4.3. Binary Logistic Regression Analysis
In
Table 5, the Case Processing Summary indicates that all 264 cases in the dataset were included in the logistic regression analysis, and there were no missing cases or unselected cases.
In
Table 6, the purpose of encoding the dependent variable is to represent the different categories or responses numerically so that they can be used in the logistic regression analysis. By assigning the internal values of 0 and 1 to the original values, the logistic regression model can estimate the relationship between the predictors (independent variables) and the likelihood of the dependent variable being “YES” based on the given encoding.
In
Table 7, “I prefer not to say” is the reference category, indicated by a frequency of 4. The parameter coding for this category is (1.000, .000), which means that when compared to the reference category, there is no difference in the parameter estimates for this category. “MALE” has a frequency of 124. The parameter coding for this category is (.000, 1.000), indicating that when compared to the reference category (“I prefer not to say”), the parameter estimate for this category is 1.000.
“FEMALE” has a frequency of 136. The parameter coding for this category is (.000, .000), indicating that when compared to the reference category (“I prefer not to say”), there is no difference in the parameter estimates for this category.
These parameter codings allow the logistic regression model to estimate the effects of each category of the categorical variable on the likelihood of the dependent variable being “YES” (as encoded earlier).
The “Omnibus Tests of Model Coefficients” in Table 8 presents the results of the omnibus tests conducted on the coefficients of the logistic regression model.
The chi-square statistic is a measure of the overall goodness-of-fit of the logistic regression model. In this table, the chi-square value is 51.010.
The degrees of freedom (df) represent the number of parameters estimated in the model. In this case, there are 8 degrees of freedom.
The significance level(Sig), also known as p-value, indicates the probability of observing the obtained chi-square value or a more extreme value under the null hypothesis of no relationship between the predictors and the dependent variable. In this analysis, the p-value is reported as .000, which means the obtained chi-square value is statistically significant at the chosen significance level.
Therefore, the omnibus tests of model coefficients suggest that the logistic regression model, as a whole, is statistically significant in predicting the dependent variable. The chi-square test indicates that the observed relationship between the predictors and the dependent variable is unlikely to have occurred by chance alone. Therefore, there is evidence to support the conclusion that the predictors included in the model have a significant influence on the likelihood of the dependent variable being “YES” (as encoded earlier).
Table 9 shows the “Model Summary” which provides information about the fit and predictive ability of the logistic regression model. The step (1) number indicates the iteration of the model. In this case, there is only one step included in the model.
The -2 log likelihood is a measure of the overall fit of the logistic regression model. It represents the log of the likelihood function multiplied by -2, and lower values indicate a better fit. In this analysis, the -2 log likelihood value is 213.756.
The Cox & Snell R Square is a measure of the proportion of variance in the dependent variable( vegetarian decision) that is accounted for by the logistic regression model. It ranges from 0 to 1, with higher values indicating a better fit. In this analysis, the Cox & Snell R Square is reported as .176, indicating that the model explains approximately 17.6% of the variance in the dependent variable.
The Nagelkerke R Square is an adjusted version of the Cox & Snell R Square, which takes into account the number of predictors and the sample size. It also ranges from 0 to 1, with higher values indicating a better fit. In this analysis, the Nagelkerke R Square is reported as .277, suggesting that the model explains approximately 27.7% of the variance in the dependent variable.
Additionally, estimation process terminated after 6 iterations because the parameter estimates changed by less than .001. This indicates that the model has reached a stable state and further iterations are not necessary. The logistic regression model shows a reasonably good fit based on the -2 log likelihood value. The Cox & Snell R Square and Nagelkerke R Square values suggest that the model explains a moderate amount of the variance in the dependent variable ranging from 17.6% to 27.7%. However, it is circumspect to note that the model may not capture all factors influencing the dependent variable, and there may be unexplained variance.
Table 10 presents The “Hosmer and Lemeshow Test” which is used to assess the goodness-of-fit of a logistic regression model by comparing the observed and expected frequencies of the dependent variable across groups defined by predicted probabilities. The step number indicates the iteration of the model. In this case, there is only one step included in the model. The chi-square statistic is calculated based on the differences between the observed and expected frequencies in the groups. In this analysis, the chi-square value is 7.742. The degrees of freedom represent the number of categories minus the number of estimated parameters. In this case, there are 8 degrees of freedom. The significance level, also known as p-value, indicates the probability of observing the obtained chi-square value or a more extreme value under the null hypothesis of good fit. In this analysis, the p-value is reported as .459, which is above the conventional threshold of .05. The Hosmer and Lemeshow Test assesses whether there is evidence of a lack of fit between the observed and expected frequencies in the logistic regression model. In this case, the test yields a non-significant result with a p-value of .459. This suggests that there is no significant lack of fit, indicating that the observed and expected frequencies are consistent with each other and
the model provides a good fit to the data.
Table 11 presents the “Variables in the Equation” and gives information about the coefficients, standard errors, Wald statistics, degrees of freedom, p-values, and odds ratios of the variables included in the logistic regression equation.
