Summary Method for "varComprob" Objects

Description

Summary method for R object of class "varComprob".

Usage

  ## S3 method for class 'varComprob'
summary(object, print.outliers = FALSE, ...)

Arguments

Value

summary(object) returns an object of S3 class "summary.varComprob", basically a list.

Author(s)

Claudio Agostinelli and Victor J. Yohai

Examples

  if (!require(nlme))
    stop()
  data(Orthodont)

  z1 <- rep(1, 4)
  z2 <- c(8,10,12,14)
  K <- list()
  K[[1]] <- tcrossprod(z1,z1) ## Int
  K[[2]] <- tcrossprod(z1,z2) + tcrossprod(z2,z1) ## Int:age
  K[[3]] <- tcrossprod(z2,z2) ## age
  names(K) <- c("Int", "Int:age", "age")
  p <- 4
  n <- 27
  groups <- cbind(rep(1:p, each=n), rep((1:n), p))

  ## Composite Tau
  OrthodontCompositeTau <- varComprob(distance ~ age*Sex, groups = groups,
    data = Orthodont, varcov = K,
    control=varComprob.control(lower=c(0,-Inf,0)))

  summary(OrthodontCompositeTau, print.outliers=TRUE)

Fitting variance component models using robust procedures

Description

varComprob and varComprob.fit fit linear mixed-effect models where the marginal variance-covariance matrix is linear in known positive semidefinite matrices. varComprob uses a formula interface, whereas varComprob.fit is the underlying working horse.

Usage

varComprob(fixed, data, random, groups, varcov, weights, subset,
  family = stats::gaussian("identity"), na.action, offset,
  control = varComprob.control(...), doFit = TRUE,
  normalizeTrace = FALSE, contrasts = NULL,
  model = TRUE, X = TRUE, Y = TRUE, K = TRUE, ...)

varComprob.fit(Y, X, V, control = varComprob.control(), ...)

Arguments

Details

The variance component model is of form

\mathbf{y} = \mathbf{X}\boldsymbol{\beta} + \mathbf{e}

where \mathbf{e} is multivariate normally distributed with mean zero and variance-covariance matrix \mathbf{\Sigma} being

\mathbf{\Sigma} = \sum_{j=1}^R \sigma_j^2 \mathbf{K}_j + \sigma_e^2 \mathbf{I}

in which \mathbf{K}_j are known positive semidefinite matrices and \mathbf{I} is the identity matrix.

In the varComprob formula interface, the \mathbf{X} matrix and response variable are specified by the fixed argument. The varcov argument specifies each variance-covariance matrix in a list.

In varComprob.fit, let p the number of observations, n the number of independent replicates and k the number of regressors. Then Y must be a matrix of dimension p \times n, X must be an array of dimension p \times n \times k and V must be an array of dimension p \times p \times R, where R is the number of variance-covariance matrices.

The model fitting process is performed by a robust procedures. See references for more details.

See varComprob.control for arguments controlling the modeling fitting.

Value

The value of any of the two functions is a list with class varComprob or varComprob.fit respectively. The following elements are present in both

• call: the actual call.

• beta: a named numeric vector of parameter estimates. These are the estimated of the fixed effect parameters.

• vcov.beta: estimated variance-covariance matrix of the estimated fixed effects parameters.

• eta: a named numeric vector of parameter estimates. These are the estimated variance components.

• vcov.eta: estimated variance-covariance matrix of the estimated random effects variance parameters.

• gamma: a named numeric vector of parameter estimates. These are the estimated ratio of each variance component relative to the error variance.

• vcov.gamma: estimated variance-covariance matrix of the estimated ratio of random effects variance parameters with respect the estimated error variance.

• eta0: the estimated error variance.

• resid: residuals in matrix form p \times n.

• weights: final weights of the iterative fixed point equations.

• dotweights: another type of weight. See references for details.

• Sigma: an estimates of the variance-covariance marginal matrix.

• scales: the scales in case of composite robust procedures otherwise NULL.

• scale: the scale in case of classical robust procedures otherwise NULL.

• min: the minimum attains by the goal function.

• scale0:

• initial.values: a list with the following components: beta: initial value for the fixed parameters; gamma: initial value for the ratio of each variance component relative to the error variance; eta0: initial value for the errot variance; scales: initial value for the scales in case of composite robust methods otherwise is not available; scale: initial value for the scale in case of classic robust methods otherwise is not available.

• iterations: number of iterations.

• control: the control argument.

• method: the robust method used to perform the estimation.

The function varComprob returns also

• fixed: the same as beta.

• parms: the same as gamma.

• sigma2: the same as eta0.

• nobs: the number of observations.

• na.action: the na.action used in the model frame.

• offset: the same as input.

• contrasts: the contrast used in the fixed-effect design matrix.

• random.labels: the labels used to differentiate random effects. Note that the error variance is not included here. It is safe to check the number of variance components specified by the model by checking the length of random.labels.

Author(s)

Claudio Agostinelli and Victor J. Yohai

References

C. Agostinelli and V.J. Yohai (2014) Composite Robust Estimators for Linear Mixed Models. arXiv:1407.2176.

M.P. Victoria-Feser and Copt (2006) High Breakdown Inference in the Mixed Linear Model. Journal of American Statistical Association, 101, 292-300.

