marginal_coefs.RdCalculates marginal coefficients and their standard errors from fitted generalized linear mixed models.
marginal_coefs(object, ...)
# S3 method for MixMod
marginal_coefs(object, std_errors = FALSE,
link_fun = NULL, M = 3000, K = 100, seed = 1,
cores = max(parallel::detectCores() - 1, 1),
sandwich = FALSE, ...)an object inheriting from class "MixMod".
logical indicating whether standard errors are to be computed.
a function transforming the mean of the repeated measurements outcome to the
linear predictor scale. Typically, this derived from the family argument of
mixed_model.
numeric scalar denoting the number of Monte Carlo samples.
numeric scalar denoting the number of samples from the sampling distribution of the maximum likelihood estimates.
integer denoting the seed for the random number generation.
integer giving the number of cores to use; applicable only when
std_errors = TRUE.
logical; if TRUE robust/sandwich standard errors are used in the
calculations.
extra arguments; currently none is used.
It uses the approach of Hedeker et al. (2017) to calculate marginal coefficients from
mixed models with nonlinear link functions. The marginal probabilities are calculated
using Monte Carlo integration over the random effects with M samples, by sampling
from the estimated prior distribution, i.e., a multivariate normal distribution with mean
0 and covariance matrix \(\hat{D}\), where \(\hat{D}\) denotes the estimated
covariance matrix of the random effects.
To calculate the standard errors, the Monte Carlo integration procedure is repeated
K times, where each time instead of the maximum likelihood estimates of the fixed
effects and the covariance matrix of the random effects, a realization is used from the
sampling distribution of the maximum likelihood estimates. To speed-up this process,
package parallel is used.
A list of class "m_coefs" with components betas the marginal coefficients,
and when std_errors = TRUE, the extra components var_betas the estimated
covariance matrix of the marginal coefficients, and coef_table a numeric matrix
with the estimated marginal coefficients, their standard errors and corresponding
p-values using the normal approximation.
Hedeker, D., du Toit, S. H., Demirtas, H. and Gibbons, R. D. (2018), A note on marginalization of regression parameters from mixed models of binary outcomes. Biometrics 74, 354--361. doi:10.1111/biom.12707
# \donttest{
# simulate some data
set.seed(123L)
n <- 500
K <- 15
t.max <- 25
betas <- c(-2.13, -0.25, 0.24, -0.05)
D <- matrix(0, 2, 2)
D[1:2, 1:2] <- c(0.48, -0.08, -0.08, 0.18)
times <- c(replicate(n, c(0, sort(runif(K-1, 0, t.max)))))
group <- sample(rep(0:1, each = n/2))
DF <- data.frame(year = times, group = factor(rep(group, each = K)))
X <- model.matrix(~ group * year, data = DF)
Z <- model.matrix(~ year, data = DF)
b <- cbind(rnorm(n, sd = sqrt(D[1, 1])), rnorm(n, sd = sqrt(D[2, 2])))
id <- rep(1:n, each = K)
eta.y <- as.vector(X %*% betas + rowSums(Z * b[id, ]))
DF$y <- rbinom(n * K, 1, plogis(eta.y))
DF$id <- factor(id)
################################################
fm1 <- mixed_model(fixed = y ~ year * group, random = ~ 1 | id, data = DF,
family = binomial())
fixef(fm1)
#> (Intercept) year group1 year:group1
#> -2.875293208 0.204144801 -0.648693468 -0.006044763
marginal_coefs(fm1)
#> (Intercept) year group1 year:group1
#> -1.3589 0.0966 -0.3298 -0.0017
marginal_coefs(fm1, std_errors = TRUE, cores = 1L)
#> Estimate Std.Err z-value p-value
#> (Intercept) -1.3589 0.1132 -12.0052 < 1e-04
#> year 0.0966 0.0049 19.5229 < 1e-04
#> group1 -0.3298 0.1593 -2.0701 0.03844
#> year:group1 -0.0017 0.0060 -0.2795 0.77983
#>
# }