I have 3 predictors which are correlated by approx. 0.57.
One measures the intensity of a task. One measures the success (profitability above x) of a task and one the failure of a task (profitability below x). above a certain threshold I code them as 1 otherwise as 0. With a higher intensity of the task the probability of success or failure also increases.
My hypothesis are that each of the 3 predictors increases the probability of quitting.
Additionally I have 4 models. Model 1-3 is one of the predictors + control variables (Age, Gender, ..). Model 4 is the combination of the 3 predictors and the control variables.
My goal is to determine the influence of the 3 predictors quitting. I want to find out which variable has a significant influence on quitting.
When I run Model 1-3 using coxph I get the result that in each Model the predictors is significant. I assume this is a result of a confounding variable.
When I run Model 4 I get the result that only one variable (intensity of task) out of the 3 predictors is significant. The other are not significant and have a exp coeff of 0.97 and 0.96.
When I use comparing nested models with anova. Run the Cox regression first with the intensity of task, then see whether adding the other predictors adds significant information with anova(). Then reverse the order, starting with the other predictors and seeing whether adding the intensity of tasks adds anything I get the result, that intensity of tasks adds significant information. The other way around it doesn't add significant information.
What can I conclude from this result? Does this mean that intensity of task is a significant predictor of quitting and the others are not? That the result of Model 1-3 is confounded by the intensity of task?
Is there a way to test directly for confounding?