6.3 BINARY LOGISTIC REGRESSION MODELS
6.3.1 Zimbabwe
6.3.1.1 Model 1
This model consists of the independent variable (use of social media) and is presented in two forms: Block 0, and Block 1. The Block 0 is a null model - that is one which only consists of the intercept, which in IBM SPSS is referred to as the constant. Table 6.16 below displays the Model 1 Block 0 output which consists of the classification table, variables in the equation and variables not in the equation.
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Table 6.16: Zimbabwe Model 1 Block 0
Classification Tablea,b
Observed
Predicted Mobile money adoption
Percentage Correct Non-adoption of Mobile Money technology Mobile Money Adoption Step 0 Mobile money adoption Non-adoption of Mobile
Money technology
1914 0 100.0
Mobile Money Adoption 1836 0 .0
Overall Percentage 51.0
a . Constant is included in the model. b. The cut value is .500
Variables in the Equation
B S.E. Wald Df Sig. Exp(B)
Step 0 Constant -.342 .0115 10.692 1 .001 .710
Variables not in the Equation
Score Df Sig.
Step 0 Variables Use of social media 424.751 1 .000
Overall Statistics 424.751 1 .000
Source: Authorโs compilation
The classification table shown in Table 6.16 above indicates how well the null model predicted mobile money adoption in Zimbabwe. Given the base rates of the two decision options of adoption or non-adoption, (1836/3750 = 49% chose to adopt mobile money adoption while 51% did not), and with no other information, the best strategy was to predict, for every case, that an individual would choose to adopt mobile money. Using that strategy, the model would be correct 51% of the time. Thus, the overall percent of cases that were correctly predicted by the null was 51%, and it could be concluded that the model was valid, and therefore a good fit for the data which could be replicated.
In Table 6.16 above, the intercept-only model is displayed under the Variables in the Equation section. The Wald Chi-square tests the null hypothesis that the constant
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equals zero. This hypothesis was rejected because Table 6.16 above shows that the p-value (0.001) was less than the critical value of 0.05. Therefore, the study concluded that the constant was not zero and the predicted odds of mobile money adoption for Zimbabwe in Model 1 Block 0 were 0.710. The Score test under the Variables not in the Equation section in Table 6.16 above was used to predict whether or not the independent variable would be significant in the model. Considering the p-values, the use of social media variable (0.000) was statistically significant at 5%. The overall statistics p-value of 0.000 shows the result of adding the use of social media (independent variable) to the null model, and in this case, it was statistically significant at 5% level.
The Model 1 Block 1 shows the results of the binary logistic regression model following the addition of the selected independent variable โ use of social media, and these are displayed in Table 6.17 below.
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Table 6.17: Zimbabwe Model 1 Block 1
Omnibus Tests of Model Coefficients
Chi-square df Sig.
Step 1 Step 442.134 1 .000
Block 442.134 1 .000
Model 442.134 1 .000
Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 4754.847a .111 .168
a. Estimation terminated at iteration number 4 because parameter estimates changed by less than .001.
Hosmer and Lemeshow Test
Step Chi-square Df Sig.
1 .000 0 .
Classification Tablea
Observed
Predicted Mobile money adoption
Percentage Correct Non-adoption of Mobile Money technology Mobile Money Adoption Step 1 Mobile money adoption Non-adoption of Mobile
Money technology
1691 223 88.3
Mobile Money Adoption 1079 757 41.2
Overall Percentage 65.3
a. The cut value is .500
Table 6.17 continued
Variables in the Equation
B S.E. Wald df Sig. Exp(B)
Step 1a Use of social media 1.671 .386 81.491 1 .000 5.317
Constant -.449 .039 13.963 1 .000 .638
a. Variable(s) entered on step 1: Use of social media.
Source: Authorโs compilation
The Omnibus tests of model coefficients give the result of the likelihood ratio test which indicates whether the addition of the independent variable (use of social media) contributes significantly to an improvement in the model fit. As indicated in Table 6.17 above, the Omnibus tests of model coefficients provided a Chi-Square of
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442.134 on 1 df, a p-value of the block (use of social media) of 0.000 which was less than the 0.05 significance level. This means that the Model 1 Block 1 was a significant improvement from Model 1 Block 0, with the use of social media positively and significantly influencing mobile money adoption in Zimbabwe. The block and step p-values were equal to the model value since all variables (constant and independent) were entered at the same time.
The model summary provided in Table 6.17 above indicates that the addition of the use of social media variable to the null model reduced the -2 Log likelihood statistic to 4754.847 from 5196.981 (4754.847 + 442.134 in the Omnibus tests of model coefficients) in the null model. Thus, a reduction of the -2 log likelihood statistic reflects an improvement in the model fit following the addition of the independent variable. In standard regression, the coefficient of regression ๐ 2 value gives an indication of how much variation in the dependent variable is explained by the model. The study notes that the coefficient of regression ๐ 2 cannot be calculated for binary logistic regression. However, the model summary in Table 6.17 provides the values of two pseudo ๐ 2 which try to measure something similar. The pseudo ๐ 2 values are thus approximations and should not be overly emphasised. This study used the Nagelkerke ๐ 2. According to Model 1 Block 1 in Table 6.17 above, the Nagelkerke ๐ 2
of the independent variable (use of social media) accounted for 16.8% of the variance in mobile money technology adoption decision in Zimbabwe. This value is low, implying a poor fit of the model; 83.2% of the variance in mobile money technology adoption decision was accounted for by other variables not included in Model 1 Block 1.
At a 95% confidence level, the Hosmer and Lemeshow test (see Table 6.17) reflected no statistical significance owing to the inclusion of only the social media in Model 1 Block 1, necessitating further blocks of the binary logistic regression estimation. Table 6.17 above shows the false positive and false negative error rates in classification, where a false positive would predict that a non-adopter individual would decide to use mobile money technology, when in fact they would not. As reflected in Table 6.17, the decision rule predicted a decision of mobile money technology adoption 980 times; the prediction was wrong 223 times. Therefore, there was a false positive of 22.8% (223/980). A false negative would predict that an
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individual would decide not to adopt mobile money technology, when in fact they would do so. The decision rule predicted the non-adoption of mobile money technology 2770 times. That prediction was wrong 1079 times, a false negative rate of 39% (1079/2770). The overall model correct classification for Model 1 Block 1 was 65.3%. Thus, Model 1 Block 1 was an improvement in the model fit compared to the null model.
As indicated in the Variables in the Equation section in Table 6.17, the B-values are the log-odds for the binary logistic regression equation for predicting mobile money adoption in Zimbabwe based on the use of social media. These estimates show the extent of the relationship between mobile money adoption and the use of social media, where the mobile money adoption variable is on the logistic scale. In terms of the Wald test, the coefficient of social media was statistically significant at the 95% confidence level, meaning that the independent variable was a significant predictor of mobile money technology adoption decision in Zimbabwe. The study concluded that use of social media variable had a positive (B = 1.671) and statistically significant effect (p-value =0.000) on mobile money adoption in Zimbabwe. Therefore, for every one-unit increase in the use of social media, a 5.317 increase in the log-odds of mobile money adoption was expected. The fitted Model 1 Block 1 equation is shown below:
Mobile money adoption = -0.449 + 1.671 ร Use of social media (10)