I am starting to use cumulative models in my research, and I have some questions regarding the interpretation of the results.
I have run a cumulative model (link= logit) with a random effect (site) to assess how different factors are related to fishers’ perceptions of wellbeing. Perceived wellbeing is an ordinal variable with four categories. I am particularly interested in the effect of one factor, “EquityOutcome_sd” (a continuous variable), on the latent variable of wellbeing. I standardized continuous variables by subtracting the mean and dividing them by two standard deviations.
I am not sure if I am correctly interpreting the log odds and odds.
This is the model:
M_wellbeing<-brm(wellbeing~ParticipDecisionSyndicate_bi +EquityOutcome_sd+TrustUnionLeaders_sd+Gender_cat+education_sd+Migrant_bi+ Monthly_expenditures_sd+prim_liv+OcMultiplicity_sd+market_dist_sd+ IncomeTURF_cat+ TrustCommunity_sd+CommunityEvents_sd+ (1|site),data=chiledata2,family=cumulative("logit"),chains = 5,control = list(adapt_delta = 0.99)
This is the summary of the model: (to simplify, I will only add relevant parts)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS Intercept -4.75 0.67 -6.08 -3.45 1.00 3323 3620 Intercept -2.70 0.64 -3.98 -1.42 1.00 3386 3547 Intercept 0.01 0.64 -1.21 1.25 1.00 3490 3701 EquityOutcome_sd 1.02 0.25 0.52 1.50 1.00 4574 4025
One way of plotting conditional effects is by showing the probability of each category of the ordinal variable, but I am more interested in plotting the latent response variable.
To visualize the conditional effects of EquityOutcome_sd on the latent variable wellbeing, I used the following code:
cond_plot_wellbeing_1<-conditional_effects(M_wellbeing, "EquityOutcome_sd",method = "posterior_linpred", prob=0.95) cond_plot_wellbeing_1
Is the following interpretation correct?
- The y-axis represents the cumulative log odds of perceiving wellbeing in the latent scale.
- The blue line represents the effect of EquityOutcome_sd on the latent variable wellbeing. With 95% CI, we can say that for 1 unit of increase in EquityOutcome_sd, wellbeing increases by 1.02 standard deviations.
- For one unit of increase in EquityOutcome_sd, the expected increase in odds of perceiving wellbeing is 2.77. I have exponentiated the coefficient of EquityOutcome_sd (which is in log odds) to obtain the odds. exp(1.02)=2.77
- The odds of perceiving wellbeing are, on average, 7.3 times higher when EquityOutcome_sd is high (EquityOutcome_sd=0.5), relative to when EquityOutcome_sd is low (EquityOutcome_sd= -1.5). To calculate this, I have calculated the difference in log odds at high values and low values of EquityOutcome_sd (2 log odds) and exponentiated this value to obtain the odds: exp(2)=7.3