Anova: Warning: In summary.rq(x, se = se, covariance = TRUE) : 2 non-positive fis

Question

I ran the following script to analyse a nonparametric quantile regression using quantreg package:

library (quantreg)

model.q = rq(Y_var ~ X1_var + X2_var + X3_var,
             data = wideformat_data,
             tau = 0.5)
summary(model.q)
model.nullq = rq(Y_var ~ 1,
                 data = wideformat_data,
                 tau = 0.5)

anova(model.q, model.nullq)

All Y and X variables were continuous and standardised. As result from anova ( ), a warning message was displayed:

Warning:
In summary.rq(x, se = se, covariance = TRUE) : 2 non-positive fis

Does anyone know why it occurred and how to handle with it?

Answer 1

It's generally harmless:

7. [Non-positive fis] "What does the message "Non-positive fis" mean?

   When method ="nid" is used in summary local density estimates are made at each x_i value, in some cases these estimates can be negative and if so they are set to zero. This is generally harmless, leading to a somewhat conservative (larger) estimate of the standard errors, however if the reported number of non-positive fis is large relative to the sample size then it is an indication of misspecification of the model. (http://www.econ.uiuc.edu/~roger/research/rq/FAQ)