The logistic regression result describes the association between the independent factors (GENDER, RELIGION, MOOD, ENVIRONMENT, HEALTH, SOCIAL, ANIMAL WELFARE) and the dependent variable (Vegetarian diet decision).
In the logistic regression analysis output, the coefficient for the variable “ANIMAL WELFARE” is 0.713, with a standard error of 0.307. The Wald statistic value is 5.398, and the related p-value is 0.020. This suggests that the variable “ANIMAL WELFARE” has a statistically significant association with the decision to pursue a vegetarian diet. The odds ratio (Exp(B)) is 2.041, which suggests that for every one-unit increase in the “ANIMAL WELFARE” variable, the odds of adopting a vegetarian diet rise by nearly 104.1%. The 95% confidence interval for the odds ratio ranges from 1.118 to 3.725.
From the results of the analysis, variable “HEALTH” has a coefficient of -0.683 and a standard error of 0.221. The Wald statistic value is 9.58, with a p-value of 0.002 correspondingly. This suggests that the variable “HEALTH” has a highly significant association with the decision of becoming vegetarian. The odds ratio (Exp(B)) is 0.505, which implies a one-unit increase in the “HEALTH” variable reduces the likelihood of selecting a vegetarian diet by approximately 49.5%. The odds ratio has a 95% confidence interval of 0.328 to 0.778. These findings imply that the perceived value of health, as well as concern for animal welfare, have a major impact on the decision to eat a vegetarian diet. Higher perceived health advantages are connected with a lower likelihood of eating vegetarian, but greater concern for animal welfare is associated with a higher likelihood of eating vegetarian.
The results show that the variable “ENVIRONMENT” has a coefficient of 0.518 and a standard error of 0.325. The Wald statistic is 2.547, and the associated p-value is 0.11. This implies that, at the standard significance level p < 0.05, the factor “ENVIRONMENT” has no statistically significant link with the decision to follow a vegetarian diet. The odds ratio (Exp(B)) is 1.679, indicating that a one-unit increase in the “ENVIRONMENT” variable increases the likelihood of adopting a vegetarian diet by about 67.9%. However, it cannot be inferred that this association is statistically significant because the p-value is more than 0.05. However, the variable “SOCIAL Peer” has a coefficient of -0.076 and a standard error of 0.203. The Wald statistic is 0.141, and the associated p-value is 0.707. This means that the variable “SOCIAL” has no statistically significant link with the decision to eat a vegetarian diet. The odds ratio (Exp(B)) is 0.927, indicating that a one-unit increase in the “SOCIAL” variable reduces the likelihood of selecting a vegetarian diet by approximately 7.3%. However, since the p-value is greater than 0.05, the relationship is not considered statistically significant. When it comes to the variable “RELIGION”, the results show that it has a coefficient of 0.075 and a standard error of 0.165. The Wald statistic is 0.207, and the associated p-value is 0.649. This means that the variable “RELIGION” has no statistically significant link with the decision to eat a vegetarian diet. The odds ratio (Exp(B)) is 1.078, showing that a one-unit increase in the “RELIGION” variable increases the probabilities of adopting a vegetarian diet by 7.8%. The association, however, is not statistically significant because the p-value is bigger than 0.05. Lastly, the variable “MOOD” has a coefficient of 0.371 and a standard error of 0.235. The Wald statistic is 2.499, and the associated p-value is 0.114. This implies that the variable “MOOD” has no statistically significant link with the decision to eat a vegetarian diet. The odds ratio (Exp(B)) is 1.45, indicating that a one-unit increase in the “MOOD” variable increases the likelihood of selecting a vegetarian diet by about 45%. The association, however, is not statistically significant because the p-value is bigger than 0.05. It seems that the factors ENVIRONMENT, SOCIAL, RELIGION, and MOOD do not have a statistically significant link with the decision to follow a vegetarian diet, according to the logistic regression analysis.
4.4. Robustness Test
Multivariate Regression Analysis:
Model Summary |
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
Durbin-Watson |
1 |
.392(a) |
0.153 |
0.134 |
0.374 |
1.397 |
a Predictors: (Constant), RELIGION, ANIMAL WELFARE, MOOD, HEALTH, SOCIAL PEER, ENVIRONMENT |
b Dependent Variable: Do you consider yourself a vegetarian or a vegan?(Vegetarian in this case includes Lacto, Lacto-Ovo, Ovo, and Vegan as defined above.) |
The correlation coefficient (R) is 0.392, indicating a moderate positive correlation between the predictors and the dependent variable. The coefficient of determination (R Square) is 0.153, indicating that approximately 15.3% of the variance in the dependent variable can be explained by the predictors in the model. The adjusted R Square is 0.134, which takes into account the number of predictors in the model. It suggests that approximately 13.4% of the variance in the dependent variable is explained by the predictors, adjusted for the model’s complexity. The standard error of the estimate is 0.374, which represents the average distance between the observed values and the predicted values. The Durbin-Watson statistic is 1.397, which is close to 2.0. It indicates that there is no significant autocorrelation present in the residuals. Therefore the model accounts for a moderate amount of variance in the dependent variable, but there may be other factors not included in the model that also contribute to the prediction. The absence of autocorrelation suggests that the residuals are independent and do not exhibit any systematic pattern.
