*3.1. Analysis Strategy*

From a preliminary check for the normality of distribution, it resulted that all the 18 GAMS-it items reported a significant deviation from normality (Shapiro-Wilk test ranged from w = 0.45, *p* < 0.01, to w = 0.86, *p* < 0.01), so Robust Maximum Likelihood estimation method with robust standard error and robust fit statistics was considered for conducting the CFA (i.e., References [34,35]). The goodness of fit of the model was consequently evaluated by means of the Satorra-Bentler (SB) scaled chi-square statistic [34], as well as other well-known fit indices such as: Root Mean Square of Approximation (RMSEA; [36]), Comparative Fit Index (CFI; [37]) and Non-Normed Fit Index (NNFI; [38]). Following guidelines by Hu and coworkers (1992) [39], the model is considered to hold approximatively in the population if the RMSEA value is below 0.08 (the closer to 0.00 the better), and if both CFI and NNFI are above 0.95, it is indicative of a reasonable goodness of fit. The same fit indexes will be used to evaluate the fit for the latent factor regression model.

Given that high- and low-frequency gamers (namely, HG and LG) may differ in terms of motivation and regulatory strategies, it is consequently crucial to test whether the same factor structure (in terms of latent means and covariance structure) is invariant across the two sub-groups. Multi-sample CFA was then performed in order to investigate how well the factor model emerging from the previous analysis could be generalized across high- vs. low-frequency gamers.

A procedure for testing factorial invariance was followed (e.g., Reference [40]). The procedure consisted of a series of hierarchical statistical invariance tests (configural, metric, scalar, unique variance, latent variance and latent means), starting with the omnibus test of the equality of covariance matrices across groups. The scaled difference chi-square statistics, ΔSB χ2, [35] were used for comparing the fit between two nested models, i.e., configural and metric invariant and to determine if the more restricted model has or not a non-worsen fit than the less restricted model. The null hypothesis of the statistical test was accepted when the estimated probability of the test was greater than 0.01.

### *3.2. Results of CFA of GAMS-it*

On the selected sample of participants who comprised of low (LG, N = 200) and high (HG N = 188) frequency gamers, a Confirmatory Factor Analysis has been performed. In general, the Six-factor structure reported satisfactory fit statistics (SBχ2(120) = 256.35, *p* < 0.01) with an RMSEA of 0.070 (90% C.I: 0.058–0.082), a NNFI of 0.969, and CFI = 0.961. As shown in Table 1, all GAMS-it items reported a significant factor loading on the expected factor; moreover, as described in Table 2, all factors correlated significantly, and the expected direction and reliability was satisfactory (ranging from 0.76 to 0.93). It is worth noting, the correlation between Integrated regulation and Identified Regulation is extremely high (θ = 0.945) and it is of the same entity of that reported by Lafreniére and colleagues [22]. We tested the hypothesis that the correlation between the two factors is equal to 1, meaning that the two factors are the same thing. The difference in model fit was significant ( ΔSBχ2(1) = 12.23, *p* < 0.01) indicating that the model with the covariance fixed to 1 has a significantly worse fit. In conclusion, even if the correlation is high, the two constructs can be seen as different.


**Table 1.** Standardized factor loadings with Robust SE for the six factors of GAMS-it (N = 388).

\*\* *p* < 0.01; N = 388.

**Table 2.** Descriptive Statistics, Cronbach' alphas and Correlations among the six GAMS-it factors (listwise missing deletion, N = 388).


Note: Int-Mot = Intrinsic motivation; Int-Reg = Integrated regulation; Id-Reg = Identified Regulation; Introj-R = Introjected Regulation; Ext-Reg = External Regulation; Amot = Amotivation [\*\* *p* < 0.01].

### *3.3. Results of Multi-Sample CFA*

Although the configural model had a significant SBχ2, the values of RMSEA were acceptable while those of NNFI and CFI not (SBχ2(240) = 743.33, *p* < 0.001, RMSEA = 0.05, NNFI = 0.86, CFI = 0.87). Under the assumption of strict metric invariance, the fit (SB χ2) did not worsen significantly (SBχ2(252) = 779.91, *p* < 0.001, RMSEA = 0.05, NNFI = 0.88, CFI = 0.88; ΔSB χ2 (12) = 10.40, *p* = 0.58) so the same six factor model with the same loadings in the two groups is tenable. However when we add to the metric invariance also the invariance of intercepts, the model fits much worse (SBχ2(264) = 896.72, *p* < 0.001, RMSEA = 0.05, NNFI = 0.84, CFI = 0.84; ΔSB χ2 (12) = 33.0, *p* = 0.0009). Given these results, we decided to do not proceed with the remaining hierarchical tests of measurement invariance, as the fit would surely worsen. In conclusion, the metric invariance for the two sub-groups was reached.

