[R] Quantile regression - violation of independence

Valeriano Parravicini valeriano.parravicini at unige.it
Mon May 17 19:58:51 CEST 2010

I am trying to perform  quantile regression (using quantreg package) and 
I am particularly interested to know whether the technique requires 
independence of observations.

I am an ecologist and, in particular, I collected data of abundance of a 
species in 15 location around an island. In each location abundance data 
of the species (response variable) have been collected in about 20 
replicate sampling units. Yet, I have just one measure of my explanatory 
variables (I have two explanatory variables) for each location. So, for 
each value of the explanatory variables I have 20 values of the response 
variable. Since my data have not normal distribution and do not show 
homogeneity of variance I would  use quantile regression. My main 
concern is about violation of independece because I can not consider my 
20 measure of abundance  as  independent since they have been collacted 
in the same location (i.e. they actually are replicates). However, I 
would not like to loose the information about the within-location 
variation by averaging my response variable at location level. I am not 
skilled in quantile regression; this is my first attempt to employ such 
a technique, but in a paper on econometrics I found that quantile 
regression do not require independence of observations. This is the only 
reference I found about that. Is it true? Can anyone suggests me any 
reference about that?

Moreover, I have two explanatory variables for each location and I am 
conducting quantile regression using backward selection. Particularly, I 
am performing the regression separately for a number of tau and each 
time I perform backward selection. What happens is that the "best model" 
changes accordingly with the tau setted. For instance, using tau = 0.5, 
backward selection indicate me that both explanatory variables are 
significant. Yet, setting tau = 0.75 just one of the two explanatory 
variables is found significant and backward selection drops the other 
one. Is  that a correct way to conduct quantile regression with more 
than one explanatory variable: i.e. performing  backward selection for 
each tau I am interested on ?

Thank you for your help


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