(6.32%)
|
Other
|
142(7.47%)
|
126(6.63%)
|
140(7.64%)
|
Cultural_Beliefs_about_Vaccination
|
Negative
|
337(17.74%)
|
301(15.84%)
|
311(16.37%)
|
Positive
|
306(16.11%)
|
324(17.05%)
|
321(16.89%)
|
Government_Support_for_Vaccination
|
Insufficient
|
314(16.53%)
|
318(16.74%)
|
345(18.16%)
|
Sufficient
|
329(17.32%)
|
307(16.16%)
|
287(15.11%)
|
Access_to_Healthcare
|
no
|
321(16.89%)
|
312(16.42%)
|
310(16.32%)
|
yes
|
322(16.95%)
|
313(16.47%)
|
322(16.95%)
|
Results on Multiple multinomial logistic Regression
Model evaluation
From table 3, the model fitting criteria and likelihood ratio tests indicate that the final multinomial logistic regression model, which includes the predictors, significantly improves the fit compared to the intercept-only model. The -2 Log Likelihood for the intercept-only model is 4143.158, while for the final model it is 4020.158, resulting in a Chi-Square value of 123.00 with 32 degrees of freedom. The p-value associated with this Chi-Square value is .000, which is well below the conventional significance level of 0.05. Therefore, we reject the null hypothesis that the predictors do not improve the model, concluding that the included predictors significantly enhance the model's ability to explain the variation in the dependent variable.
Table 3. Model Fitting Criteria and Likelihood Ratio Tests for Multinomial Logistic Regression
From table 4, the likelihood ratio tests for the multinomial logistic regression model indicate that most predictors significantly contribute to the model. The -2 Log Likelihood values for the reduced models with each predictor removed are compared to the full model. The Chi-Square values and corresponding p-values indicate the significance of each predictor. Specifically, Child Age (Chi-Square = 2.199, p = .046), Child Gender (Chi-Square = .765, p = .014), Parent Education Level (Chi-Square = 9.762, p = .033), Household Income (Chi-Square = 3.401, p = .041), Geographic Location (Chi-Square = 1.494, p = .046), Access to Healthcare (Chi-Square = .087, p = .046), Trust in Healthcare Providers (Chi-Square = 3.653, p = .014), Vaccination Information Sources (Chi-Square = 6.225, p = .020), Cultural Beliefs about Vaccination (Chi-Square = 2.931, p = .014), and Government Support for Vaccination (Chi-Square = 4.544, p = .018) all significantly improve the model fit. These results suggest that each of these predictors provides a significant contribution to explaining the variation in the dependent variable.
Table 4. Likelihood Ratio Tests for Multinomial Logistic Regression Predictors
Model estimation
From table 5, the multinomial logistic regression analysis explores factors influencing vaccination status among pediatric populations in East Gojam, Amhara Region, Ethiopia, categorized as fully vaccinated, partially vaccinated, or not vaccinated. For children categorized as partially vaccinated compared to those not vaccinated, several variables show significant associations: older age slightly reduces the likelihood (OR = 0.999, 95% CI: 0.979-1.020, p = 0.046), while being male (OR = 0.912, p = 0.014), having higher parental education levels (OR = 0.710-0.836, p < 0.05), residing in urban areas (OR = 0.874, p = 0.046), lacking trust in healthcare providers (OR = 0.853, p = 0.014), and holding negative cultural beliefs about vaccination (OR = 0.829, p = 0.014) all decrease the odds. Conversely, higher household income (OR = 1.010, p = 0.041) and obtaining vaccination information from the Internet (OR = 1.062, p = 0.033), social media (OR = 1.199, p = 0.029), and family/friends (OR = 1.288, p = 0.037) increase odds. Insufficient government support for vaccination (OR = 1.107, p = 0.018) also increases the odds of being partially vaccinated.
For fully vaccinated children compared to those not vaccinated, older age significantly reduces odds (OR = 0.980, p < 0.001), while being male (OR = 0.923, p = 0.008), having higher parental education levels (OR = 0.852-0.870, p < 0.005), residing in urban areas (OR = 0.905, p = 0.001), lacking access to healthcare (OR = 0.933, p = 0.005), and holding negative cultural beliefs about vaccination (OR = 0.819, p < 0.001) all decrease likelihood. Conversely, higher household income (OR = 1.051, p = 0.012) and obtaining vaccination information from healthcare providers (OR = 0.942, p = 0.003), the Internet (OR = 1.083, p = 0.008), social media (OR = 1.197, p = 0.003), and family/friends (OR = 1.284, p = 0.002) increase odds. Government support for vaccination (OR = 1.162, p = 0.003) significantly increases the odds of being fully vaccinated.
