## 3 Case Study
### Confirmatory Analysis: Dimension Reduction, Results and Discussion
\begin{table}
\begin{tabular}{c  
To compare with FA and improve data interpretation, a DPCA was also carried out using three components. In Table 8, we can see the loading matrix that was obtained with classical components. The last row shows the percentage of variance captured by each component. In total, the three components capture 56.35% of the variability of the data. The disjoint components help us to improve the interpretation of the loading matrix. When computing disjoint components, Table 9 reports the loading matrix. Now, the three components capture 54.95% of the data variability. Therefore, we lose 1.4% of the information, but we gain in data interpretation. Figure 5 shows the reduced dimension space for the 14 WhatsApp items with disjoint components. We conclude that items #3 and #9-13 are grouped in component 1 (COMP1), that component 2 (COMP2 ) catches items #1, #2, #4, and #5, and that, then, items #6, #7, #8, and #14 are represented by component 3 (COMP3). By comparing Tables 5 and 9, we can say that COMP1 is FACT1, COMP2 is FACT2, and COMP3 is FACT3. Note that COMP1 represents a high dependency on WhatsApp. Two items that we could incorporate for future studies, to further support this conclusion, could be: \"During lunch or dinner, I frequently use WhatsApp\" and \"While watching TV, I frequently use WhatsApp\". Observe that COMP2 states the isolation to which a person is subjected by the use of WhatsApp. Items that can be added in the future that are aligned with this component could be \"If I am in a meeting with family or friends, I use WhatsApp a lot\" and \"When I am on a date, I use WhatsApp a lot\". We note that COMP3 indicates a growing use of WhatsApp; that is, as the days go by, the percentage of daily use of WhatsApp increases. To support this conclusion, we could in the future consider for example adding these two items: \"I have stopped doing some activities since using WhatsApp\" and \"I see less and less of my family or friends since using WhatsApp\". All feedback obtained allows us to improve the instrument for future research. In [50], we can see another data analysis using DPCA with COVID-19 data. In [47; 51], we identify alternating least squares algorithms to compute disjoint components in three-way tables. In Table 10, we report a summary of the dimensional reduction analysis. The three latent dimensions have been clearly characterized. The methodology that we propose in Algorithm 1, based on the use of disjoint components and component rotation techniques, was employed to obtain these conclusions. Furthermore, in Figure 5, we observe the WhatsApp items clearly grouped. The results have provided with important feedback that will allow us to improve the measurement instrument in future studies. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Variables** & \(\mathbf{p}\)**-Value** & **Result** \\ \hline Age group & 0.162 & Non-significant \\ Program & 0.161 & Non-significant \\ Academic year & 0.341 & Non-significant \\ GPA & 0.014 & Significant \\ How many academic groups you have joined? & \textless{}0.001 & Significant \\ Are you connected with your teachers over WhatsApp? & 0.003 & Significant \\ How long you have been using WhatsApp? & 0.008 & Significant \\ How many hours do you normally spend using WhatsApp? & 0.735 & Non-significant \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Crosstabulated results of WhatsApp usage during academic activity with several variables of the Indian data.