Calculates 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, ...)

## Arguments

object 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.

## Details

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.

## Value

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.

## References

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

## Author

Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

mixed_model

## Examples

# \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
#> # }