### *3.4. Differences between Heavy Gamers and Light Gamers*

Finally, we compared the Heavy (HG) and Light Gamers (LG) groups with respect to the six GAMS-it factors and to the CESD and STAI scores (Table 3). HG scored significantly higher than LG on Intrinsic Motivation, Integrated Regulation, Identified Regulation, Introjected Regulation, and on External Regulation, but not on Amotivation. Concerning psycho-pathological measures, we found that HG reported significantly lower scores than LG on STAI but not on CESD (Table 3). Nonetheless, it should be stressed that such a difference could be a direct consequence of unbalanced gender composition between HG and LG.

**Table 3.** Descriptive statistics (M, SD) comparing Heavy Gamers (HG) and Light Gamers (LG) on each of the six GAMS-it factors and for CESD and STAI scores.


Note: Int-Mot = Intrinsic motivation; Int-Reg = Integrated regulation; Id-Reg = Identified Regulation; Introj-R = Introjected Regulation; Ext-Reg = External Regulation; Amot = Amotivation; CES-D = Center for Epidemiologic Studies Depression; STAI = State-Trait Anxiety Inventory. a Data for this combination of variables was available only on 172 participants. So d.f. for this ANOVA was (1, 170).

### *3.5. Predicting Depression and Trait Anxiety with GAMS-it Factors*

As stated before, the main objective of the study was to investigate discriminant validity aspects of GAMS by correlating the six factors of GAMS with psychopathological factors like those assessed by CES-D (depression level) and by STAI (trait anxiety). We performed a latent regression structural equation model by predicting the CES-D and STAI scores with the six latent GAMS-it factors and covarying for the effect of sex (Male vs. Female) and type of gamer (LG vs. HG). We preferred this statistical approach because it is a common model for two outcome variables, also giving the possibility of obtaining latent correlations. As for CFA and for MG-CFA, we used Robust estimation methods.

Results of the fitted Structural Equation Model (as depicted in Figure 1) showed the following fit indices: SBχ2(180) = 484.94, *p* < 0.01, with a Robust RMSEA of 0.112 (90% C.I: 0.100–0.124), a NNFI of 0.857, and CFI = 0.888. Table 4 shows the estimated latent regression parameters of the six GAMS-it factors on both CES-D and STAI scores. Regarding CES-D scores, we found that only one of the six GAMS-it factors, Amotivation, significantly and positively predicts (b = 0.209, se = 0.077, *p* = 0.007) depression level. Females (b = 0.400, s.e. = 0.092, *p* = 0.000) as well as HG (b = 0.343, s.e. = 0.091, *p* < 0.001) reported a positive and significant effect. While concerning STAI scores, we found that not only Amotivation has a positive and significant effect (b = 0.381, se = 0.073, *p* < 0.001), but also Intrinsic motivation has a negative and significant effect (b = −0.640, se = 0.231, *p* = 0.006) on the trait anxiety measure. Also, in this case, females reported significantly higher levels of anxiety with respect to males

(b = 0.208, s.e. = 0.091, *p* = 0.022); however, HG did not report anxiety scores significantly higher than that of LG (b = 0.119, s.e. = 0.091, *p* = 0.189).

Finally, it should be stated that the two clinical measures, CES-D and STAI, reported a significant and positive latent correlation (r = 0.717, se = 0.047, *p* < 0.001).

**Figure 1.** Path Model of the effects (completely standardized regression coefficients) of GAMS latent factors on Depression (CES-D scores) and Anxiety (STAI scores).



Note: Int-Mot = Intrinsic motivation; Int-Reg = Integrated regulation; Id-Reg = Identified Regulation; Introj-R = Introjected Regulation; Ext-Reg = External Regulation; Amot = Amotivation.
