df <- brglm2::endometrial
set.seed(525243)

fit <- MCMCglmm::MCMCglmm(
    NV ~ EH + HG,
    family = "categorical",
    data = df,
    prior = list(
        B = list(
            mu = rep(0, 3),
            V = MCMCglmm::gelman.prior(
                ~ EH + HG, 
                data = df, 
                scale = sqrt(pi^2/3+1)
            )
        ),
        R = list(V = 1, fix = 1)
    ),
    nitt = 100000,
    burnin = 1000,
    thin = 10,
    verbose = FALSE
)

summary(fit)
#> 
#>  Iterations = 1001:99991
#>  Thinning interval  = 10
#>  Sample size  = 9900 
#> 
#>  DIC: 42.77461 
#> 
#>  R-structure:  ~units
#> 
#>       post.mean l-95% CI u-95% CI eff.samp
#> units         1        1        1        0
#> 
#>  Location effects: NV ~ EH + HG 
#> 
#>             post.mean l-95% CI u-95% CI eff.samp   pMCMC   
#> (Intercept)   -1.3239  -4.6634   1.8131   1430.6 0.43071   
#> EH            -1.8184  -3.4936  -0.1290    987.7 0.03131 * 
#> HG             2.9383   0.8804   5.1687    733.0 0.00182 **
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1