## 4 Experimental Analysis
The following Table 1 shows the parameter estimation results of multinomial logistic regression analysis of two models, that is, medium-EMI (denoted by 'Class = 2') relative to weak-EMI (denoted by 'Class = 1') and high-EMI (denoted by 'Class = 3') relative to weak-EMI (denoted by 'Class = 1'), that is, weak-EMI is the base response. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Logit 1 (Class 2/Class 1)** & **Coefficient** & **Std. Error** & **t-Value** & \(p\)**-Value** & **95\% Conf. Interval** \\ \hline Constant & \(-47.089\) & \(14.562\) & \(-3.234\) & \(0.001\) & \(-75.630\) & \(-18.548\) \\ Area & \(-119.993\) & \(34.415\) & \(-3.487\) & \(0.000\) & \(-187.446\) & \(-52.541\) \\ Perimeter & \(117.116\) & \(35.142\) & \(3.333\) & \(0.001\) & \(48.239\) & \(185.992\) \\ Rectangle & \(16.981\) & \(5.672\) & \(2.994\) & \(0.003\) & \(5.865\) & \(28.098\) \\ Extend & \(99.605\) & \(26.771\) & \(3.721\) & \(0.000\) & \(47.134\) & \(152.076\) \\ Solidity & \(-23.303\) & \(9.242\) & \(-2.521\) & \(0.012\) & \(-41.416\) & \(-5.189\) \\ \hline
**Logit 2 (Class 3/Class 1)** & **Coefficient** & **Std. Error** & **t-Value** & \(p\)**-Value** & **95\% Conf. Interval** \\ \hline Constant & \(-42.351\) & \(14.465\) & \(-2.928\) & \(0.003\) & \(-70.702\) & \(-13.999\) \\ Area & \(-102.472\) & \(34.147\) & \(-3.001\) & \(0.003\) & \(-169.400\) & \(-35.544\) \\ Perimeter & \(97.804\) & \(34.683\) & \(2.820\) & \(0.005\) & \(29.827\) & \(165.781\) \\ Rectangle & \(21.816\) & \(6.316\) & \(3.454\) & \(0.001\) & \(9.438\) & \(34.194\) \\ Extend & \(96.730\) & \(27.277\) & \(3.546\) & \(0.000\) & \(43.267\) & \(150.192\) \\ Solidity & \(-28.523\) & \(10.313\) & \(-2.766\) & \(0.006\) & \(-48.736\) & \(-8.309\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of multinomial logistic regression analysis. Figure 4: Results of the 1 st edge detection. Figure 5: Comparison of EMI-generated SEM images. Several different types of goodness-of-fit measures have been developed since the conventional \(R^{2}\) cannot be applied to assess goodness of fit in logistic regression analysis. One of the popular goodness-of-fit measures in logistic regression analysis is [PERSON]'s pseudo-\(R\)-squared statistic based on the ratio of the log-likelihood functions as follows:  
\[R^{2}=1-\frac{\ln(L_{M})}{\ln(L_{0})} \tag{6}\]  
where \(L_{M}\) and \(L_{0}\) are the maximum log-likelihood functions for the full model and the intercept-only model (also called the null model), respectively. From the analysis results, it is found that [PERSON]'s pseudo-\(R\)-squared value of the fitted model is 0.245, and thus, we may conclude that the regression model fits the data moderately well since [PERSON]'s pseudo-\(R\)-squared value ranges from 0.2 to 0.4, which indicates a very good model fit [45]. And, to test whether all the regression coefficients of predictors in the fitted logistic regression model are simultaneously zero or not (i.e., \(H_{0}:\ \beta=0\) vs. \(H_{1}:\ \beta\
eq 0\)), the following log-likelihood ratio (i.e., LLR) statistic can be used:  
\[LLR=-2\text{ln}\bigg{(}\frac{L_{M}}{L_{0}}\bigg{)} \tag{7}\]  
The LLR \(p\)-value for testing the fitted full model (\(L_{M}\)) versus the intercept-only model (\(L_{0}\)) is \(5.800\text{e}\times 10^{-10}\), and thus, we can conclude that the model fits the data better than the intercept-only model since the LLR \(p\)-value is less than the significance level of \(\alpha=0.05\), that is, including all the measures as predictors significantly improves the model fit compared to the intercept-only model. Finally, all the estimates of regression coefficients of both 'Logit 1' and 'Logit 2' models are statistically significant at the significance level of 0.05. The estimated logistic models of the two classes are  
\[