# Engineering the Future: Evaluation of Virtual Reality Across Project Lifecycle Stages
## 3 Methodology
### Statistical Analysis Framework for Evaluating Perceived Practically of VR
**In the fourth stage**, a multigroup SEM approach [65] was estimated to assess how the same set of independent variables predicted perceived practicality of VR at each project lifecycle stage separately. As in the second (CFA) and third (SEM) stages, the model was implemented using the _lavaan_ package in R. This stage-specific model enabled detailed examination of how predictors such as education, familiarity with VR, and willingness to adopt VR influenced perceptions at different points in the lifecycle. The analysis employed the Diagonally Weighted Least Squares (DWLS) estimator and NLMINB optimization--both of which were also used in the second and third stages--as they are appropriate for ordinal indicators and well suited to handle complex constraints in nonlinear models, respectively. In stages 2, 3, and 4, SEM-related procedures were evaluated using the chi-square (\(\chi^{2}\)), the Comparative Fit Index (CFI), the Tucker-Lewis Index (TLI) [66], the Root Mean Square Error of Approximation (RMSEA) with a 90% confidence interval [66; 67], and the Standardized Root Mean Square Residual (SRMR) [66]. **In the fifth stage**, a Categorical Principal Components Analysis (CATPCA) [59] was conducted to validate the unidimensionality of the perceived practicality of VR construct, using optimal scaling for ordinal data [68]. The model included bootstrap validation and internal consistency checks, complemented by component loadings and inter-item correlations [69]. CATPCA was performed in IBM SPSS Statistics version 28 [59]. **In the sixth stage**, a CHAID (Chi-squared Automatic Interaction Detection) classification tree analysis [70] was conducted using IBM SPSS Statistics version 28 [59] to identify predictors of perceived practicality of VR, using the CATPCA-derived dimension as the outcome variable. CHAID is a decision tree technique based on chi-square statistics, suitable for exploring interactions between categorical variables and identifying optimal splits. This method enabled the inclusion of nominal predictors not appropriate for SEM, such as professional domain and organizational characteristics. The model was validated through cross-validation and assessed for predictive accuracy [71]. **In the seventh stage**, a focused CATPCA analysis was conducted using bootstrap resampling and object scores output for selected background variables, also in IBM SPSS Statistics version 28 [59]. The purpose of this step was to identify which background characteristics were associated with meaningful variation in the latent variable of perceivedpractically of VR by examining whether the 95% confidence intervals of their object scores excluded zero. The CFA diagram (Figure 2 below) and the SEM path models (Figures 3 and 4 below) were created using IBM SPSS Amos version 28.0.0 [72], and the CHAID Classification Tree (Figure 5) was generated using IBM SPSS Statistics version 28. Starting from Section 4, only statistical abbreviations were used in place of full terms. These seven stages form an integrated analytical framework that combines measurement validation, structural modeling, classification analysis, and individual-level exploration using bootstrap-enhanced dimensional reduction techniques. To further support transparency and replicability, we clarify that all statistical analyses adhered to the underlying assumptions of each technique, with specific adjustments for small sample sizes and ordinal data. For instance, the use of the Diagonally Weighted Least Squares (DWLS) estimator was selected due to its robustness in small-sample, non-normally distributed ordinal data environments, as supported by simulation studies (e.g., Mindrila, [63]). All the analyses were conducted using the following tools: (a) IBM SPSS Statistics 28 for GLM, CATPCA, and CHAID; (b) IBM SPSS Amos 28.0.0 for SEM visualization; and (c) the lavaan package in R (version 0.6-15) for all SEM-related models, including multigroup comparisons. The NLMINB optimization algorithm was used to handle nonlinearity in model constraints.