quantreg.m - quantile regression

Quantile regression with bootstrapping confidence intervals

Description

Quantile Regression

  USAGE: [p,stats]=quantreg(x,y,tau[,order,nboot]);
  
  INPUTS:
    x,y: data that is fitted. (x and y should be columns)
         Note: that if x is a matrix with several columns then multiple
         linear regression is used and the "order" argument is not used.
    tau: quantile used in regression.
    order: polynomial order. (default=1)
    nboot: number of bootstrap surrogates used in statistical inference.(default=200)
 
  stats is a structure with the following fields:
       .pse: standard error on p. (not independent)
       .pboot: the bootstrapped polynomial coefficients.
       .yfitci: 95% confidence interval on polyval(p,x)
 
 
  Note: uses bootstrap on residuals for statistical inference. (see help bootstrp)
  check also: http://www.econ.uiuc.edu/~roger/research/intro/rq.pdf
 
  EXAMPLE:
  x=(1:1000)';
  y=randn(size(x)).*(1+x/300)+(x/300).^2;
  [p,stats]=quantreg(x,y,.9,2);
  plot(x,y,x,polyval(p,x),x,stats.yfitci,'k:')
  legend('data','2nd order 90th percentile fit','95% confidence interval','location','best')
  
  For references on the method check e.g. and refs therein:
  http://www.econ.uiuc.edu/~roger/research/rq/QRJEP.pdf
 
   Copyright (C) 2008, Aslak Grinsted

• Required Products: Statistics Toolbox
• MATLAB release: MATLAB 7 (R14)

[AS]

One unexpected thing with this code. Suppose I have a Y vector and want to regress it on one explanatory variable, but also include a constant in my regression. Then my X matrix has 2 columns, the first column is just ones, the second is the explanatory variable. It should still be possible to plot this along with the results from the regression.

Currently, however, if you run:
quantreg([ones(length(x),1) x], y,.5)
You get an error because it tries to plot it, but order has been set (line 44) to [], so things get messed up.

Additionally, the plots that do get produced look odd because the default is to draw lines between all of the points, which usually isn't what you want. For example, this doesn't look like what it should:
x=randn(1000,1);
y=1+5*x+randn(1000,1);
quantreg(x,y,0.5)

Finally, there's a problem with the error checking of inputs (lines 41-47) because it's all one big if-else statement. If you only put in three inputs, then line 44 runs and order gets set to [], but then the program exits the if-else statement and so Nboot never gets set correctly. You should split these up into separate if statements because if there are only 3 inputs then you need to set both order and Nboot.

[Aslak Grinsted]

Thanks for the comment, and suggestions for improvement. I've just uploaded a new version (it should be online shortly).

[Mohammad]

In fact I wanted to run this M-file for multi column X, but I got error, so it is not implement for MLR? if it is , could you please put an example? because when I do not mention Order , I get error when i mention it is not MLR

[Aslak Grinsted]

@mohammad: The code does do MLR. Here's an example with multiple predictors:

X=randn(100,4);
y=X*[4 2 4 1]'+randn(100,1)*.2;
[p,stats]=quantreg(X,y,.9);

[Satis]

If X and y have some missing observations, then

[p,stats]=quantreg(X,y,.9); does not work. I got error message.

Could you please suggest me how to resolve this problem??