DETERMINANT OF SUKUK RATINGS
V. EMPIRICAL RESULT AND INTERPRETATIONS
V.1. Screening for Normality, Collinearity, Homoscedasticity, Outliers and Extreme Values
- Outliers and Extreme Values
We use the Steam-and-Leaf Plot graph of SPSS to explore the raw data for individual extreme values and influential outliers» cases. Several extreme values and outliers were identified from the raw data. Touray (2004) with reference to Tabachnick and Fidel (1989) noted that deleting individual influential outlier cases or single variables that contain most of the influential cases is one of several ways of reducing outlier influence. As mentioned earlier, this further reduced our sample size to 30 valid observations.
- Normality
Touray (2004) with reference to Tabachnick and Fidel (1989) indicated that group data distributions are better evaluated using graphical methods; this allow as to see the overall shape distributions and help in deciding on the appropriate transformation type. Since our data distributions has shown considerable level of left-side skewness, the decision to transform the variables was taken, and Logarithmic and Square Root transformations were used, based on Touray (2004) with reference to McLeay and Omar (1999). This finding is supported also by Gujarati (1995). After the transformation, we computed the two normality test again and plotted the graphs as appear in Error! Reference source not found.Error! Reference source not found.Error! Reference source not found.Error! Reference source not found.Error! Reference source not found. and Error! Reference sourceError! Reference sourceError! Reference sourceError! Reference sourceError! Reference source not found.
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- Collinearity and Homoscedasticity
Using Pearson Correlation matrix for the raw and transformed data separately show in Table V.2 and Table V.3. No high significant correlation among variables both raw and transformed data. Gujarati (2003) mentioned in his book if the correlation that high correlation between variables is above 0.8.
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Determinant of Sukuk Ratings
Table V.2
Pearson Correlation matrix
ASET Pearson Correlation 1 -.070 -.120 -.129 -.137 -.083
Sig. (2-tailed) .674 .486 .441 .413 .620
N 38 38 36 38 38 38
BETA Pearson Correlation -.070 1 -.240 -.050 -.403* .404*
Sig. (2-tailed) .674 .159 .761 .012 .012
N 38 39 36 39 38 38
INTCOV Pearson Correlation -.120 -.240 1 .132 .425** -.485**
Sig. (2-tailed) .486 .159 .442 .010 .003
N 36 36 36 36 36 36
RATGUAR1 Pearson Correlation -.129 -.050 .132 1 .217 .159
Sig. (2-tailed) .441 .761 .442 .191 .339
N 38 39 36 39 38 38
ROA Pearson Correlation -.137 -.403* .425** .217 1 -.311
Sig. (2-tailed) .413 .012 .010 .191 .057
N 38 38 36 38 38 38
LTLEV Pearson Correlation -.083 .404* -.485** .159 -.311 1
Sig. (2-tailed) .620 .012 .003 .339 .057
N 38 38 36 38 38 38
ASET BETA INTCOV RATGUAR1 ROA LTLEV
*. Correlation is significant at the 0.05 level (2-tailed).
**. Correlation is significant at the 0.01 level (2-tailed).
Table V.3
Pearson Correlation matrix
LNASSET Pearson Correlation 1 -.440* .200 -.102 -.018 .571** -.170
Sig. (2-tailed) .012 .229 .573 .915 .000 .308
N 38 32 38 33 38 38 38
LNROA Pearson Correlation -.440* 1 -.334 .451* -.149 -.152 .438*
Sig. (2-tailed) .012 .061 .012 .414 .405 .012
N 32 32 32 30 32 32 32
SQBETA Pearson Correlation .200 -.334 1 -.452** .354* .158 -.095
Sig. (2-tailed) .229 .061 .008 .025 .342 .561
N 38 32 40 33 40 38 40
LNCOV Pearson Correlation -.102 .451* -.452** 1 -.654** .061 .116
Sig. (2-tailed) .573 .012 .008 .000 .735 .520
N 33 30 33 33 33 33 33
SQLEV Pearson Correlation -.018 -.149 .354* -.654** 1 -.104 .026
Sig. (2-tailed) .915 .414 .025 .000 .534 .873
N 38 32 40 33 40 38 40
LNREC Pearson Correlation .571** -.152 .158 .061 -.104 1 .068
Sig. (2-tailed) .000 .405 .342 .735 .534 .685
N 38 32 38 33 38 38 38
RATGUAR1 Pearson Correlation -.170 .438* -.095 .116 .026 .068 1
Sig. (2-tailed) .308 .012 .561 .520 .873 .685
N 38 32 40 33 40 38 40
LNASSET LNROA SQBETA LNCOV SQLEV LNREC RATGUAR1
*. Correlation is significant at the 0.05 level (2-tailed).
