## 5 Classification of Selected Household Characteristics
### Accuracy Measures  
For the purpose of model evaluation, four performance measures were used, i.e., classification accuracy, sensitivity, specificity and area under the ROC curve (AUC) [27]. For the binary classification problem, i.e., having positive class and negative class, four possible outcomes exist, as shown in Table 4.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{2}{c}{**Predicted Value**} \\ \cline{3-4}  & & **Positive (P)** & **Negative (N)** \\ \hline \multirow{2}{*}{**Real Value**} & **Positive (P)** & True positive (TP) & False negative (FN) \\  & **Negative (N)** & False positive (FP) & True negative (TN) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Confusion matrix for binary classification.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Category**} & \multicolumn{2}{c}{**Person’s Age**} & **Number of Appliances** \\ \cline{2-3}  & **What Age Were You on Your Last Birthday?** &
\begin{tabular}{c} **Approximately How Many** \\ **Appliances Are in Your Home?** \\ \end{tabular} \\ \hline
1 & 18–35 & \(\leq\)8 appliances \\
2 & 36–65 & between 9 and 11 \\
3 & 65+ & \(>\)11 appliances \\ \hline \multirow{2}{*}{**Category**} & \multicolumn{2}{c}{**Number of Bedrooms**} & **Floor Area** \\ \cline{2-3}  & **How many bedrooms are in your home?** &
\begin{tabular}{c} **Approximately what is the area of** \\ **your home?** \\ \end{tabular} \\ \hline
1 & \(\leq\)2 bedrooms & Not available \\
2 & 3 bedrooms & \(<\)100 m\({}^{2}\) \\
3 & 4 bedrooms & between 100 m\({}^{2}\) and 200 m\({}^{2}\) \\
4 & \(\geq\)5 bedrooms & \(>\)200 m\({}^{2}\) \\ \hline \multirow{2}{*}{**Category**} & **Employment** & **Family type** \\ \cline{2-3}  & **What is the employment status of the chief** & **What best describes the people you** \\ \multicolumn{3}{c}{**income earner in your household?**} & **live with?** \\ \hline \multirow{2}{*}{1} & An employee, Self-employed (with employees), & I live alone \\ \cline{2-3}  & Self-employed (with no employees) & \\ \hline \multirow{2}{*}{2} & Unemployed (actively seeking work), & All people in my home are over 15 \\  & Unemployed (not actively seeking work), Retired, & years of age, both adults and children \\ \cline{2-3}  & Carer: Looking after relative family & under 15 years of age live in my home \\ \hline \multirow{2}{*}{**Category**} & **House Age** & **House Type** \\ \cline{2-3}  & **Approximately how old is your home?** & **Which best describes your home?** \\ \hline
1 & \(\leq\)30 years & Semi-detached house, Terraced house \\ \hline
2 & \(>\)30 years &
\begin{tabular}{c} Apartment, Detached house, \\ Bungalow \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 3: Questionnaire questions and their corresponding category labels.  
Based on Table 4, the accuracy (AC) measure can be computed, which is the proportion of the total number of predictions that were correct:  
\[AC=\frac{TP+TN}{TP+FP+TN+FN}. \tag{5}\]  
AUC estimation requires two indicators defined as: true positive rate \(Tpr=\frac{TP}{TP+FN}\), and false positive rate \(Fpr=\frac{FP}{FP+TN}=1-Tnr\). These measures can be calculated for different decision threshold values. An increase of the threshold from 0 to 1 will yield a series of points \((Fpr,\,Tpr)\) constructing the curve with \(Tpr\) and \(Fpr\) on the horizontal and vertical axes, respectively. In a general form, the value of AUC is given by \(AUC=\int_{0}^{1}ROC(u)du\).  
From another point of view, AUC can be understood as \(P\big{(}X_{p}>X_{n}\big{)}\) where \(X_{p}\) and \(X_{n}\) denote the markers for positive and negative cases, which can be interpreted as the probability that in a randomly drawn pair of positive and negative cases, the classifier probability is higher for the positive one.