summary.iqr: Summary After Quantile Regression Coefficients Modeling
In qrcm: Quantile Regression Coefficients Modeling

Description Usage Arguments Details Value Note Author(s) See Also Examples

Summary of an object of class “iqr”.

1 2	## S3 method for class 'iqr' summary(object, p, cov = FALSE, ...)

`object`	an object of class “`iqr`”, the result of a call to `iqr`.
`p`	an optional vector of quantiles.
`cov`	logical. If `TRUE`, the covariance matrix of β(p) is reported. Ignored if `p` is missing.
`...`	for future methods.

If p is missing, a summary of the fitted model is reported. This includes the estimated coefficients, their standard errors, and other summaries (see ‘Value’). If p is supplied, the quantile regression coefficients of order p are extrapolated and summarized.

If p is supplied, a standard summary of the estimated quantile regression coefficients is returned for each value of p. If cov = TRUE, the covariance matrix is also reported.

If p is missing (the default), a list with the following items:

`converged`	logical value indicating the convergence status.
`n.it`	the number of iterations.
`n`	the number of observations.
`free.par`	the number of free parameters in the model.
`coefficients`	the matrix of estimated coefficients. Each row corresponds to a covariate, while each column corresponds to an element of b(p), the set of functions that describe how quantile regression coefficients vary with the order of the quantile. See ‘Examples’.
`se`	the estimated standard errors.
`test.x`	Wald test for the covariates. Each row of `coefficients` is tested for nullity.
`test.p`	Wald test for the building blocks of the quantile function. Each column of `coefficients` is tested for nullity.
`obj.function`	the minimized loss function (`NULL` if the data are censored or truncated).
`call`	the matched call.

In version 1.0 of the package, a chi-squared goodness-of-fit test was provided. The test appeared to be unreliable and has been removed from the subsequent versions. Use test.fit.

Paolo Frumento paolo.frumento@unipi.it

iqr, for model fitting; predict.iqr and plot.iqr, for predicting and plotting objects of class “iqr”. test.fit.iqr for a goodness-of-fit test.

# using simulated data

set.seed(1234); n <- 1000
x1 <- rexp(n)
x2 <- runif(n)
qy <- function(p,x){qnorm(p)*(1 + x)}
# true quantile function: Q(p | x) = beta0(p) + beta1(p)*x, with
   # beta0(p) = beta1(p) = qnorm(p)

y <- qy(runif(n), x1) # to generate y, plug uniform p in qy(p,x)
                      # note that x2 does not enter

model <- iqr(y ~ x1 + x2, formula.p = ~ I(qnorm(p)) + p + I(p^2))
# beta(p) is modeled by linear combinations of b(p) = (1, qnorm(p),p,p^2)

summary(model)
# interpretation: 
  # beta0(p) = model$coef[1,]*b(p)
  # beta1(p) = model$coef[2,]*b(p); etc.
# x2 and (p, p^2) are not significant


summary(model, p = c(0.25, 0.75)) # summary of beta(p) at selected quantiles