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
Valeriano
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