## 2 Materials and Methods
An inferential statistical design was employed using the 13 safety climate determinants as independent variables (IVs) that predicted the construction site's safety climate evaluations, which served as the dependent variable (DV). Given that both the IVs and the DV were rated on the aforementioned scales, they were treated as discrete ordinal categorical variables. As appropriate for such a statistical design, a generalized linear model approach using multiple ordinal logistic regression was implemented. Ordinal logistic regression is a maximum-likelihood-estimation-based method. It models proportional odds using a logit link function that performs logarithmic transformations of cumulative probabilities to express non-linear relationships between the IVs and DV in a linear model [47, 48, 49, 50, 51, 52]. Accordingly, the Statistical Package for Social Sciences software (SPSS version 23.0) [53] was used to fit the following ordinal logit model in Equation (1):  
\[logit\big{(}\gamma_{j}\big{)}=\ ln\Bigg{(}\frac{\gamma_{j}}{1-\gamma_{j}} \Bigg{)}=\ \theta_{j}\ -\ \beta_{1}X_{1}+\ \beta_{2}X_{2}+\ldots+\beta_{k}X_{k}+\varepsilon, \tag{1}\]  
where  
_j_: 1 to (number of DV categories - 1),  
_\(\gamma_{j}\)_: cumulative probability for the \(j\)th category,  
_\(\theta_{j}\)_: threshold for the \(j\)th DV category,  
_\(\beta_{1}\)_ to \(\theta_{k}\): regression coefficients of IVs,  
_\(X_{1}\)_ to \(X_{k}\): IVs,  
_\(k\)_: number of IVs, and  
_\(\varepsilon\)_: error term. Thus, by finding the antilog of Equation (1), the estimated regression model will be Equation (2) or (3):  
\[\hat{\gamma}_{j}=\ \ e^{\theta_{j}\ -(\beta_{1}X_{1}+\ \beta_{2}X_{2}+\ldots+ \beta_{k}X_{k})}\Big{/}\Big{(}1+\ e^{\theta_{j}\ -(\beta_{1}X_{1}+\ \beta_{2}X_{2}+\ldots+\beta_{k}X_{k})}\Big{)}, \tag{2}\]  
\[\hat{\gamma}_{j}=\ 1/\Big{(}1+\ e^{(-\theta_{j}\ +\ \beta_{1}X_{1}+\ \beta_{2}X_{2}+\ldots+ \beta_{k}X_{k})}\Big{)}, \tag{3}\]  
where \(\hat{\gamma}_{j}\) is the estimated cumulative probability of a construction safety climate evaluation score based on the importance ratings of safety climate determinants, included in the model as predictors \(X\)s and their associated \(\beta\)s. Moreover, the odds and the odds ratio (OR) can be estimated by Equations (4) and (5), respectively, which also enables the estimation of the proportional change in the odds resulting from a unit change in the predictor (i.e., one score unit change in \(X\)). \[Odds=\gamma_{j}/\big{(}1-\gamma_{j}\big{)}, \tag{4}\]  
\[OR=\Big{(}Odds_{\text{\emph{one score unit change}}}\Big{)}/\Big{(}Odds_{ \text{\emph{original score}}}\Big{)} \tag{5}\]  
Accordingly, the cumulative probability of observing a particular construction site safety climate evaluation score or a lower score can be estimated by modeling all odds following the form in Equation (6). Thus, the probabilities for the individual construction site safety climate evaluation scores (i.e., \(P\) (score = \(j\))) can also be calculated using Equation (7). \[odds=\ P(score\leq\ j)/\big{(}1\ -P(score\leq\ j)\big{)}, \tag{6}\]Figure 1:0  
The decision to build the prediction model by entering the 13 IVs as predictors and retaining the significant predictors was based on the principle of parsimony, as suggested by [3]. The IVs were entered in a stepwise hierarchical fashion based on the theory previously proven by [PERSON] and [PERSON] [46] of their key component classifications as determinants (Table 1). The overall fit of the model was tested using a -2 log-likelihood \(\chi^{2}\) statistic (-2 LL \(\chi^{2}\)) between the intercept-only model (i.e., baseline model) and the final model including the predictors (i.e., new model). The significance level (\(p<0.05\), \(p<0.01\), \(p<0.001\)) of the safety climate determinants selected as IVs in predicting the construction site's safety climate evaluations as the DV was assessed using Equations (8) and (9). Figure 1:1  
Figure 1:2  
Moreover, a goodness-of-fit test using Pearson and deviance \(\chi^{2}\) statistics was conducted.