R: Intra-Cluster Correlation for Binomial Data

iccbin {aod} | R Documentation

## Intra-Cluster Correlation for Binomial Data

### Description

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.

### Usage

    iccbin(n, y, data, method = c("A", "B", "C"), nAGQ = 1, M = 1000)

### Arguments

`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 `glmer` of package lme4. Only for methods “A” and “B”. Default to 1.
`M` | Number of Monte Carlo (MC) replicates used in method “B”. Default to 1000.

### Details

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).

### Value

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.

### Author(s)

Matthieu Lesnoff matthieu.lesnoff@cirad.fr, Renaud Lancelot renaud.lancelot@cirad.fr

### References

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.

### See Also

`iccbin-class`, `glmer`

### Examples

    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)

[Package aod version 1.3 Index]