Correlation estimates > 1 with unstructured working correlation

[DavidLukeThiessen]

When a working correlation structure is used in geeglm or geese the resulting correlation estimates can be outside [-1,1].

Ideally this should never happen. But until this can be corrected a warning should be created so the user is alerted to any potential problem.

library(MASS)
library(geepack)
library(tidyr)
generate_data <- function(nobs = 100) {
  sig <- matrix(data = c(1, 0.5, 0.5,
                         0.5, 1, 0.9,
                         0.5, 0.9, 1),
                nrow = 3, ncol = 3)
  y <- mvrnorm(n = nobs,
               mu = c(0, 0, 0),
               Sigma = sig)
  dat <- data.frame(id = factor(1:nobs),
                    y1 = y[,1],
                    y2 = y[,2],
                    y3 = y[,3])
  pivot_longer(dat,
               cols = c(y1, y2, y3),
               names_to = "Time",
               values_to = "vals")
}
set.seed(3045)
simdat <- generate_data(100)
mod <- geeglm(vals ~ 1, id = id,
              data = simdat,
              corstr = "unstructured")
summary(mod)
#> 
#> Call:
#> geeglm(formula = vals ~ 1, data = simdat, id = id, corstr = "unstructured")
#> 
#>  Coefficients:
#>             Estimate Std.err  Wald Pr(>|W|)
#> (Intercept)   0.1008  0.0841 1.437    0.231
#> 
#> Correlation structure = unstructured 
#> Estimated Scale Parameters:
#> 
#>             Estimate Std.err
#> (Intercept)    1.083  0.1374
#>   Link = identity 
#> 
#> Estimated Correlation Parameters:
#>           Estimate Std.err
#> alpha.1:2   0.4274 0.07357
#> alpha.1:3   0.4448 0.06583
#> alpha.2:3   1.1153 0.04518
#> Number of clusters:   100  Maximum cluster size: 3