Type: Package
Title: Rank-Based Estimation and Prediction in Random Effects Nested Models
Version: 0.5
Date: 2018-01-08
Author: Yusuf Bilgic, Herb Susmann and Joseph McKean
Maintainer: Yusuf Bilgic <bilgic@geneseo.edu>
Description: Estimates robust rank-based fixed effects and predicts robust random effects in two- and three- level random effects nested models. The methodology is described in Bilgic & Susmann (2013) https://journal.r-project.org/archive/2013/RJ-2013-027/.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Imports: MASS, quantreg, nlme, mgcv, stringr, magic, robustbase, Rcpp, stats, utils, graphics
Suggests: testthat
NeedsCompilation: yes
LinkingTo: Rcpp
Repository: CRAN
RoxygenNote: 6.0.1
Packaged: 2018-01-09 15:42:36 UTC; herb
LazyData: true
Date/Publication: 2018-01-09 17:35:55 UTC

rlme

Description

An R package for rank-based robust estimation and prediction in random effects nested models

Details

Package: rlme
Type: Package
Version: 0.2
Date: 2013-07-07
License: GPL (>= 2)

Author(s)

Yusuf Bilgic bilgic@geneseo.edu, Herb Susmann hps1@geneseo.edu and Joseph McKean joemckean@yahoo.com

Maintainer: Yusuf Bilgic bilgic@geneseo.edu or yusuf.k.bilgic@gmail.com

See Also

rlme

Examples



library(rlme)
data(schools)
formula = y ~ 1 + sex + age + (1 | region) + (1 | region:school)
rlme.fit = rlme(formula, schools)
summary(rlme.fit)

GEER: General Estimating Equation Rank-Based Estimation Method

Description

The package rlme calls this function for gee method, one of the methods proposed in Bilgic's study (2012). Also see Kloke et al. (2013). concise (1-5 lines) description of what the function does. ~~

Usage

GEER_est(x, y, I, sec, mat, school, section, weight = "wil",
  rprpair = "hl-disp", verbose = FALSE)

Arguments

x

Design matrix, pxn, without intercept.

y

Response vector of nx1.

I

Number of clusters.

sec

A vector of subcluster numbers in clusters.

mat

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

school

A vector of clusters, nx1.

section

A vector of subclusters, nx1.

weight

When weight="hbr", it uses hbr weights in GEE weights. By default, ="wil", it uses Wilcoxon weights. See the theory in the references.

rprpair

By default, it uses "hl-disp" in the random prediction procedure (RPP). Also, "med-mad" would be an alternative.

verbose

Boolean indicating whether to print out diagnostic messages.

Value

theta

Fixed effect estimates.

ses

Standard error for the fixed esimates.

sigma

Variances of cluster, subcluster, and residual.

ehat

Raw error.

ehats

Independence error from last weighted step.

effect_sch

Cluster random error.

effect_sec

Subcluster random error.

effect_err

Epsilon error.

Author(s)

Yusuf K. Bilgic, yekabe@hotmail.com

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.

A. Abebe, J. W. McKean, J. D. Kloke and Y. K. Bilgic. Iterated reweighted rank-based estimates for gee models. 2013. Submitted.

See Also

rlme, GR_est, JR_est, rprmeddisp

Examples


# See the rlme function.

GR Method

Description

Fits a model using the GR method

Usage

GR_est(x, y, I, sec, mat, school, section, rprpair = "hl-disp",
  verbose = FALSE)

Arguments

x

Covariate matrix or data frame.

y

Response matrix or data frame.

I

Number of clusters

sec

A vector of subcluster numbers in clusters.

mat

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

school

A vector of clusters, nx1.

section

A vector of subclusters, nx1.

rprpair

By default, it uses "hl-disp" in the random prediction procedure (RPP). Also, "med-mad" would be an alternative.

verbose

Boolean indicating whether to print out messages from the algorithm.