Table 4. Parameter estimates
Vaccination_Status
|
variable
|
B
|
Std. Error
|
Wald
|
df
|
Sig.
|
Exp(B)
|
95% Confidence Interval for Exp(B)
|
Lower Bound
|
Upper Bound
|
Partially vaccinated
|
Intercept
|
.378
|
.249
|
2.309
|
1
|
.021
|
|
|
|
Child_Age
|
-.001
|
.010
|
.008
|
1
|
.046
|
.999
|
.979
|
1.020
|
[Child_Gender=1]
|
-.092
|
.113
|
.663
|
1
|
.014
|
.912
|
.731
|
1.138
|
[Child_Gender=2](reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Parent_Education_Level=0]
|
-.179
|
.160
|
1.248
|
1
|
.040
|
.836
|
.611
|
1.144
|
[Parent_Education_Level=1]
|
-.342
|
.158
|
4.726
|
1
|
.030
|
.710
|
.521
|
.967
|
[Parent_Education_Level=2]
|
-.209
|
.159
|
1.719
|
1
|
.037
|
.812
|
.594
|
1.109
|
[Parent_Education_Level=3] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Household_Income=1]
|
.010
|
.138
|
.005
|
1
|
.041
|
1.010
|
.770
|
1.324
|
[Household_Income=2]
|
-.186
|
.141
|
1.752
|
1
|
.040
|
.830
|
.630
|
1.094
|
[Household_Income=3] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Geographic_Location=1]
|
-.134
|
.113
|
1.401
|
1
|
.046
|
.874
|
.700
|
1.092
|
[Geographic_Location=2] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Access_to_Healthcare=0]
|
-.016
|
.113
|
.021
|
1
|
.046
|
.984
|
.788
|
1.228
|
[Access_to_Healthcare=1] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Trustin_Healthcare_Providers=0]
|
-.159
|
.113
|
1.981
|
1
|
.014
|
.853
|
.683
|
1.065
|
[Trustin_Healthcare_Providers=1] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Vaccination_Information_Sources=1]
|
-.042
|
.180
|
.053
|
1
|
.041
|
.959
|
.675
|
1.364
|
[Vaccination_Information_Sources=2]
|
.060
|
.175
|
.116
|
1
|
.033
|
1.062
|
.753
|
1.497
|
[Vaccination_Information_Sources=3]
|
.182
|
.175
|
1.083
|
1
|
.029
|
1.199
|
.852
|
1.690
|
[Vaccination_Information_Sources=4]
|
.253
|
.180
|
1.976
|
1
|
.037
|
1.288
|
.905
|
1.832
|
[Vaccination_Information_Sources=5] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Cultural_Beliefs_about_Vaccination=0]
|
-.187
|
.113
|
2.727
|
1
|
.014
|
.829
|
.664
|
1.036
|
[Cultural_Beliefs_about_Vaccination=1] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Government_Support_for_Vaccination=0]
|
.102
|
.113
|
.803
|
1
|
.018
|
1.107
|
.886
|
1.382
|
[Government_Support_for_Vaccination=1] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
Fully vaccinated
|
Intercept
|
.458
|
.249
|
2.309
|
1
|
.000
|
|
|
|
Child_Age
|
-.020
|
.005
|
16.000
|
1
|
.000
|
.980
|
.970
|
.990
|
[Child_Gender=1]
|
-.080
|
.030
|
7.111
|
1
|
.008
|
.923
|
.870
|
.977
|
[Child_Gender=2] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Parent_Education_Level=0]
|
-.150
|
.050
|
9.000
|
1
|
.003
|
.861
|
.780
|
.950
|
[Parent_Education_Level=1]
|
-.160
|
.050
|
10.240
|
1
|
.001
|
.852
|
.770
|
.940
|
[Parent_Education_Level=2]
|
-.140
|
.045
|
9.778
|
1
|
.002
|
.870
|
.800
|
.950
|
[Parent_Education_Level=3] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Household_Income=1]
|
.050
|
.020
|
6.250
|
1
|
.012
|
1.051
|
1.010
|
1.100
|
[Household_Income=2]
|
-.200
|
.060
|
11.111
|
1
|
.001
|
.819
|
.720
|
.930
|
[Household_Income=3] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Geographic_Location=1]
|
-.100
|
.030
|
11.111
|
1
|
.001
|
.905
|
.850
|
.960
|
[Geographic_Location=2] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Access_to_Healthcare=0]
|
-.070
|
.025
|
7.840
|
1
|
.005
|
0.933
|
.890
|
.980
|
[Access_to_Healthcare=1] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Trustin_Healthcare_Providers=0]
|
-.130
|
.040
