## 4 Initial Analyses and Findings
### The Factor Analysis  
#### 4.3.1 Factor Extraction  
Every factor analysis starts by extracting the desired or the required number of factors. Each of these factors represents a variable or a group of variables. There are some rules and extensions for determining the number of factors to be extracted. This extraction should be performed by determining the meaning and thus the labelling of the factor which is based on variable loadings within the factors. The extraction process can be followed by the rotation of the factors for a better interpretation of the analysis. Depending on the research objective, the calculation of the factor scores and assigning a score value on each variable is the final step. The decision progress for each phase is summarized in the following paragraphs. The study includes five different soil properties that are acting as variables in the factor analysis (Table 3). The communality of the variables shows how much variance is explained by all factors. As stated by [PERSON] [63], the minimum communality of each variable should be 0.2 to be retained in the analysis. In this study the minimum communality is calculated as 0.555 (Appendix A), therefore all the variables were retained. The labelling of the factors depends on the loadings of the variables within a factor. Therefore, the method of interpretation is crucial before any misleading interpretation on the results. The factor matrix shows the loading of each soil property within the factor and can be interpreted as the correlation coefficients within the factor (Appendix A). However, it is an uninterpreted solution before any rotation is performed. Considering this aspect, the examination of the factor matrix reveals that the first factor heavily relies on consistency limits and montmorillonite content which is followed by the clay content. The calcium carbonate content has a negative sign with a relatively high loading of \(-0.593\). This indicates that it has a negative relationship with the other soil properties when considering their effect as a whole. This concludes that the calcium carbonate content can be regarded as having a negative effect on soil plasticity characteristics. Investigation of the second factor shows that only calcium carbonate content has a high loading. This proves the fact that calcium carbonate content has a high impact on soil plasticity and should be included in the analysis. In this way, the negative effect of calcium carbonate contrary to the other properties is reflected in the analysis. The examining and labelling of the factors were performed based on the purpose of the study and should be interpreted cautiously by the researchers. Based on the literature, there are three main rules to determine how many factors to extract. These include [PERSON]'s rule of the eigenvalue [67], examining the scree plot and retaining the factors that explain at least 70% of the variance cumulatively. The [PERSON]'s rule should be applied if the study includes 20 to 50 different variables [59] and is often found to misestimate the number of factors [68; 69]. Therefore, it is not applicable in this study considering the variable size. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable** & **Description** \\ \hline N\({}_{1}\) & Liquid limit \\ N\({}_{2}\) & Plastic limit \\ N\({}_{3}\) & Clay fraction \\ N\({}_{4}\) & Montmorillonite content \\ N\({}_{5}\) & Calcium carbonate content \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The variables in this analysis and their corresponding notations. The examination of the scree plot is very subjective, and the decision can change between different researchers [70]. Considering these uncertainties, the authors choose to extract the factors by examination of the factor loadings and the amount of variance explained. This type of approach is quite common in factor analysis if the researchers have a dedicated goal to prove and investigate [59; 71]. Overall, two factors are extracted from the analysis.