Value

theta

Fixed effect estimates.

ses

Standard error for the fixed esimates.

sigma

Variances of cluster, subcluster, and residual.

ehat

Raw error.

ehats

Independence error from last weighted step.

effect_sch

Cluster random error.

effect_sec

Subcluster random error.

effect_err

Epsilon error.

Author(s)

Yusuf Bilgic

Examples


# See rlme function

JR Method

Description

Fit a model using the JR method

Usage

JR_est(x, y, I, sec, mat, school, section, rprpair = "hl-disp",
  verbose = FALSE)

Arguments

x

Covariate matrix or data frame

y

Response matrix or data frame

I

Number of clusters.

sec

A vector of subcluster numbers in clusters.

mat

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

school

A vector of clusters, nx1.

section

A vector of subclusters, nx1.

rprpair

By default, it uses "hl-disp" in the random prediction procedure (RPP). Also, "med-mad" would be an alternative.

verbose

Boolean indicating whether to print out diagnostic messages.

Value

theta

Fixed effect estimates.

ses

Standard error for the fixed esimates.

sigma

Covariate variance estimates using RPP (Groggel and Dubnicka's procedure).

ehat

Raw error.

effect_sch

Cluster random error.

effect_sec

Subcluster random error.

effect_err

Epsilon error.

Author(s)

Yusuf Bilgic

See Also

rlme

Linear Model Estimation using the nlme package.

Description

This gets the REML or ML estimates and predictions of random effects from the nlme package. function does.

Usage

LM_est(x, y, dat, method = "REML")

Arguments

x

Design matrix, (p+1)xn, with intercept.

y

Response vector of nx1.

dat

Data frame

method

Character string indicating method to use, either "ML" or "REML" (defaults to REML).

Value

theta

Fixed effects esimates.

ses

Standard error for fixed effects.

varb

Variances.

sigma

Error.

ehat

Raw residuals

standr.lme

Standardized residual

effect_sch

Cluster random error.

effect_sec

Subcluster random error.

effect_err

Epsilon error.

Author(s)

Yusuf Bilgic

References

J. Pinheiro, D. Bates, S. DebRoy, D. Sarkar and R Development Core Team. nlme linear and non- linear mixed effects models. The R Journal, 2011. URL http://CRAN.R-project.org/package=nlme. R package version 3.1-98.

See Also

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.

Compare Fits

Description

Compares two model fits. It returns tdbeta value and cfits values of two fits. The function uses the fixed effects estimates from fit 1 and fit 2 along with the covariance of the rank-based fit.

Usage

compare.fits(x, fit1, fit2)

Arguments

x

Matrix of covariates

fit1

A class of type rlme.

fit2

A class of type rlme.

Value

Returns tdbeta and cfits values.

See Also

fitdvcov

Examples



data(schools)
model = y ~ 1 + sex + age + (1 | region) + (1 | region:school)

# Extract covariants into matrix
cov = as.matrix(data.frame(schools[,"sex"], schools[,"age"]))

# Fit the models using each method
reml.fit = rlme(model, schools, method="reml")
gr.fit = rlme(model, schools, method="gr")

compare.fits(cov, reml.fit, gr.fit)

Rank-based dispersion estimate.

Description

This is an unbiased estimator with a correction factor for standard deviation when normal errors.

Usage

dispvar(x, score = 1)

Arguments

x

vector

score

score type - 1 or 2

References

T. P. Hettmansperger and J. W. McKean. Robust Nonparametric Statistical Methods. Chapman Hall, 2012.

Fitdvcov

Description

Obtains measurement for the fits based on estimates beta1, beta2 and covariance matrix from a rank based methods.