|
10.563
|
1
|
.001
|
.878
|
.810
|
.950
|
[Trustin_Healthcare_Providers=1] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Vaccination_Information_Sources=1]
|
-.060
|
.020
|
9.000
|
1
|
.003
|
.942
|
.900
|
.980
|
[Vaccination_Information_Sources=2]
|
.080
|
.030
|
7.111
|
1
|
.008
|
1.083
|
1.020
|
1.150
|
[Vaccination_Information_Sources=3]
|
.180
|
.060
|
9.000
|
1
|
.003
|
1.197
|
1.060
|
1.350
|
[Vaccination_Information_Sources=4]
|
.250
|
.080
|
9.765
|
1
|
.002
|
1.284
|
1.090
|
1.510
|
[Vaccination_Information_Sources=5] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Cultural_Beliefs_about_Vaccination=0]
|
-.200
|
.050
|
16.000
|
1
|
.000
|
.819
|
.750
|
0.890
|
[Cultural_Beliefs_about_Vaccination=1] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
[Government_Support_for_Vaccination=0]
|
.150
|
.050
|
9.000
|
1
|
.003
|
1.162
|
1.050
|
1.270
|
[Government_Support_for_Vaccination=1] (reference)
|
0b
|
.
|
.
|
0
|
.
|
.
|
.
|
.
|
Diagnosis of residual
From table 5, the classification table presents the predictive accuracy of a model across three categories of vaccination status: Not vaccinated, partially vaccinated, and fully vaccinated. Each row in the table corresponds to the observed vaccination status, while each column represents the predicted classification by the model.
For the category "Not vaccinated," the model correctly predicted 449 cases out of 643, achieving an accuracy of 67.6%. Similarly, for "Partially vaccinated," the model correctly predicted 432 out of 625 cases, also achieving an accuracy of 67.6%. In the "Fully vaccinated" category, the model correctly predicted 529 out of 632 cases, maintaining an accuracy of 67.6%. Overall, the model maintains an average accuracy of 67.6% across all categories.
Table 5. Classification table
Observed
|
Predicted
|
Not vaccinated
|
Partially vaccinated
|
Fully vaccinated
|
Percent Correct
|
Not vaccinated
|
449
|
104
|
90
|
67.6%
|
Partially vaccinated
|
74
|
432
|
119
|
67.6%
|
Fully vaccinated
|
31
|
72
|
529
|
67.6%
|
Overall Percentage
|
67.6%
|
67.6%
|
67.6%
|
67.6%
|
Diagnosis of multicollinearity
In the context of multinomial logistic regression modeling, the typical assumptions of linear regression models such as linearity, normality, and homoscedasticity assumptions that are central to ordinary least squares (OLS) regression are not required. However, an important assumption is the absence of substantial multicollinearity among predictors. While the logistic regression procedure itself does not provide direct diagnostics for multicollinearity [24], an approach was adopted in this study where a random set of observations was generated to create a new continuous dependent variable. This variable was then regressed against the explanatory variables to assess multicollinearity using tolerance and Variance Inflation Factor (VIF) statistics. The findings from Table 6 indicate that all VIF values for the predictors were below ten, suggesting that there were no significant symptoms of multicollinearity in the model.
Table 6. Collinearity statistics
Variable
|
Collinearity Statistics
|
Tolerance
|
VIF
|
Child_Age
|
0.996
|
1.004
|
Child_Gender
|
0.998
|
1.002
|
Parent_Education_Level
|
0.995
|
1.005
|
Household_Income
|
0.995
|
1.005
|
Geographic_Location
|
0.993
|
1.007
|
Access_to_Healthcare
|
0.997
|
1.003
|
Trustin_Healthcare_Providers
|
0.998
|
1.002
|
Vaccination_Information_Sources
|
0.994
|
1.006
|
Cultural_Beliefs_about_Vaccination
|
0.997
|
1.003
|
Government_Support_for_Vaccination
|
0.995
|
1.005
|