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Median Odds Ratio

Source: R/performance_mor.R
performance_mor.Rd

A measure of cluster-level variation in multilevel logistic regression, defined as the median odds ratio between two randomly chosen individuals from different clusters with identical covariates, comparing the person at higher risk to the person at lower risk. median_odds_ratio() is an alias for performance_mor().

Usage

performance_mor(x)

median_odds_ratio(x)

Arguments

x

A (logistic) multilevel model.

Value

A data frame with two columns, one with the group (cluster) names and one with the median odds ratios.

Details

The MOR is always greater than or equal to 1 and can be interpreted as follows:

  • MOR close to 1: No Cluster Effect. There is (almost) no between-cluster heterogeneity, meaning cluster membership plays no role in the outcome.

  • MOR > 1: Presence of Heterogeneity. Indicates meaningful variation across clusters. If two persons are randomly picked from two different clusters, the MOR represents the median factor by which the odds of the outcome increase for the individual from the higher-risk cluster compared to the individual in the lower-risk cluster.

References

Larsen K, Merlo J. Appropriate Assessment of Neighborhood Effects on Individual Health: Integrating Random and Fixed Effects in Multilevel Logistic Regression. American Journal of Epidemiology (2005) 161:81–88. doi:10.1093/aje/kwi017

Merlo J, Wagner P, Ghith N, Leckie G. An Original Stepwise Multilevel Logistic Regression Analysis of Discriminatory Accuracy: The Case of Neighbourhoods and Health. PLoS ONE (2016) 11:e0153778. doi:10.1371/journal.pone.0153778

See also

performance_ior() and performance_poor() as additional metrics specifically for logistic multilevel regression models, and icc() for multilevel models in general.

Examples

data(sleepstudy, package = "lme4")
sleepstudy$mygrp <- sample(1:5, size = 180, replace = TRUE)
sleepstudy$high_reaction <- as.factor(datawizard::categorize(sleepstudy$Reaction))

m <- lme4::glmer(
  high_reaction ~ Days + (1 | Subject),
  data = sleepstudy,
  family = "binomial"
)
performance_mor(m)
#> Median Odds Ratio
#> 
#> Group   |   MOR
#> ---------------
#> Subject | 14.73

m <- suppressWarnings(lme4::glmer(
  high_reaction ~ Days + (1 | mygrp) + (1 | Subject),
  data = sleepstudy,
  family = "binomial"
))
#> boundary (singular) fit: see help('isSingular')
performance_mor(m)
#> boundary (singular) fit: see help('isSingular')
#> Median Odds Ratio
#> 
#> Group   |   MOR
#> ---------------
#> Subject | 14.73
#> mygrp   |  1.00