# Effect of Contextual Motivation in Sports on the Evolution of Situal Intrinsic Motivation
## 3 Results
### Over-Time Trajectories of Intrinsic Motivation  
Then, the models incorporating only the linear parameter of the trajectories were compared with their respective versions including both linear and quadratic functions, as well as those integrating linear, quadratic, and cubic versions. The results of chi-square tests revealed a significant improvement of fit with the quadratic and cubic parameters for the high self-determined group. In line with the view of parsimony, the model with the linear, quadratic, and cubic parameters was used for the high self-determined group, whereas only the linear parameter was used for the total, low, and moderate self-determined groups. The results of the MGCAs are presented in Table 2.  
The results revealed a significant positive linear effect of time (\(\beta=25.28\), \(p<0.01\)), a significant negative quadratic effect of time (\(\beta=-2.77\), \(p<0.01\)), and a significant positive cubic effect of time (\(\beta=0.08\), \(p<0.01\)) on the situational motivation of subjects belonging to the high self-determined group. In contrast, the MGCAs conducted on the total sample, moderate, and low self-determined groups revealed no significant effect of time on participants' situational motivation (all \(p\)s \(>0.05\)).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Samples**} & **Fixed Effect** & \multicolumn{2}{c}{**Random Effects**} & \multirow{2}{*}{\(-2^{\bullet}\)**log**} \\  & \(\gamma_{00}\) **(SE)** & \(\sigma^{2}\) **(SD)** & \(\tau_{00}\) **(SD)** & \\ \hline Total sample & 416.69 *** (12.64) & 7026 (83.82) & 9235 (96.10) & 14,220.9 \\ High self-determined & 455.35 *** (19.99) & 7808 (88.36) & 7599 (87.17) & 4780.7 \\ Moderate & 402.14 *** (22.06) & 9368 (96.79) & 7346 (85.71) & 4761.4 \\ Low self-determined & 392.58 *** (20.91) & 8451 (91.93) & 5921 (76.95) & 4665.8 \\ \hline \hline \end{tabular} Notes: SE = standard errors; SD = standard deviations; \(\gamma_{00}\) is the group mean of situational intrinsic motivation; \(\sigma^{2}\) = var(rij) variance in level 1 residual (i.e., variance in rij); \(\tau_{00}\) = var(U0j) variance in level 2 residual (i.e., variance in U0j). *** \(p<0.001\).  
\end{table}
Table 1: Parameter estimates and variance components of the null models.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Total Sample** & \begin{tabular}{c} **High Self-** \\ **Determined** \\ \end{tabular} & \
\begin{tabular}{c} **Moderate Self-** \\ **Determined** \\ \end{tabular} &
\begin{tabular}{c} **Low Self-** \\ **Determined** \\ \end{tabular} \\ \hline \multicolumn{5}{c}{Fixed effects—Estimates (Standard errors)} \\ \hline Intercept & 415.73 *** (13.42) & 404.70 *** (26.61) & 412.24 *** (27.95) & 385.23 *** (19.51) \\ Time & 0.10 (0.98) & 25.28 ** (9.92) & \(-1.06\) (1.88) & 0.78 (1.24) \\ Time2 & – & \(-2.77\) ** (0.89) & – & – \\ Time3 & – & 0.08 *** (0.03) & – & – \\ \multicolumn{5}{c}{Random effects—Variance (Standard deviation)} \\ \hline Intercept & 9827.74 (99.13) & 1202 (109.63) & 14,672.80 (121.13) & 6662 (81.62) \\ Time & 49.39 (7.03) & 1498 (38.70) & 62.97 (7.94) & 23 (4.76) \\ Time2 & – & 8.64 (2.94) & – & – \\ Time3 & – & 0.005 (0.07) & – & – \\ Residual & 5295.50 (72.77) & 3815 (61.76) & 5102.35 (71.43) & 5094 (71.38) \\ \(-2^{\bullet}\)loglikelihood & 14,012.3 & 4614.5 & 4667.3 & 4633.0 \\ \hline \hline \end{tabular} Notes: *** \(p<0.001\) *** \(p<0.01\); Time, linear time; Time2, square time; Time3, cubic time.  
\end{table}
Table 2: Unstandardized parameter estimates of the growth curve models of participants’ situational intrinsic motivation.