I have a multilevel regression model in which I predict participants’ risk Propensity ratings (7-point scale) for 12 activities from their ratings of the Risk (7-point scale) they perceive and Reward (7-point scale) they expect for each activity. Random intercepts are included for participants (Part), and random slopes are included for the Risk and Reward predictors:
Ma ← brm(Propensity_rating ~ Risk_rating + Reward_rating + (Risk_rating + Reward_rating | Part), data=data)
After rating the activities, participants identified which strategies (e.g., risk, reward, experience, imagination, knowledge etc.) they used to inform their risk propensity ratings. I would like to know if participants who reported using risk (Risk_Strategy; 1 if yes, 0 if no) or reward (Reward_Strategy; 1 if yes, 0 if no) strategies to inform their risk propensity ratings more consistently integrated their risk and reward ratings to inform their risk propensity ratings. In other words, I want to know whether the residuals in the estimated risk propensity, predicted from risk and reward ratings, is smaller for participants who reported that they used either a risk or reward strategy to inform their risk propensity ratings. To do so, I ran this model:
Mb ← brm(bf(Propensity_rating ~ Risk_rating + Reward_rating + Risk_Strategy + Reward_Strategy + (Risk_rating + Reward_rating | Part),
sigma ~ Risk_rating + Reward_rating + Risk_Strategy + Reward_Strategy + (Risk_rating + Reward_rating | Part)),
data=data, family = gaussian())
In Mb, under “Population-Level Effects” this model gives me:
Population-Level Effects: Estimate l-95% CI u-95% CI
sigma_ Risk_Strategy1 -0.07 -0.08 -0.06
sigma_ Reward_Strategy1 -0.05 -0.06 -0.04
I interpret this to mean that the residual in the risk propensity ratings predicted from participants’ risk and reward ratings was smaller for participants who reported using the risk or reward strategy compared to those who did not. Am I correct?
Many thanks in advance.