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Interval Odds Ratio

Source: R/performance_ior.R
performance_ior.Rd

The Interval Odds Ratio (IOR) evaluates the fixed effect of a cluster-level (level 2) covariate by explicitly incorporating the residual between-cluster heterogeneity. interval_odds_ratio() is an alias for performance_ior().

Usage

performance_ior(x)

interval_odds_ratio(x)

Arguments

x

A (logistic) multilevel model.

Value

A data frame with the parameter names and their interval odds ratios.

Details

Unlike a standard confidence interval (which reflects sample estimation uncertainty around the coefficients), the IOR reflects the variation in odds ratios across clusters due to residual cluster heterogeneity.

  • IOR does not contain 1: If the entire interval is above 1 (or below 1), the cluster-level covariate has a strong effect. Even when moving from a "good" unexposed cluster to a "bad" exposed cluster (or vice versa), the directional effect of the covariate remains dominant.

  • IOR contains 1: When the interval contains 1, the between-cluster heterogeneity is larger than the effect of the covariate itself. This means an individual moving from an unexposed cluster to an exposed cluster could actually experience lower odds of the outcome if the new cluster happens to have a very low unobserved random effect.

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_poor() and performance_mor() 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_ior(m)
#> Interval Odds Ratio
#> 
#> Parameter   |   Group |         80% CI
#> --------------------------------------
#> (Intercept) | Subject | [0.00,   5.21]
#> Days        | Subject | [0.01, 348.24]

m <- suppressWarnings(lme4::glmer(
  high_reaction ~ Days + (1 | mygrp) + (1 | Subject),
  data = sleepstudy,
  family = "binomial"
))
#> boundary (singular) fit: see help('isSingular')
performance_ior(m)
#> boundary (singular) fit: see help('isSingular')
#> Interval Odds Ratio
#> 
#> Parameter   |   Group |         80% CI
#> --------------------------------------
#> (Intercept) | Subject | [0.00,   5.21]
#> Days        | Subject | [0.01, 348.24]
#> (Intercept) |   mygrp | [0.03,   0.03]
#> Days        |   mygrp | [2.10,   2.10]