Usage

fitdvcov(x1, beta1, beta2, vcw)

Arguments

x1

data

beta1

model 1 beta estimate

beta2

model 2 beta estimate

vcw

variance matrix

See Also

compare.fits

Examples



# Compare GR and JR methods

data(schools)

model = y ~ 1 + sex + age + (1 | region) + (1 | region:school)

# Extract covariants into matrix
cov = as.matrix(data.frame(schools[,"sex"], schools[,"age"]))

# Fit the models using each method
jr.fit = rlme(model, schools, method="jr")
gr.fit = rlme(model, schools, method="gr")

# Extract beta estimates, ignoring the intercept
jr.beta = jr.fit$fixed.effects$Estimate[c(2, 3)]
gr.beta = gr.fit$fixed.effects$Estimate[c(2, 3)]

# Extract beta variance matrix
var.b = jr.fit$var.b

fitdvcov(cov, jr.beta, gr.beta, var.b)

Q-Q Plot and Standardized Residual Plot for the GR fit.

Description

It gets Q-Q Plot and Standardized Residual Plot of residuals.

Usage

getgrstplot(rlme.fit)

Arguments

rlme.fit

RLME fit object

Details

The fit is obtained from rlme()

See Also

rlme

Q-Q Plot and Standardized Residual Plot for the REML or ML fit.

Description

It gets Q-Q Plot and Standardized Residual Plot of residuals. concise (1-5 lines) description of what the function does.

Usage

getlmestplot(rlme.fit)

Arguments

rlme.fit

The fit is obtained from rlme()

See Also

rlme

HBR Weight

Description

Calculates hbr weights for the GEER method. This turns a vector of weights for a vector of errors. Used to make factor space more robust, up to 50% breakdown. See HM (2012) and Terpstra and McKean (2005) for details. The ww package produces this weights as well.

Usage

hbrwts_gr(xmat, y, percent = 0.95, intest = ltsreg(xmat, y)$coef)

Arguments

xmat

Design matrix, pxn, without intercept.

y

Response vector in nx1.

percent

This is 0.95.

intest

This is obtained from myltsreg(xmat, y)$coef

Details

The ww package explains how it is obtained.

Author(s)

J. W. McKean

References

T. P. Hettmansperger and J. W. McKean. Robust Nonparametric Statistical Methods. Chapman Hall, 2012.

J. T. Terpstra and J. W. McKean. Rank-based analysis of linear models using R. Journal of Statistical Software, 14(7):1 - 26, 7 2005. ISSN 1548-7660. URL http://www.jstatsoft.org/v14/i07.

See Also

GEER_est

Instruction

Description

A data frame on school instruction results.

Format

A data frame with 1190 observations on the following 13 variables.

X

a numeric vector

girl

a numeric vector

minority

a numeric vector

mathkind

a numeric vector

mathgain

a numeric vector

ses

a numeric vector

yearstea

a numeric vector

mathknow

a numeric vector

housepov

a numeric vector

mathprep

a numeric vector

classid

a numeric vector identifying the class within school

schoolid

a numeric vector identifying the school

childid

a numeric vector

Source

West, B., Welch, K. B., & Galecki, A. T. (2006). Linear mixed models: a practical guide using statistical software. Chapman & Hall/CRC.

Examples


# The following code takes a few minutes to run.
# In the interest of saving CRAN's example testing time,
# it has been commented out. If you want to use it,
# just uncomment and run.

# data(instruction)
# attach(instruction)

# data = data.frame(
#   y = mathgain,
#   mathkind = mathkind, 
#   girl = girl,
#   minority = minority,
#   ses = ses, 
#   school = factor(schoolid), 
#   section = factor(classid))


# fit.rlme = rlme(y ~ 1 + mathkind + girl + minority + ses + (1 | school) + (1 | school:section),
#  data = data,
#  method = "gr")
  
# summary(fit.rlme)

Rank Based Fixed Effect Regression

Description

Computes rank based regression estimates for fixed effect models.

