# Predictors of Engagement in Virtual Reality Storytelling Environments about Migration
## 5 Hypotheses Testing and Results
### Evaluation of the Structural Model  
To evaluate the structural model in SmartPLS, the recommended method is bootstrapping [72]. Table 2 shows the results of R\({}^{2}\) and R\({}^{2}\) adjusted for each endogenous latent construct (dependent variables) in the model as well as the total effects and indirect effects for exogenous constructs (independent variables). In Table 2, the R\({}^{2}\) and R\({}^{2}\) adjusted are the coefficients of determination, and this is a measure of the predictive power of the proposed model. It means the amount of explained variance. This measure is calculated as the squared correlation between each endogenous construct actual values with respect to the predicted values. When there is more than one exogenous construct (for instance, immersion, presence, agency, and usability), that predicts one endogenous construct (for instance, engagement), and the coefficient represents the combined amount of variance in the endogenous construct that is explained by the exogenous construct. Values for the R\({}^{2}\) coefficient range between 0 to 1, with values close to 1 indicating higher explained variance. The R\({}^{2}\) adjusted compensates for adding other nonsignificant constructs, which might increase the explained variance, but affects the reliability of the model. The R\({}^{2}\) adjusted can be used to compare models with different exogenous variables or datasets with different sample sizes [72]. The results in Table 2 (above) show that the model explains 55.2% of the variance in engagement. All the factors have a positive effect on engagement, and the factor with the strongest effect is agency (0.291) followed by usability (0.239). Moreover, presence explains 8.5% of immersion because of its positive effect (0.291). Table 3 shows the paths in the hypothesized model together with the path coefficients, effect size, t-value, \(p\)-value, and an indicator of whether the hypothesis is supported or not as a result of the PLS-SEM analysis. Table 3 shows that 6 out of the 6 hypotheses in the model are supported. In Table 3, the effect size (f\({}^{2}\)) indicates the impact on endogenous constructs when each exogenous construct is removed from the model. The effect size can be calculated with the following equation, where R\({}^{2}\)included is the R\({}^{2}\) coefficient when the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dependent Variable** & **Independent Variable** & **R\({}^{2}\) (R\({}^{2}\) Adjusted)** & **Total Effects** \\ \hline \hline \multirow{4}{*}{Engagement} & & 0.552 (0.541) & \\  & Immersion & & 0.212 \\  & Presence & & 0.195 \\  & Agency & & 0.291 \\  & Usability & & 0.239 \\  & UX & & 0.193 \\  & & 0.085 (0.081) & \\  & Immersion & & 0.291 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of R\({}^{2}\), R\({}^{2}\) adjusted, total effects, and indirect effects of the structural model. exogenous construct is included in the model while the \(\text{R}^{2}_{\text{excluded}}\) is the \(\text{R}^{2}\) coefficient when the exogenous construct is removed from the model [72]:  
\[\text{f}^{2}\ =\ \frac{\text{R}^{2}_{\text{included}}-\text{R}^{2}_{\text{ excluded}}}{1-\text{R}^{2}_{\text{included}}}\]  
Values of 0.02, 0.15, and 0.35 indicate small, medium, and large effect sizes, respectively. Regarding the t-value, these data correspond to Student's \(t\)-test calculated with the following formula, where \(w\) is the weight in the original model estimation and \(se\) is the standard error:  
\[\text{t}\ =\ \frac{\text{w}_{1}}{\text{se}_{\text{w}1}}\]  
Finally, the \(p\)-value indicates the significance of each path in the model. The \(p\)-value is the probability that random sampling using bootstrapping yields a t-value of at least 1.96. Figure 5 shows the validated model of predictors of engagement, including the path coefficients and outer loadings. Figure 5: A validated model of predictors of engagement.