ANOVA |
Model |
|
Sum of Squares |
df |
Mean Square |
F |
Sig. |
1 |
Regression |
6.495 |
6 |
1.082 |
7.757 |
.000 |
|
Residual |
35.865 |
257 |
0.14 |
|
|
|
Total |
42.36 |
263 |
|
|
|
a Dependent Variable: Do you consider yourself a vegetarian or a vegan?(Vegetarian in this case includes Lacto, Lacto-Ovo, Ovo, and Vegan as defined above.) |
b Predictors: (Constant), RELIGION, ANIMAL WELFARE, MOOD, HEALTH, SOCIAL, ENVIRONMENT |
The regression component accounts for 6.495 units of variation, with 6 degrees of freedom. The mean square is 1.082. The F-statistic is 7.757, and the associated p-value is 0.000. This indicates that the regression model is statistically significant in predicting the dependent variable. The residual component accounts for 35.865 units of variation, with 257 degrees of freedom. The mean square is 0.140. The total variation in the dependent variable is 42.360 units, with a total of 263 degrees of freedom. Overall, the significant F-statistic suggests that the independent variables (Religion, ANIMAL Welfare, Mood, Health, Social peer, Environment) collectively have a significant impact on predicting the dependent variable (considering oneself as a vegetarian or a vegan).
Coefficients |
Variables |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
Collinearity Statistics |
B |
Std. Error |
Beta |
Tolerance |
VIF |
(Constant) |
-0.113 |
0.099 |
|
-1.14 |
0.255 |
|
|
Animal Welfare |
0.083** |
0.035 |
0.229 |
2.366 |
0.019 |
0.351 |
2.848 |
Social Peer |
-0.004 |
0.027 |
-0.011 |
-0.134 |
0.894 |
0.482 |
2.073 |
Health |
-0.095*** |
0.028 |
-0.266 |
-3.465 |
0.001 |
0.561 |
1.784 |
Environment |
0.065* |
0.039 |
0.17 |
1.656 |
0.099 |
0.311 |
3.217 |
Mood |
0.040 |
0.027 |
0.116 |
1.48 |
0.14 |
0.534 |
1.873 |
Religion |
-0.011 |
0.022 |
-0.037 |
-0.477 |
0.633 |
0.554 |
1.805 |
*,** and *** represent statistical significance at 10%, 5% and 1% respectively. |
The regression output provides information about the coefficients of the independent variables (Animal Welfare, Social peer, Health, Environment, Mood, and Religion) and their relationship with the dependent variable (Vegetarian Decision). The Collinearity Statistics suggest that there is no significant issue with multicollinearity in the model. The predictor variables demonstrate acceptable levels of independence from each other, which strengthens the reliability of the regression coefficients and their interpretations. The coefficients represent the estimated effect of each independent variable on the dependent variable, while the standardized coefficients (Beta) provide a measure of the relative importance of each independent variable in predicting the dependent variable. In this model:
Animal Welfare has a positive coefficient of 0.083, indicating that an increase in ethical and animal welfare considerations is associated with a higher likelihood of considering oneself a vegetarian. This coefficient is statistically significant (p < 0.05), suggesting a meaningful impact.
Social peer influence variable(family and friends) has a small negative coefficient of -0.004, suggesting a weak negative relationship with the likelihood of being a vegetarian. However, this coefficient is not statistically significant (p > 0.05), indicating that Social connections may not have a significant effect.
Health has a negative coefficient of -0.095, indicating that higher Health concerns are associated with a lower likelihood of being a vegetarian. This coefficient is statistically significant (p < 0.001), indicating a significant impact. Students might worry that the complete exclusion of conventional animal proteins might weigh on their health.
The environmental variable has a positive coefficient of 0.065, suggesting that greater environmental concerns are associated with a higher likelihood of being a vegetarian. However, this coefficient is not statistically significant (p > 0.05), indicating that the relationship may not be significant.
The mood variable has a positive coefficient of 0.040, suggesting a small positive relationship with the likelihood of being a vegetarian. However, this coefficient is not statistically significant (p > 0.05), indicating that Mood may not have a significant effect.
Religion has a small negative coefficient of -0.011, suggesting a weak negative relationship with the likelihood of being a vegetarian. However, this coefficient is not statistically significant (p > 0.05), indicating that Religion may not have a significant effect.
Overall, the regression analysis indicates that animal welfare and health are major factors determining the likelihood of being a vegetarian. However, it is crucial to stress that the importance and degree of these associations should be taken with caution, taking into account the study’s specific context and constraints.