Usage

lmr(f, data, se = FALSE, method = "L-BFGS-B")

Arguments

f

A model formula

data

Data to use for model fitting

se

Boolean indicating whether or not to calculate standard errors for intercept and slope estimates

method

Optimization method to use. Will accept any method usable by optim, e.g. one of c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", "Brent"). "BFGS" or "L-BFGS-B" are reccomended. "L-BFGS-B" should be used for large datasets to conserve memory.

Value

fixed.effects

Fixed effect estimates

ehat

Residuals from model

Author(s)

Herb Susmann

See Also

rlme, optim

Examples


# load schools data
data(schools)

# Fit fixed effects model with lmr
lmr.fit = lmr(y ~ age + sex, data=schools)

summary(lmr.fit)

# Fit with lmr and calculate standard errors
lmr.fit = lmr(y ~ age + sex, data=schools, se=TRUE)

summary(lmr.fit)

Minimize Dispersion Function

Description

Uses optim to find regression estimates which minimize dispersion function on X and Y input matrices

Usage

minimize_dispersion(X, Y, method = "BFGS", init.guess = "quantreg",
  verbose = FALSE, se = TRUE)

Arguments

X

Input matrix

Y

Response vector

method

Method optim should use - one of "Nelder-Mead", "BFGS", "CG", "L-BFGS-B", "SANN", or "Brent".

init.guess

How to calculate the first regression estimate. Defaults to using quantile regression.

verbose

Whether to print out verbose messages.

se

Whether or not to calculate standard errors of regression estimates.

Value

theta

Regression parameter estimates

ehat

Regression residuals

Author(s)

Herb Susmann

Plot rlme Fit

Description

Generates Normal Q-Q plot of residuals from rlme fit

Usage

## S3 method for class 'rlme'
plot(x, ...)

Arguments

x

A list of class rlme. Store as fit.rlme.

...

not used

Examples


data(schools)
rlme.fit = rlme(y ~ 1 + sex + age + (1 | region) + (1 | region:school), schools, method="gr")
plot(rlme.fit)

Cluster Correlation Coefficient Estimate

Description

Moment estimate version of correlation coefficient in a cluster in a three-level nested design.

Usage

rhosch(ahat, school, section)

Arguments

ahat

A vector of scores. Wilcoxon scores are used in the package.

school

A vector of clusters.

section

A vector of subclusters.

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.

Subcluster Correlation Coefficient Estimate

Description

Moment estimate version of correlation coefficient in a subcluster in a three-level nested design.

Usage

rhosect(ahat, school, section)

Arguments

ahat

A vector of scores. Wilcoxon scores are used in the package.

school

A vector of clusters.

section

A vector of subclusters.

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.

Rank-based Estimates for Mixed-Effects Nested Models

Description

This function estimates fixed effects and predicts random effects in two- and three-level random effects nested models using three rank-based fittings (GR, GEER, JR) via the prediction method algorithm RPP.

Usage

rlme(f, data, method = "gr", print = FALSE, na.omit = TRUE,
  weight = "wil", rprpair = "hl-disp", verbose = FALSE)

Arguments

f

An object of class formula describing the mixed effects model. The syntax is same as in the lme4 package. Example: y ~ 1 + sex + age + (1 | region) + (1 | region:school) - sex and age are the fixed effects, region and school are the nested random effects, school is nested within region.

data

The dataframe to analyze. Data should be cleaned prior to analysis: cluster and subcluster columns are expected to be integers and in order (e.g. all clusters and subclusters )

method

string indicating the method to use (one of "gr", "jr", "reml", and "geer"). defaults to "gr".

print

Whether or not to print a summary of results. Defaults to false.

na.omit

Whether or not to omit rows containing NA values. Defaults to true.

weight

When weight="hbr", it uses hbr weights in GEE weights. By default, ="wil", it uses Wilcoxon weights. See the theory in the references.

rprpair

By default, it uses "hl-disp" in the random prediction procedure (RPP). Also, "med-mad" would be an alternative.

verbose

Boolean indicating whether to print out diagnostic messages.

