power.rq.test: Power and sample size for quantile regression.

In tnt198785/rqsamplesize: Sample size estimation for quantile regression

Description

Compute power and sample size of test under alternative hypothesis to obtain target power (same as power.anova.test)

Usage

     power.rq.test(x, n = NULL, sig.level = 0.05, power = NULL, 
     tau = 0.5, beta = 1, sd = 1, dist = "Norm", kernel.smooth = "norm", 
     bw = NULL, alternative = c("two.sided", "one.sided"))

 

Arguments

x	A rqfun object.See "Details" and "Examples". It can also be a dataset if one is available.
n	Given sample size to compute power.
sig.level	Significance level of the test(Type I error probability). The default is 0.05.
power	Power of the test between 0 and 1(One minus Type II error probability). It is required to compute sample size.
tau	The desired regression quantile between 0 and 1. The default is 0.5.
delta	The desired quantile regression coefficient. It can be a number or a vector.
sd	Standard deviation or scale of error distribution.
dist	The error distribution for the purpose of power/sample size calculation. It takes "Norm","Cauchy","Gamma" or a vector of residuals when distribution is unknown and to be estimated.
kernel.smooth	It takes values 1,2,3,4 indicating the number of kernels used. 1 is for a uniform variable bounded by -1/2 and 1/2. 2 is for triangle density bounded by -1 and 1. 3 is for three-piece density bounded by -3/2 and 3/2. 4 is for four-piece density bounded by -2 and 2. Standard normal kernel is used by default if no values are specified.
bw	The bandwidth used in kernel smoothing. Small bandwidth results in under-smoothing whereas large bandwidth causes over-smoothing. Default is NULL and bandwidth is estimated by normal distribution approximation or Silverman's (1986) rule of thumb by default.
alternative	Choose either "one.sided" for one sided test or "two.sided" for two sided test.

Details

A rqfun object needs to be defined in univariate regression situation. Here "univariate" means the independent variables are transformation of a single variable. It is defined as following: x = rqfun(mu=0, sd=1, dist='norm', term=c('1'), pos=2, method='exact', a =NA, b=NA). It contains the information of the independent variable.

It is assumed that error distribution is independently identically distributed, so the calculation of variance of regression coefficients are based on Section 3.2.2 of Quantile Regression(2005).

Value

Object of class "power.htest", a list of the arguments (including the computed one) augmented with method and note elements.

Note

Either n or power needs to be defined. They can not be NULL at the same time. If estimated sample size is desired, power should be given; if estimated power is desired, actual sample size n should be given.

uniroot is used to solve power equation for unknowns, so you may see errors from it, notably about inability to bracket the root when invalid arguments are given.

Author(s)

Zhenxian Gong

References

Roger Koenker. (2005)Quantile Regression. Cambridge University Press.

Silverman, B.W. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman & Hall/CRC.

See Also

rq, rqfun, power.anova.test, uniroot

Examples

 #Construct x
 x = rqfun(mu = 5, sd = 1.5, dist = "norm", pos = 2, term = c('1'),a=NA,b=NA, method = 'exact')
 #Compute estimated sample size when power is 0.8
 power.rq.test(x=x, power = 0.8, tau = 0.2, beta = c(1,0.5),
                sd = 10, dist = "Norm", alternative = 'two.sided')
 

tnt198785/rqsamplesize documentation built on May 31, 2019, 4:43 p.m.