icc {aod}R Documentation

Intra-Cluster Correlation

Description

This function computes the intra-cluster correlation \rho from clustered binomial data (n, y), using the ML/REML and ANOVA methods.

Usage

icc(n, y, data, method = c("REML", "ML"), R = NULL)

Arguments

n The denominator of the proportion.
y The numerator of the proportion.
data A data frame containing the data.
method A character string “ML” (maximum likelihood) or “REML” (restricted ML) used in the first estimation method for \rho. Default to “REML”.
R A scalar indicating the number of Monte Carlo (MC) replicates used to estimate the confidence interval of \rho (ML/REML estimate). When R is NULL (the default value), the MC confidence interval is not computed.

Details

The function ungroups the clustered data into binary (0/1) observations y_{ij} (obs. j in cluster i).
For the ML/REML method, a linear mixed-effect model is fitted:

y_{ij} = \mu + u_i + e_{ij}

where \mu is the general mean, a_i is the random cluster effect and e_{ij} is the residual error. Model assumptions are: u ~ N(0, \sigma_u^2) and e_{ij} ~ N(0, \sigma_e^2). The intra-cluster correlation is computed as

\rho = \sigma_u^2 / (\sigma_u^2 + \sigma_e^2)

Variance components \sigma_u^2 and \sigma_e^2 (actually, vector \nu = log(\sigma_u, \sigma_e)) are estimated with lme (package nlme): see Pinheiro and Bates, 2000. The variance of \rho is estimated with the Delta method. An F test is provided to assess whether \rho = 0 (actually, whether \sigma_u^2 = 0: see Searle et al, 1992, p. 76). If the argument R is not null, a MC confidence interval of \rho is computed assuming that \nu ~ N(\nu, Var[\nu]), where Var[\nu] is the matrix apVar provided in the lme output.
For the ANOVA method, see Donner (1989), Searle et al. (1992) or Zou and Donner (2004).
The function assumes an homogeneous proportion p across the clusters.

Value

An object of formal class “icc”, with 7 slots:
CALL The call of the function.
rho A numeric vector with 2 components: REML (or ML) and ANOVA, containing the estimated values of \rho according to these 2 methods.
varrho A numeric scalar giving the approximate variance of \rho (ML/REML estimate) estimated with the Delta method.
f A numeric vector with the results of the F test.
rho.MC A numeric vector with the MC replicates of \rho.
method A character string taking values “ML” or “REML”.
features A numeric vector with 3 components summarizing the main features of the data: N = number of clusters, n = number of subjects, y = number of cases.

Author(s)

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

References

Donner, A., 1989. Statistical methods in ophthalmology: an adjusted chi-squared approach. Biometrics 45, 605-611.
Pinheiro, J.C., Bates, D.M., 2000. Mixed-effects models in S and S-PLUS. Springer-Verlag, New York.
Searle, S.R., Casella, G., McCulloch, C.E., 1992. Variance components. Wiley, New York.
Zou, G., Donner, A., 2004. Confidence interval estimation of the intraclass correlation coefficient for binary outcome data. Biometrics 60, 807-811.

See Also

icc-class, lme
icc in the contributed packages irr and psy.

Examples

  data(rats)
  icc(n, y, rats[rats$group == "CTRL", ])
  ## Not run: 
    res <- icc(n, y, rats[rats$group == "TREAT", ], R = 5000)
    res
    hist(res@rho.MC)
    
## End(Not run)
  by(rats,
     list(group = rats$group),
     function(x) icc(n, y, data = x))
  

[Package aod version 1.1-31 Index]