loggammacenslmrob: Robust estimation of an Accelerated Failure Time model with...
In robustloggamma: Robust Estimation of the Generalized log Gamma Model

Description Usage Arguments Value Author(s) References See Also Examples

View source: R/loggammacenslmrob.R

Three different type of robust procedures are provided for the estimation of the parameters in an Accelerated Failure Time model with extended Log Gamma errors in presence of censored observations. Maximum Likelihood is also provided.

loggammacenslmrob(formula, delta, data, subset, weights,
  na.action, method = c("oneTML", "oneWL", "TWQTau", "TQTau",
  "ML"), model = TRUE, x = !control$compute.rd, y = FALSE,
  singular.ok = TRUE, contrasts = NULL, offset = NULL,
  control = NULL, init = NULL, ...)

`formula`	a symbolic description of the model to be fit. See `lm` and `formula` for more details.
`delta`	numeric, 0 or 1. 0 indicated censored observations.
`data`	an optional data frame, list or environment (or object coercible by `as.data.frame` to a data frame) containing the variables in the model. If not found in `data`, the variables are taken from `environment(formula)`, typically the environment from which `loggammacenslmrob` is called.
`subset`	an optional vector specifying a subset of observations to be used in the fitting process.
`weights`	an optional vector of weights to be used in the fitting process (in addition to the robustness weights computed in the fitting process).
`na.action`	a function which indicates what should happen when the data contain `NA`s. The default is set by the `na.action` setting of `options`, and is `na.fail` if that is unset. The “factory-fresh” default is `na.omit`. Another possible value is `NULL`, no action. Value `na.exclude` can be useful.
`method`	string specifying the estimator-chain. Default is TML one step.
`model, x, y`	logicals. If `TRUE` the corresponding components of the fit (the model frame, the model matrix, the response) are returned.
`singular.ok`	logical. If `FALSE` (the default in S but not in R) a singular fit is an error.
`contrasts`	an optional list. See the `contrasts.arg` of `model.matrix.default`.
`offset`	this can be used to specify an a priori known component to be included in the linear predictor during fitting. An `offset` term can be included in the formula instead or as well, and if both are specified their sum is used.
`control`	a `list` specifying control parameters; use the function `loggammarob.control` and see its help page.
`init`	an optional argument to specify or supply the initial estimate. See Details.
`...`	additional arguments can be used to specify control parameters directly instead of (but not in addition to!) via `control`.

An object of class lmrob; a list including the following components:

`coefficients`	The estimate of the coefficient vector for the regression part. First element is the intercept and it would be equals to the parameter `mu`.
`mu`	The estimate of the intercept parameter.
`sigma`	The estimate of the scale parameter.
`lambda`	The estimate of the shape parameter.
`fitted.values`	Fitted values associated with the estimator.
`residuals`	Residuals associated with the estimator.
`cut.lower, cut.upper`	Cut points for the method based on TML (missing for the other methods).
`iter`	number of iterations.
`weights`	the specified weights (missing if none were used).
`errors`	errors messages.
`n.ret`	number of non zero robust weights for the method based on TML.
`control`	`control` argument.
`converged`	`TRUE` if the procedure converged.
`method`	method used during the fit.
`rank`	the numeric rank of the fitted linear model.
`rweights`	the “robustness weights”.
`df.residual`	the residual degrees of freedom.
`degree.freedom`	the same as df.residual
`delta`	as in input.
`df`	a vector with 3 components: (number of linearly independent regressors, df.residual, number of regressors).
`xlevels`	(only where relevant) a record of the levels of the factors used in fitting.
`call`	the matched call.
`terms`	the `terms` object used.

`model`	if requested (the default), the model frame used.
`x`	if requested, the model matrix used.
`y`	if requested, the response used.
`scale`	square root of the `sigma` parameter.
`na.action`	(where relevant) information returned by `model.frame` on the special handling of `NA`s.
`offset`	the offset used (missing if none were used).
`contrasts`	(only where relevant) the contrasts used.

In addition, non-null fits will have qr relating to the linear fit, for use by extractor functions such as summary.

C. Agostinelli, A. Marazzi and V.J. Yohai

C. Agostinelli, I. Locatelli, A. Marazzi and V.J. Yohai (2015) Robust estimators of accelerated failure time regression with generalized log-gamma errors. Submitted.

loggammacensrob for the case of censored observations without covariates.

  ## Not run: 
    n <- 50
    p <- 2
    set.seed(1234)
    X <- matrix(rnorm(p*n, sd=2), ncol=p)
    mu <- 2
    beta <- rep(2,p)
    sigma <- 2
    lambda <- 1
    linear <- mu + X
    y <- rloggamma(n=n, mu=linear, sigma=sigma, lambda=lambda)
    cens <- rloggamma(n=n, mu=linear+3, sigma=sigma, lambda=lambda)
    delta <- as.numeric(y <= cens)
    y[delta==0] <- cens[delta==0]
    x <- data.frame(y=as.vector(y), x1=X[,1], x2=X[,2])
    res <- loggammacenslmrob(y~x1+x2, delta=delta, data=x)
    summary(res)
  
## End(Not run)

Call:
loggammacenslmrob(formula = y ~ x1 + x2, delta = delta, data = x)
 \--> method = "oneTML"
Residuals:
     Min       1Q   Median       3Q      Max 
-10.4920  -3.9314  -1.7702   0.1927   2.7951 

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)   2.5424     0.8958   2.838  0.00454 ** 
x1            0.6750     0.1366   4.942 7.74e-07 ***
x2            0.9997     0.1458   6.856 7.09e-12 ***
Sigma         2.1807     0.4055                     
Lambda        1.5111     1.5087   1.002  0.31654    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Robust residual standard error: 1.477 

Robustness weights: 
 2 observations c(50,64) are outliers with |weight| = 0 ( < 0.001); 
 98 weights are ~= 1.