Calculate Median Odds Ratio from a fitted multilevel binary logistic model object.

Usage

mor(object, conf.int = TRUE, conf.level = 0.95, ...)

Arguments

object: An glmerMod object created by lme4::glmer() or an MixMod object created by GLMMadaptive::mixed_model() or an glmmTMB object created by glmmTMB::glmmTMB(). See Details.
conf.int: Logical indicating whether or not to include a confidence interval using the Delta method in the tidied output. Defaults to TRUE.
conf.level: The confidence level to use for the confidence interval if conf.int = TRUE. Must be strictly greater than 0 and less than 1. Defaults to 0.95, which corresponds to a 95 percent confidence interval.
...: Currently not used.

Value

a tibble with columns,

term: Name of the estimate
estimate: Estimate of Median Odds Ratio (MOR)
ci_lower: Lower bound of the confidence interval of MOR
ci_upper: Upper bound of the confidence interval of MOR

Details

Median Odds Ratio (MOR) is suggested as a measure of heterogeneity that quantifies cluster heterogeneity and facilitates a direct comparison between covariate effects and the magnitude of heterogeneity in terms of well-known odds ratios (Larsen et al. 2000; Larsen and Merlo 2005)

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.

Larsen K, Petersen JH, Budtz-Jørgensen E, Endahl L (2000). “Interpreting parameters in the logistic regression model with random effects.” Biometrics, 56(3), 909–914.

Examples

data("mlm_data1")
data("mlm_data2")

# fitting two level random intercept model using lme4 package
model <- lme4::glmer(Yij ~ X1c + X2b + (1 | cluster),
  family = "binomial", data = mlm_data1
)

mor(model)
#> # A tibble: 1 × 4
#>   term        estimate ci_lower ci_upper
#>   <chr>          <dbl>    <dbl>    <dbl>
#> 1 mor_cluster     4.42     3.51     5.58
## to get 90% CI
mor(model, conf.level = 0.90)
#> # A tibble: 1 × 4
#>   term        estimate ci_lower ci_upper
#>   <chr>          <dbl>    <dbl>    <dbl>
#> 1 mor_cluster     4.42     3.64     5.38

# fitting two level random intercept model using GLMMadaptive package
model1 <- GLMMadaptive::mixed_model(
  fixed = Yij ~ X1c + X2b,
  random = ~ 1 | cluster,
  family = binomial("logit"),
  data = mlm_data1
)

mor(model1)
#> # A tibble: 1 × 4
#>   term        estimate ci_lower ci_upper
#>   <chr>          <dbl>    <dbl>    <dbl>
#> 1 mor_cluster     4.43     3.51     5.60

# fitting two level random intercept model using glmmTMB package
model2 <- glmmTMB::glmmTMB(Yij ~ X1c + X2b + (1 | cluster),
  family = binomial("logit"), data = mlm_data1
)

mor(model2)
#> # A tibble: 1 × 4
#>   term        estimate ci_lower ci_upper
#>   <chr>          <dbl>    <dbl>    <dbl>
#> 1 mor_cluster     4.42     3.50     5.59

# fitting three level random intercept model using glmmTMB package
model3 <- glmmTMB::glmmTMB(Yijk ~ X1c + X2b + (1 | ea) + (1 | ea:hh),
  family = "binomial", data = mlm_data2
)

mor(model3)
#> # A tibble: 2 × 4
#>   term      estimate ci_lower ci_upper
#>   <chr>        <dbl>    <dbl>    <dbl>
#> 1 mor_ea:hh     4.21     3.78     4.68
#> 2 mor_ea        6.29     5.38     7.36

# fitting three level random intercept model using lme4 package
model4 <- lme4::glmer(Yijk ~ X1c + X2b + (1 | ea) + (1 | ea:hh),
  family = "binomial", data = mlm_data2
)


mor(model4)
#> # A tibble: 2 × 4
#>   term      estimate ci_lower ci_upper
#>   <chr>        <dbl>    <dbl>    <dbl>
#> 1 mor_ea:hh     4.21     3.78     4.68
#> 2 mor_ea        6.29     5.38     7.36