# Engineering the Future: Evaluation of Virtual Reality Across Project Lifecycle Stages
## 3 Methodology
### Statistical Analysis Framework for Evaluating Perceived Practically of VR  
A range of robust statistical analysis techniques was applied to examine participants' perceptions of the practicality of VR across different stages of the project lifecycle, as well as to explore the influence of various background and perceptual factors. The term 'robust' is used here to reflect the applied methodologies choices to ensure reliability under realistic data conditions--including small-to-moderate sample sizes, ordinal measurement scales, and potential violations of normality assumptions. Techniques such as General Linear Model (GLM) Repeated Measures with sphericity corrections, Structural Equation Modeling (SEM) using the Diagonally Weighted Least Squares (DWLS) estimator, Categorical Principal Components Analysis (CATPCA) with bootstrap validation, and non-parametric classification via CHAID trees were employed. Each of these methods was explicitly selected for its ability to generate stable, interpretable, and statistically sound results under challenging conditions. The analysis was divided into seven primary stages, as depicted in Figure 1 and explained below. In the first stage, a General Linear Model (GLM) Repeated Measures analysis was conducted to evaluate how perceived practicality of VR varied across the eight predefined project lifecycle stages. This procedure allowed for within-subject comparisons across stages and included checks for sphericity and polynomial contrasts to detect patterns in stage-wise differences [57; 58]. The analysis was conducted using IBM SPSS 28 [59]. In the analytical stages 2 through 4, Structural Equation Modeling (SEM) methods were applied. All SEM-related procedures--including CFA, structural modeling, and multigroup SEM--were conducted using the _lavaan_ package (version 0.6-15) in R [60], which supports categorical SEM by accommodating ordinal variables. This was achieved through the use of the Diagonally Weighted Least Squares (DWLS) estimator [61] and NLMINB optimization [62], both suitable for modeling with ordinal indicators and complex nonlinear constraints. Although the sample size of 56 may seem modest for SEM, the use of DWLS is particularly well-suited for small-to-moderate samples with ordinal data and has been  
Figure 1: Major stages of the analysis. shown to produce robust and reliable estimates under such conditions. Simulation studies like Mindrila [63] support the adequacy of samples as small as 50 for unidimensional models with strong loadings, provided that model complexity is not excessive. In this study, the excellent model fit indices observed (e.g., CFI > 0.95, RMSEA < 0.08) further validate the appropriateness of the SEM approach for this sample size. Specifically, as the second stage of analysis, Confirmatory Factor Analysis (CFA) [64] was used to assess the factorial validity of a unidimensional latent variable representing perceived practicality of VR. Modification indices were reviewed to identify areas for improvement, and selected residual covariances were added to refine model fit. Following the establishment of the factor structure, the internal consistency reliability of the scale measuring the perceived practicality of VR was evaluated using Ordinal Alpha and McDonald's Omega, which are suitable for ordinal data and provide robust reliability estimates. **In the third stage**, a Structural Equation Modeling (SEM) approach [65] was applied to examine how a range of demographic and perceptual independent variables predicted the latent variable of perceived practicality of VR. The model estimation was conducted using the _lavaan_ package in R, consistent with the CFA analysis. It employed the Diagonally Weighted Least Squares (DWLS) estimator, which is suitable for ordinal indicators, along with NLMINB optimization, for handling complex model constraints. The analysis focused on evaluating the significance of regression paths and assessing overall model fit.