Details

The iterative methods GR and GEER can be quite slow for large datasets; try JR for faster analysis. If you want to use the GR method, try using rprpair='med-mad'. This method avoids building a NxN covariance matrix which can quickly become unwieldly with large data.

Value

The function returns a list of class "rlme". Use summary.rlme to see a summary of the fit.

formula

The model formula.

method

The method used.

fixed.effects

Estimate of fixed effects.

random.effects

Estimate of random effects.

standard.residual

Residuals.

intra.class.correlations

Intra/inter-class correlationa estimates obtained from RPP.

t.value

t-values.

p.value

p-values.

location

Location.

scale

Scale.

y

The response variable y.

num.obs

Number of observations in provided dataset.

num.clusters

The number of clusters.

num.subclusters

The number of subclusters.

effect.err

Effect from error.

effect.cluster

Effect from cluster.

effect.subcluster

Effect from subcluster.

var.b

Variances of fixed effects estimate (Beta estimates).

xstar

Weighted design matrix with error covariance matrix.

ystar

Weighted response vector with its covariance matrix.

ehat

The raw residual.

ehats

The raw residual after weighted step. Scaled residual.

Author(s)

Yusuf Bilgic yekabe@hotmail.com and Herb Susmann hps1@geneseo.edu

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.

T. P. Hettmansperger and J. W. McKean. Robust Nonparametric Statistical Methods. Chapman Hall, 2012.

See Also

summary.rlme, plot.rlme, compare.fits

Examples


data(schools)

rlme.fit = rlme(y ~ 1 + sex + age + (1 | region) + (1 | region:school), schools, method="gr")
summary(rlme.fit)

# Try method="geer", "reml", "ml" and "jr" along with 
# rprpair="hl-disp" (not robust), and "med-mad" (robust),
# weight="hbr" is for the gee method.

Cluster and Subcluster effects

Description

Partitions model residuals into cluster and subcluster effects using RPP algorithm.

Usage

rpr(f, resd, data, rprpair = "hl-disp")

Arguments

f

A model formula which specifices the random effects (see example)

resd

The residuals from the fitted model

data

The data the model was fitted on

rprpair

Character string indicating the location and scale parameters to use. Default to "hl-disp", but may also be "med-mad". See Bilgic (2012).

Value

siga2

Variance from cluster

sigw2

Variance from subcluster

sigmae2

Remaining variance not accounted for by variance of cluster and subcluster

Author(s)

J. W. McKean and Y. K. 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.

See Also

rprmeddis, dispvar

Examples


# Load school data
data(schools)

# Fit fixed effects model with lmr
lmr.fit = lmr(y ~ age + sex, data=schools)

# Three level design
# Partition residuals into school and region effects with rpp algorithm
rpr(y ~ age + sex + (1 | school) + (1 | school:region), lmr.fit$ehat, schools)

# Two level design
# Estimate variance in residuals from school
rpr(y ~ age + sex + (1 | school), lmr.fit$ehat, schools)

Rprmeddis

Description

Robust rank-based prediction algorithm that gets predictions for random errors in three-level nested design. It needs one location and scale estimators. Hodges-Lehmann location estimate and dispersion functional estimate pair is called with rprpair="hl-disp" -by default- ; median and MAD pair is called with rprpair="med-mad" in rlme().

Usage

rprmeddis(I, sec, mat, ehat, location, scale, rprpair = "hl-disp")

Arguments

I

Number of clusters.

sec

A vector of subcluster numbers in clusters.

mat

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

ehat

The residuals that inherits random effects and error effect to be predicted.

location

If location = scale = 1 then use Median and MAD in RPP If location = scale = 2 then use HL & Dispvar in RPP Note: this is deprecated. You should specify the location & scale parameters by using the rprpair parameter.

scale

1 means mad, 2 means disp as scale estimators

rprpair

Character string indicating the location and scale parameters to use. Default to "hl-disp", but may also be "med-mad". See Bilgic (2012).

