I have a question about model interpetation. I originally posed a question about the type of model I should run, and Solomon was very kind to help Setting priors and interpreting ordered logistic model).
I am trying to determine whether three different continents (Africa, Asia, Europe) have different numbers of life expectancies at different levels (low, med, high) (this data and question are entirely fabricated)
Essentially: does continent predict how many low/med/high life expectancies in that group?
#load libraries library(brms) library("gapminder") library("dplyr") #Edit data data(gapminder) gapminder <-gapminder #select columns of interest gapminder <-gapminder %>% select(continent,lifeExp, pop) #select continents of interest gapminder <-gapminder %>% filter(continent == c("Africa","Asia","Europe")) #Make ordered factors gapminder$lifeExp<- cut(gapminder$lifeExp, 3, labels=c("low","med","high"), ordered_result=TRUE)
After advice, I have settled on an ordinal cumulative model with probit link:
mod2selection_fit <- brm( formula = lifeExp ~ 1 + continent, data = gapminder, family = cumulative(probit), prior = c( prior(normal(0, 2), class = Intercept), prior(normal(0, 1), class = b)))
Family: cumulative Links: mu = probit; disc = identity Formula: lifeExp ~ 1 + continent Data: gapminder (Number of observations: 460) Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1; total post-warmup draws = 4000 Population-Level Effects: Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS Intercept 0.10 0.08 -0.06 0.26 1.00 3951 2911 Intercept 1.47 0.11 1.26 1.69 1.00 2764 3112 continentAsia 1.17 0.13 0.91 1.42 1.00 2899 2919 continentEurope 3.03 0.21 2.64 3.44 1.00 2482 2857 Family Specific Parameters: Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS disc 1.00 0.00 1.00 1.00 NA NA NA Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS and Tail_ESS are effective sample size measures, and Rhat is the potential scale reduction factor on split chains (at convergence, Rhat = 1).
My question is about interpreting this, what it means to the average person (me!)
Lets taker the continent Asia as an Example, the estimate is 1.17, and the 95%CI do not cross 0. Could I interpret this as Asia has 1.17 years more life expectancy than Africa? Or should I transform this as it is a probit link?Or is it in terms of risk? I’m trying to understand exactly what the numbers in the output are telling me.
Also, what if the 95%CI did NOT cross 0, then I couldn’t be confident in the estimate?
Finally, does anyone have any suggestions for how one would report this in a paper, is there a Bayes equivalent of the frequentist (p value, confidence intervals) reporting?
Thank you so much and Happy new year to all!