Intra-Cluster Correlation for Clustered Binomial data
The function estimates the intraclass correlation ρ from clustered binomial data:
{(n_1, m_1), (n_2, m_2), ..., (n_N, m_N)},
where n_i is the size of cluster i, m_i the number of “successes” (proportions are y = m/n), and N the number of clusters. The function uses a one-way random effect model. Three estimates, corresponding to methods referred to as “A”, “B” and “C” in Goldstein et al. (2002), can be returned.
iccbin(n, m, method = c("A", "B", "C"), nAGQ = 1, M = 1000)
## S3 method for class 'iccbin'
print(x, ...)n |
A vector of the sizes of the clusters. |
m |
A vector of the numbers of successes (proportions are eqny = m / n). |
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. |
x |
An object of class “iccbin”. |
... |
Further arguments to ba passed to “print”. |
Before computations, the clustered data are split to binary “0/1” observations y_{ij} (observation j in cluster i). The methods of calculation are described in Goldstein et al. (2002).
Methods "A" and "B" use the 1-way logistic binomial-Gaussian model
y_{ij} | μ_{ij} \sim Bernoulli(μ_{ij})
logit(μ_{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_{ik}] is then calculated from a first-order model linearization around E[u_i]=0 in method “A”, and with Monte Carlo simulations in method “B”.
Method "C" provides the common ANOVA (moment) estimate of ρ. For details, see for instance Donner (1986), Searle et al. (1992) or Ukoumunne (2002).
An object of class iccbin, printed with print.iccbin.
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)
z <- rats[rats$group == "TREAT", ]
# A: glmm (model linearization)
iccbin(z$n, z$m, method = "A")
iccbin(z$n, z$m, method = "A", nAGQ = 10)
# B: glmm (Monte Carlo)
iccbin(z$n, z$m, method = "B")
iccbin(z$n, z$m, method = "B", nAGQ = 10, M = 1500)
# C: lmm (ANOVA moments)
iccbin(z$n, z$m, method = "C")
## Not run:
# Example of CI calculation with nonparametric bootstrap
require(boot)
foo <- function(X, ind) {
n <- X$n[ind]
m <- X$m[ind]
iccbin(n = n, m = m, method = "C")$rho
}
res <- boot(data = z[, c("n", "m")], 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.