Fixed effect variance estimation for Joint Rank Method (JR). It assumes Compound Symmetric (CS) structure of error terms. For k-level design, there are k-1 intra/inter-class parameters to place in a correlation matrix of errors.
beta_var(x, school, tauhat, v1, v2, v3, section, mat)Data frame of covariates.
A vector of cluster.
This is obtained from Rank-based fitting.
tauhat here~~
This is 1, main diagonal element for correlation matrix of observations. Correlation of an observation with itself is 1.
Intra-cluster correlation coefficient.
Intra-subcluster correlation coefficient.
A vector of subclusters, nx1.
A matrix of numbers of observations in subclusters. Dimension is Ixmax(number ofsubclusters). Each row indicates one cluster.
The variance of fixed estimated.
Correlation coefficients are obtained using Moment Estimates. See Klole et. al (2009), Bilgic (2012) and HM (2012)
Y. K. Bilgic. Rank-based estimation and prediction for mixed effects models in nested designs. 2012. URL http://scholarworks.wmich.edu/dissertations/40. Dissertation.
J. Kloke, J. W. McKean and M. Rashid. Rank-based estimation and associated inferences for linear models with cluster correlated errors. Journal of the American Statistical Association, 104(485):384-390, 2009.
T. P. Hettmansperger and J. W. McKean. Robust Nonparametric Statistical Methods. Chapman Hall, 2012.