Examples

  if (!require(nlme))
    stop()
  data(Orthodont)

  z1 <- rep(1, 4)
  z2 <- c(8,10,12,14)
  K <- list()
  K[[1]] <- tcrossprod(z1,z1) ## Int
  K[[2]] <- tcrossprod(z1,z2) + tcrossprod(z2,z1) ## Int:age
  K[[3]] <- tcrossprod(z2,z2) ## age
  names(K) <- c("Int", "Int:age", "age")
  p <- 4
  n <- 27
  groups <- cbind(rep(1:p, each=n), rep((1:n), p))

  ## Not run: 

  ## Composite S
  OrthodontCompositeS <- varComprob(distance ~ age*Sex, groups = groups,
      data = Orthodont, varcov = K,
      control=varComprob.control(method="compositeS", lower=c(0,-Inf,0)))
  
## End(Not run)

  ## Composite Tau
  OrthodontCompositeTau <- varComprob(distance ~ age*Sex, groups = groups,
      data = Orthodont, varcov = K,
      control=varComprob.control(lower=c(0,-Inf,0)))

  ## Not run: 

  summary(OrthodontCompositeTau)

  ## Classic S
  OrthodontS <- varComprob(distance ~ age*Sex, groups = groups,
      data = Orthodont, varcov = K,
      control=varComprob.control(lower=c(0,-Inf,0),
      method="S", psi="rocke"))

  summary(OrthodontS)
  
## End(Not run)
  ## Not run: 

  if (!require(WWGbook))
    stop()
  if (!require(nlme))
    stop()
  data(autism)
  autism <- autism[complete.cases(autism),]
  completi <- table(autism$childid)==5
  completi <- names(completi[completi])
  indici <- as.vector(unlist(sapply(completi,
              function(x) which(autism$childid==x))))
  ind <- rep(FALSE, nrow(autism))
  ind[indici] <- TRUE
  autism <- subset(autism, subset=ind) ## complete cases 41
  attach(autism)
  sicdegp.f <- factor(sicdegp)
  age.f <- factor(age)
  age.2 <- age - 2
  sicdegp2 <- sicdegp
  sicdegp2[sicdegp == 3] <- 0
  sicdegp2[sicdegp == 2] <- 2 
  sicdegp2[sicdegp == 1] <- 1
  sicdegp2.f <- factor(sicdegp2)
  autism.updated <- subset(data.frame(autism, 
                    sicdegp2.f, age.2), !is.na(vsae))
  autism.grouped <- groupedData(vsae ~ age.2 | childid, 
                    data=autism.updated, order.groups = FALSE)
  p <- 5
  n <- 41
  z1 <- rep(1, p)
  z2 <- c(0, 1, 3, 7, 11)
  z3 <- z2^2
  K <- list()
  K[[1]] <- tcrossprod(z1,z1)
  K[[2]] <- tcrossprod(z2,z2)
  K[[3]] <- tcrossprod(z3,z3)
  K[[4]] <- tcrossprod(z1,z2) + tcrossprod(z2,z1)
  K[[5]] <- tcrossprod(z1,z3) + tcrossprod(z3,z1)
  K[[6]] <- tcrossprod(z3,z2) + tcrossprod(z2,z3)
  names(K) <- c("Int", "age", "age2", "Int:age", "Int:age2", "age:age2")

  groups <- cbind(rep(1:p, each=n), rep((1:n), p))

  ## Composite Tau
  AutismCompositeTau <- varComprob(vsae ~ age.2 + I(age.2^2)
    + sicdegp2.f + age.2:sicdegp2.f + I(age.2^2):sicdegp2.f, 
    groups = groups,
    data = autism.grouped, varcov = K,
    control=varComprob.control(
    lower=c(0.01,0.01,0.01,-Inf,-Inf,-Inf)))

  summary(AutismCompositeTau)

  ## Classic S
  AutismS <- varComprob(vsae ~ age.2 + I(age.2^2)
    + sicdegp2.f + age.2:sicdegp2.f + I(age.2^2):sicdegp2.f, 
    groups = groups,
    data = autism.grouped, varcov = K,
    control=varComprob.control(
    method="S", psi="rocke", cov.init="covOGK",
    lower=c(0.01,0.01,0.01,-Inf,-Inf,-Inf)))
  summary(AutismS)
  
## End(Not run)

Tuning Parameters for varComprob() and Auxiliaries

Description

Tuning Parameters for varComprob() which performs S, composite S and Tau estimators for variance component models.

Usage

varComprob.control(init = NULL, lower = 0, upper = Inf, epsilon = 0.001,
  tuning.chi = NULL, bb = 0.5, tuning.psi = NULL,
  arp.chi = 0.1, arp.psi = NULL, max.it = 100,
  rel.tol.beta = 1e-06, rel.tol.gamma = 1e-05, rel.tol.scale = 1e-05,
  trace.lev = 0,
  method = c("compositeTau", "compositeS", "compositeMM",
    "Tau", "S", "MM"),
  psi = c("optimal", "bisquare", "rocke"),
  beta.univ = FALSE, gamma.univ = FALSE,
  fixed.init = c("lmrob.S", "lmRob"),
  cov.init = c("TSGS", "2SGS", "covOGK"),
  cov = TRUE, ...)

Arguments

Value

returns a named 'list' with over twenty components, corresponding to the arguments.

Author(s)

Claudio Agostinelli and Victor J. Yohai

Examples

   ## Show the default settings:
     str(varComprob.control())