# summary.iMqr: Summary After M-Quantile Regression Coefficients Modeling In Mqrcm: M-Quantile Regression Coefficients Modeling

 summary.iMqr R Documentation

## Summary After M-Quantile Regression Coefficients Modeling

### Description

Summary of an object of class “iMqr”.

### Usage

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


### Arguments

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

### Details

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 M-quantile regression coefficients of order p are extrapolated and summarized.

### Value

If p is supplied, a standard summary of the estimated M-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 M-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. call the matched call.

### Author(s)

Paolo Frumento paolo.frumento@unipi.it

iMqr, for model fitting; predict.iMqr and plot.iMqr, for predicting and plotting objects of class “iMqr”.

### Examples


# using simulated data

set.seed(1234); n <- 250
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 <- iMqr(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



Mqrcm documentation built on May 29, 2024, 9:09 a.m.