Details

The rprmeddisp() function yields predictions of random effects and errors vectors along with scale estimates in each level. This function was designed for three-level nested design. See rprmeddisp2() in the package, this is for two-level nested design.

Author(s)

Yusuf Bilgic yekabe@hotmail.com

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.

See Also

rpr dispvar

PISA Literacy Data

Description

The data in Program for International Assessment (PISA) on academic proficiency in schools around the world.

Format

A data frame with 334 observations on the following 6 variables.

y

a numeric vector indicating student literacy

socio

a numeric vector

sex

a numeric vector

age

a numeric vector

region

a numeric vector indicating four regions

school

a numeric vector indicating the schools within region

References

OECD (2010). PISA 2009 Results. http://www.oecd.org/

Examples


#
# The example takes a few seconds to run, so in order to 
# save CRAN's testing time it has been commented out. 
# To run, simply uncomment and execute.
#

# data(schools)
# rlme.fit = rlme(y ~ 1 + sex + age + (1 | region) + (1 | region:school), 
#	schools, method="gr")
# summary(rlme.fit)

Calculate Standard Residuals

Description

Standardizes the residuals obtained from the GR fitting.

Usage

stanresidgr(x, y, resid, delta = 0.8, param = 2, conf = 0.95)

Arguments

x

Design matrix.

y

Response vector.

resid

Residuals obtained from the rank-based fitting.

delta

See HM (2012).

param

See HM (2012).

conf

See HM (2012).

Author(s)

J. W. McKean

References

T. P. Hettmansperger and J. W. McKean. Robust Nonparametric Statistical Methods. Chapman Hall, 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.

rlme Summary

Description

Summarizes a model fit from the rmle function

Usage

## S3 method for class 'rlme'
summary(object, ...)

Arguments

object

A list of class rlme

...

not used

Author(s)

Herb Susmann hps1@geneseo.edu

See Also

rlme plot.rlme

Wilcoxon estimate for independent linear models

Description

This function gets weighted rank based fittings.

Usage

wilonestep(y, x)

Arguments

y

Response vector of nx1.

x

Design matrix, pxn, without intercept.

References

J. T. Terpstra and J. W. McKean. Rank-based analysis of linear models using R. Journal of Statistical Software, 14(7) 1 – 26, 7 2005. ISSN 1548-7660. URL http://www.jstatsoft.org/v14/i07.

Wilcoxon One Step Rank-based Estimate in GR Method

Description

Gets weighted rank based fittings for nested designs.

Usage

wilstep(I, sec, mat, init = F, y, x, sigmaa2 = 1, sigmaw2 = 1,
  sigmae2 = 1, thetaold = c(0), eps = 1e-04, iflag2 = 0,
  rprpair = "hl-disp")

Arguments

I

Number of clusters.

sec

A vector of subcluster numbers in clusters.

mat

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

init

boolean

y

Response vector of nx1.

x

Design matrix, pxn, without intercept.

sigmaa2

Initial sigma for cluster in three-level design.

sigmaw2

Initial sigma for subcluster in three-level design.

sigmae2

Initial sigma for error in three-level design.

thetaold

Initial input.

eps

Epsilon value

iflag2

y or n

rprpair

Either 'hl-disp' or 'med-mad'

Details

Initial inputs are from the independent model.

Author(s)

J. W. McKean and Y. K. Bilgic

References

Y. K. Bilgic and J. W. McKean. Iteratively reweighted generalized rank-based method in mixed models. 2013. Under preperation.

J. T. Terpstra and J. W. McKean. Rank-based analysis of linear models using R. Journal of Statistical Software, 14(7) 1 - 26, 7 2005. ISSN 1548-7660. URL http://www.jstatsoft.org/v14/i07.

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