icc {aod} | R Documentation |
This function computes the intra-cluster correlation \rho from clustered binomial data (n, y), using the ML/REML and ANOVA methods.
icc(n, y, data, method = c("REML", "ML"), R = NULL)
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. |
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.
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. |
Matthieu Lesnoff matthieu.lesnoff@cirad.fr, Renaud Lancelot renaud.lancelot@cirad.fr
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.
icc-class
, lme
icc
in the contributed packages irr and psy.
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))