Median Odds Ratio (MOR) for a logistic MAIHDA model
Source:R/discriminatory_accuracy.R
maihda_mor.RdThe Median Odds Ratio translates the between-stratum variance of a logistic
MAIHDA model onto the odds-ratio scale: the median relative change in the odds
of the outcome when comparing two individuals from randomly chosen strata
(higher- vs lower-risk). MOR = exp(sqrt(2 * V_A) * qnorm(0.75)), where
V_A is the between-stratum (latent, logit-scale) variance. An MOR of 1
indicates no between-stratum heterogeneity. The MOR is defined only for the
logit link (it is the median odds ratio); a non-logit binomial
fit such as probit is rejected, because its latent variance is on a
different scale and the exp(...) above would not be an odds ratio.
For a cumulative-logit (ordinal) MAIHDA model the same formula applies to the latent logit-scale between-stratum variance and is the median cumulative odds ratio: the median relative change in the odds of being at or below any given outcome category between two randomly chosen strata (under the model's proportional-odds assumption it is the same for every category split).
Arguments
- model
A
maihda_modelfromfit_maihdafitted with abinomial(lme4),bernoulli(brms), orcumulative(ordinal) family and a logit link.
Value
A single number (the MOR, \(\ge 1\)), or NA_real_ if the
between-stratum variance is unavailable.
References
Larsen, K., & Merlo, J. (2005). Appropriate assessment of neighborhood effects on individual health: integrating random and fixed effects in multilevel logistic regression. American Journal of Epidemiology, 161(1), 81-88.