Interpretation of conditional effects in cumulative models using posterior linpred

Modeling
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1

Hello,

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[1]                     -4.75      0.67    -6.08    -3.45 1.00     3323     3620
Intercept[2]                     -2.70      0.64    -3.98    -1.42 1.00     3386     3547
Intercept[3]                      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

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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

Thank you