# The Effect of Situational Variables on Women's Rink Hockey Match Outcomes
## 3 Results  
Table 2 displays both the absolute and relative frequencies of the six categorical variables incorporated into the full model. The Wilson method was used to compute the 95% confidence interval for a proportion (95% CI for \(\pi\)). A total of 31 models were estimated using the method of all possible regressions. Table 3 presents the top five models based on the AIC criteria. The full model, which comprised five situational predictors (MatLoc, TeaLeV, OpPev, ScoFir, and MatStaHal), had the lowest AIC (1238.7) and the highest AUC (0.9163). However, the third model in Table 3 was chosen as the best predictive model for several reasons. It was a more parsimonious model than the first model because it excluded the ScoFir predictor and had a lower AIC (1245.7) and a higher AUC (0.9143). Additionally, it exhibited a balanced Se (78.9%) and Sp (88.1%) for the cut-off point \(\pi\) = 0.5, demonstrated a good fit in the Hosmer-Lemeshow test (\(p\) = 0.145), and only had a non-significant 0.20% decrease in the AUC compared to the full model (\(p\) = 0.116). In contrast, the remaining models in Table 3 were not selected as the best predictive model because they did not meet certain selection criteria. For instance, the second model had a significant \(p\)-value in the Hosmer-Lemeshow test, while the fourth and fifth models experienced a significant decrease in the AUC compared to the full model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & & & \multicolumn{2}{c}{**95\% CI for \(\pi\)**} \\ \cline{3-6}
**Variable** & **Category** & \(n\) & \% & \(LL\) & \(UL\) \\ \hline Match outcome & Not won & 923 & 54.9 & 52.6 & 57.3 \\  & Won & 757 & 45.1 & 42.7 & 47.4 \\ Match location & Away & 839 & 49.9 & 47.6 & 52.3 \\  & Home & 841 & 50.1 & 47.7 & 52.4 \\ Team level & Relegation & 379 & 22.6 & 20.6 & 24.6 \\  & Remained & 775 & 46.1 & 43.8 & 48.5 \\  & Champions & 526 & 31.3 & 29.1 & 33.6 \\ Opponent’s level & Champions & 528 & 31.4 & 29.3 & 33.7 \\  & Remained & 774 & 46.1 & 43.7 & 48.5 \\  & Relegation & 378 & 22.5 & 20.6 & 24.6 \\ Scoring first & No & 842 & 50.1 & 47.7 & 52.5 \\  & Yes & 838 & 49.9 & 47.5 & 52.3 \\ Match status at halftime & Loses & 667 & 39.7 & 37.4 & 42.1 \\  & Draws & 347 & 20.7 & 18.8 & 22.7 \\  & Wins & 666 & 39.6 & 37.3 & 42.0 \\ \hline \hline \end{tabular} Note. \(n\) = number of observations; CI = confidence interval; \(LL\) = lower limit; \(UL\) = upper limit.  
\end{table} 
Table 2: Descriptive and inferential analyses of the categorical variables. Regarding the reliability of the chosen model, cross-validation yielded a pseudo-\(\mathbf{R_{\text{Mean}}^{2}}=0.528\), while bootstrap resampling resulted in an AUC of 0.908. Both of these values affirm the model's true predictive capability when applied to external samples. Concerning the diagnostic assessment of the selected model, 205 observations were identified, which accounted for 12.2% of the total, with notable influence statistics. However, it was opted not to exclude them from the model because they had been accurately recorded. Furthermore, no evidence of collinearity was found among the predictors, with the mean VIF standing at 1.51. It was also observed a slight infra-dispersion between the observed and expected variance (RMD = 0.73). Consequently, the standard errors of the model coefficients were marginally overestimated, leading to a slight increase in the type II error (\(\beta\)). Table 4 displays the parameters of the chosen model, including their b coefficients, odds ratios (exponentials of the b coefficients), confidence intervals, and \(p\)-values. The global likelihood ratio test demonstrated that the set of parameters within the estimated model significantly predicted the match outcome (\(\chi^{2}_{LR}=1082.9\), \(df=7\), \(p<0.001\)). The pseudo-\(R^{2}\) measures revealed that the estimated model accounted for between 46.1% and 63.6% of the variability in the data (\(R^{2}_{\text{Cox-Snell}}=0.475\), \(R^{2}_{\text{Naggelkerke}}=0.636\), \(R^{2}_{\text{addMcFadden}}=0.461\)).