# Gamifying Massive Online Courses: Effects on the Social Networks and Course Completion Rates
## 4 Results
### Reduction in Dimensionality
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Experimental Group**} & \multicolumn{3}{c}{**Control Group**} \\ \hline
**Variable** & **F1** & **F2** & **F3** & **F1** & **F2** & **F3** \\ \hline Blogs & **0.773** & 0.011 & 0.017 & **0.496** & 0.244 & 0.004 \\ \hline Tweets & **0.743** & 0.110 & 0.030 & 0.382 & **0.530** & 0.000 \\ \hline Likes & **0.618** & 0.224 & 0.003 & **0.520** & 0.003 & 0.048 \\ \hline Messages & 0.021 & 0.000 & **0.864** & 0.265 & 0.020 & 0.058 \\ \hline Comments & **0.742** & 0.108 & 0.001 & **0.462** & 0.350 & 0.000 \\ \hline Followers & **0.897** & 0.031 & 0.003 & **0.825** & 0.013 & 0.112 \\ \hline Following & **0.787** & 0.046 & 0.002 & **0.441** & 0.171 & 0.114 \\ \hline Logins & **0.589** & 0.001 & 0.002 & **0.486** & 0.191 & 0.001 \\ \hline Interactions & **0.758** & 0.135 & 0.008 & **0.604** & 0.338 & 0.008 \\ \hline Achievements & **0.831** & 0.014 & 0.008 & - & - & - \\ \hline Points & **0.822** & 0.002 & 0.019 & - & - & - \\ \hline Degree & **0.926** & 0.004 & 0.003 & **0.757** & 0.112 & 0.006 \\ \hline Eccentricity & **0.477** & 0.340 & 0.000 & **0.587** & 0.113 & 0.028 \\ \hline Closeness centrality & **0.451** & 0.346 & 0.001 & **0.573** & 0.111 & 0.026 \\ \hline Betweenness centrality & **0.648** & 0.100 & 0.014 & **0.518** & 0.071 & 0.073 \\ \hline Clustering coefficient & 0.090 & **0.326** & 0.039 & **0.754** & 0.025 & 0.001 \\ \hline Eigenvector centrality & **0.884** & 0.050 & 0.002 & 0.085 & 0.009 & **0.705** \\ \hline Authority & **0.894** & 0.037 & 0.003 & **0.699** & 0.021 & 0.235 \\ \hline Hub & **0.879** & 0.023 & 0.009 & **0.759** & 0.015 & 0.158 \\ \hline PageRank & **0.855** & 0.015 & 0.014 & **0.752** & 0.124 & 0.030 \\ \hline
**EigenValue** & 13.687 & 1.922 & 1.041 & 9.965 & 2.459 & 1.608 \\ \hline
**Variability (\%)** & 68.44 & 9.61 & 5.20 & 55.36 & 13.67 & 8.93 \\ \hline
**Cumulative \%** & 68.44 & 78.05 & 83.25 & 55.36 & 69.03 & 77.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the PCA: squared cosines of the variables, eigenvalues, and variability of the factors. Values in bold correspond to the factor for which the squared cosine is the largest. create predictive models, as shown in the next section, significantly reduces the effect of collinearity in variable prediction. If we compare the results of both groups, we can see that they are similar in terms of how variables group together and that, also in both cases, the first component (F1) is a good descriptor of students' work since it includes most variables. We can use this information to build predictive models of course completion based on the activity completed by students as represented by F1. This can also provide valuable information to instructors monitoring future courses since we can focus only on a subset of 2-3 instead of all variables, or on F1 if they can perform a PCA, to analyze the results of the learning action. For instance, we could study the scores of students for F1 during the course to determine the levels of participation of students and decide whether to take further action to motivate them or even provide automated individual feedback based on the results of this score. Figure 4: Principal component analysis (PCA) factor loading biplot for the experimental group. Figure 5: PCA factor loading biplot for the control group.