# Validation of the Player Personality and Dynamics Scale
## 3 Results  
The confirmatory factor analysis of the final 21-item instrument was performed using Mplus [13]. The five-factor solution yielded a \(\chi^{2}\) = 342.09 with df = 115 (\(p\) < 0.001). Although the \(\chi^{2}\) test was significant, expected given the large sample size, the model achieved acceptable fit according to alternative indices: RMSEA = 0.06 (90% CI [0.05, 0.06]), CFI = 0.95, TLI = 0.91, SRMR = 0.03, and CMIN = 2. Model selection followed an iterative process: we compared solutions with one to ten factors (see Table 1). These optimal fit indices were obtained using a five-factor factorial structure, after testing multiple solutions ranging from one to ten factors. A summary visualization of the RMSEA, CFI, and TLI values across models with one to ten factors is provided in Figure 3, highlighting the inflection point at five factors. The final structure consisted of 21 items with factor loadings ranging from 0.436 to 0.801. Only items with loadings above 0.40 were retained. According to McDonald's omega, the overall reliability of the scale was \(\mathbf{\omega}\) = **0.93**. The five factors extracted from the confirmatory factor analysis were as follows: **Toxic Profile** (\(\omega\) = 0.81), 5 items; **Joker Profile** (\(\omega\) = 0.66), 4 items; **Tryhard Profile** (\(\omega\) = 0.68), 5 items; **Aesthetic Profile** (\(\omega\) = 0.62), 3 items; **Coacher Profile** (\(\omega\) = 0.78), 4 items. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Factor** & **Factor/Item** & \(\mathbf{X^{2}}\) & \(\mathbf{df}\) & **RMSEA** & **90\%** & **CFI** & **TLI** & **SRMR** \\ \hline
1 & 1 & 2883.87 & 189 & 0.15 & 0.15–0.16 & 0.40 & 0.34 & 0.12 \\
2 & 2 & 1560.30 & 169 & 0.11 & 0.11–0.12 & 0.70 & 0.62 & 0.07 \\
3 & 3 & 1045.74 & 150 & 0.097 & 0.09–0.10 & 0.80 & 0.72 & 0.06 \\
4 & 4 & 677.314 & 132 & 0.08 & 0.08–0.09 & 0.88 & 0.81 & 0.04 \\
**5** & **5** & **342.09** & **115** & **0.06** & **0.05–0.06** & **0.95** & **0.91** & **0.03** \\
6 & 5 & 238.13 & 99 & 0.05 & 0.04–0.06 & 0.97 & 0.94 & 0.02 \\
7 & 5 & 170.82 & 84 & 0.04 & 0.03–0.05 & 0.98 & 0.95 & 0.02 \\
8 & 5 & 124.10 & 70 & 0.04 & 0.03–0.05 & 0.99 & 0.97 & 0.02 \\
9 & 5 & 87.31 & 57 & 0.03 & 0.02–0.04 & 0.99 & 0.98 & 0.01 \\
10 & 6 & 64.08 & 45 & 0.03 & 0.01–0.04 & 0.99 & 0.98 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model fit indices for the five-factor model. Figure 3: Fit indices (RMSEA, CFI, TLI) across models with 1 to 10 factors. The selected model (k = 5) is marked with a vertical line. A detailed list of the 19 excluded items, their initial profile assignment, and the primary reason for exclusion is provided in Table 2.  
While conventional guidelines suggest McDonald's omega values of 0.70 or higher for well-established scales, the Joker (\(\Omega\) = 0.66) and Aesthetic (\(\Omega\) = 0.62) subscales of the PPDS remain in the final model for several reasons. First, each subscale is composed of only four items; shorter scales inherently yield lower reliability coefficients, yet they can still capture coherent and meaningful constructs when their content validity is robust. Second, the PPDS is in an exploratory validation phase: values above 0.60 are generally deemed acceptable at this stage, particularly when theoretical justification supports the construct's inclusion [27]. Third, both subscales address motivational-narrative dynamics that are central to educational gamification: playful creativity (Aesthetic) and strategic unpredictability (Joker). Excluding them would omit important pedagogical levers. The factorial structure of the Player Personality and Dynamics Scale is shown in the Table 2.