Intra-Cluster Correlation for Binomial Data
This function calculates point estimates of the intraclass correlation ρ from clustered binomial data {(n_1, y_1), (n_2, y_2), ..., (n_K, y_K)} (with K the number of clusters), using a 1-way random effect model. Three estimates, following methods referred to as “A”, “B” and “C” in Goldstein et al. (2002), can be obtained.
iccbin(n, y, data, method = c("A", "B", "C"), nAGQ = 1, M = 1000)n |
Vector of the denominators of the proportions. |
y |
Vector of the numerators of the proportions. |
data |
A data frame containing the variables n and y. |
method |
A character (“A”, “B” or “C”) defining the calculation method. See Details. |
nAGQ |
Same as in function |
M |
Number of Monte Carlo (MC) replicates used in method “B”. Default to 1000. |
Before computations, the clustered data are split into binary (0/1) observations y_{ij} (obs. j in cluster
i).
The calculation methods are described in Goldstein et al. (2002).
Methods "A" and "B" assume a 1-way generalized linear mixed model,
and method "C" a 1-way linear mixed model.
For "A" and "B", function iccbin uses the logistic binomial-Gaussian model:
y_{ij} | p_{ij} \sim Bernoulli(p_{ij}),
logit(p_{ij}) = b_0 + u_i,
where b_0 is a constant and u_i a cluster random effect with u_i \sim N(0, s^2_u).
The ML estimate of the variance component s^2_u is calculated with the function glmer of package lme4.
The intra-class correlation ρ = Corr[y_{ij}, y_{ij'}] is then calculated with a first-order model linearization
around E[u_i]=0 in method “A”, and with Monte Carlo simulations in method “B”.
For “C”, function iccbin provides the common ANOVA (moments) estimate of ρ.
For details, see for instance Donner (1986), Searle et al. (1992) or Ukoumunne (2002).
An object of formal class “iccbin”, with 3 slots:
CALL |
The call of the function. |
features |
A character vector summarizing the main features of the method used. |
rho |
The point estimate of the intraclass correlation ρ. |
Matthieu Lesnoff matthieu.lesnoff@cirad.fr, Renaud Lancelot renaud.lancelot@cirad.fr
Donner A., 1986, A review of inference procedures for the intraclass correlation coefficient in the one-way random
effects model. International Statistical Review 54, 67-82.
Searle, S.R., Casella, G., McCulloch, C.E., 1992. Variance components. Wiley, New York.
Ukoumunne, O. C., 2002. A comparison of confidence interval methods for the intraclass
correlation coefficient in cluster randomized trials. Statistics in Medicine 21, 3757-3774.
Golstein, H., Browne, H., Rasbash, J., 2002. Partitioning variation in multilevel models.
Understanding Statistics 1(4), 223-231.
data(rats)
tmp <- rats[rats$group == "TREAT", ]
# A: glmm (model linearization)
iccbin(n, y, data = tmp, method = "A")
iccbin(n, y, data = tmp, method = "A", nAGQ = 10)
# B: glmm (Monte Carlo)
iccbin(n, y, data = tmp, method = "B")
iccbin(n, y, data = tmp, method = "B", nAGQ = 10, M = 1500)
# C: lmm (ANOVA moments)
iccbin(n, y, data = tmp, method = "C")
## Not run:
# Example of confidence interval calculation with nonparametric bootstrap
require(boot)
foo <- function(X, ind) {
n <- X$n[ind]
y <- X$y[ind]
X <- data.frame(n = n, y = y)
iccbin(n = n, y = y, data = X, method = "C")@rho[1]
}
res <- boot(data = tmp[, c("n", "y")], statistic = foo, R = 500, sim = "ordinary", stype = "i")
res
boot.ci(res, conf = 0.95, type = "basic")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.