**. Correlation is significant at the 0.01 level (2-tailed).
V.2. Assessing the Multinomial Logistic Regression Result (significance tests) V.2.1. Interpretation of Result (Parameter Estimates)
The result in the parameter estimates is extracted here as shown below:
Equation 1 Predicted logit (AA/A), AA contrasted to A
= 4.76 + (1.877)*lnasset + (-13.9)*sqbeta + (-4.96)*ratguar*D Equation 2 Predicted logit (AAA/A), AAA contrasted to A
= 12.5 + (4.877)*lnasset + (-49.7)*sqbeta + (-29.3)*ratguar*D
According to the signs of coefficients of the M-Logit model here, the log of the odds of getting AAA or AA compared to getting A rating is positively related to total asset and negatively related to beta and bond guarantee status. Only three variables are selected as significant variable in determining bond rating. The negative coefficient associated with dummy independent variable (guarantee status) suggest that, holding all other variables constant, sukuk without guarantee are less likely to get an AAA rating as compared to get A rating. The positive coefficient tells the opposite. The above statistical significance findings are not to be taken seriously because Wald statistic is said to be inaccurate sometimes especially when coefficients are larger as seen in Table V.4. Our final conclusion is base on the model as well as individual independent significance test using Likelihood Ratio.
Table V.4 Parameter Estimates
2.00 Intercept 4.759 4.781 .991 1 .320
SQBETA -13.918 6.738 4.267 1 .039 9.02E-007 1.66E-012 .490
LNASSET 1.877 1.086 2.988 1 .084 6.537 .778 54.950
[RATGUAR1=.00] -4.963 2.695 3.391 1 .066 .007 3.55E-005 1.377
[RATGUAR1=1.00] 0b - - 0 - - - -
3.00 Intercept 12.516 12.435 1.013 1 .314
SQBETA -49.683 47.004 1.117 1 .291 2.65E-022 2.59E-062 2.709E+018
LNASSET 4.877 5.863 .692 1 .406 131.194 .001 12848646.39
[RATGUAR1=.00] -29.304 .000 - 1 - 1.88E-013 1.88E-013 1.88E-013
[RATGUAR1=1.00] 0b - - 0 - - - -
RATINGa B Std. Error Wald df Sig. Exp(B)
a. The reference category is: 1.00.
b. This parameter is set to zero because it is redundant.
95% Confidence Interval for Exp(B) Lower Bound
Upper Bound
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Determinant of Sukuk Ratings
V.2.2. Testing overall fit
The 2-log-likelihood value shown below is examined to determine the improvement of the final M-Logit model over the intercept term only and thus it is an overall model test. As can be seen from the table below, the difference between the value of Chi-Square in Table V.5 column 3 is 42.269 with 6 degrees of freedom is highly significant (p<0.000). Therefore, since the observed significance level is very small, we can reject the null hypothesis that the effects of all coefficients in the model are zero and hence conclude that our final model is significantly better than the intercept only model.
Table V.5 2 Log Likelihood
Intercept Only 61.742
Final 19.473 42.269 6 .000
Model
Likelihood Ratio Tests Model Fitting
Criteria
-2 Log Likelihood Chi-Square df Sig.
V.2.3. Testing the significance of Individual coefficients.
The Likelihood Ratio test shown in table below presents the test result for the effect of individual independent variables in the final model. The -2-Log-Likelihood is highly significant with (p<0,000) for beta, (p<0.001) for rating guarantor and (p<0.006) for total asset. As mentioned earlier, Norusis (1999) indicated that the Likelihood Test method not only provides an overall significant test for the model, but also it provides the most accurate and reliable test for the effect of individual independent variables in the model. As shown in Table V.6.
Table V.6 Likelihood Ratio Test
Intercept 19.473(a) .000 0 .
LNASSET 29.629 10.156 2 .006
SQBETA 43.066 23.593 2 .000
RATGUAR1 34.652 15.179 2 .001
Effect
Likelihood Ratio Tests Model Fitting
Criteria -2 Log Likelihood of Reduced Model
Chi-Square df Sig.
The Pseudo-R2 test shows the measurement from Cox and Snell, Negelkerke and McFadden»s Pseudo-R2. As seen in the table McFadden»s R2 is about 67%, Negelkerke R2 is about 86.1% and Cox and Snell is about 75.6%. Thus, we can say that our model has explained on average more than half of the variations observed in the dependent variables based on Pseudo-R2.
V.2.4. M-Logit Model Classification Result
Table V.7 presents the prediction results of the estimated M-Logit coefficients in the previous section. The columns are the predicted values and the rows are the actual values. The result shows 80% (24/30) of all valid cases are correctly classified into their original rating classes. The highest correct classification rate is in AAA rating category in which 83.3% (5/6) of all cases in that group being correctly classified. Next to that is the A rating category with 81.8% (9/11) of all cases in that group being correctly classified. The lowest hit rate is AA rating category, with few different from other categories 76.9% (10/13) of all cases in that group being correctly classified.