beta_var {rlme}

Estimate fixed-effect variance for Joint Rank Method (JR) in three-level nested design.

Description

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.

Usage

beta_var(x, school, tauhat, v1, v2, v3, section, mat)

Arguments

x

Data frame of covariates.

school

A vector of cluster.

tauhat

This is obtained from Rank-based fitting. tauhat here~~

v1

This is 1, main diagonal element for correlation matrix of observations. Correlation of an observation with itself is 1.

v2

Intra-cluster correlation coefficient.

v3

Intra-subcluster correlation coefficient.

section

A vector of subclusters, nx1.

mat

A matrix of numbers of observations in subclusters. Dimension is Ixmax(number ofsubclusters). Each row indicates one cluster.

Details

Correlation coefficients are obtained using Moment Estimates. See Klole et. al (2009), Bilgic (2012) and HM (2012)

Value

var

The variance of fixed estimated.

Author(s)

Yusuf Bilgic

References

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.