Interpreting P values in Sqreg versus Qreg

[Melissa Sherry]

Hello,

I am trying to understand how to interpret the p values I get after using sqreg versus qreg. I am running quantile regressions looking at the dependent variable of cost, and my independent variable is a neighborhood deprivation score. I am trying to understand whether or not different levels of my neighborhood variable are significantly associated with total cost at various quantiles, and also whether the affects of the neighborhood on cost change across quantiles. I am using sqreg and qreg to answer this.

Where I am getting confused is in interpreting the pvalues when I run sqreg versus qreg, since at various quantiles, my neighborhood is significant with qreg, but not sqreg, or vice versa. For example, at the .3 quantile, I am getting significant p values for my neighborhood index score at the .3 quantile when I run sqreg (.3 .4 .5 .6 .7), but insignificant p values for the same variable when i run qreg at .3 . I understand that sqreg uses bootstap errors, and the coefficients are of course the same. I just do not understand how to properly interpret the significance of my variable modeled with my outcome when the two methods produce different pvalues. Any help explaining how to interpret the p values of qreg versus sqreg would be very helpful!

Best,
Melissa

[FernandoRios]

Hi Melissa
First of all, do you think you can share some of those output results to provide a more informed advice?
Second, I think you are on the right track. sqreg uses bootstrap standard errors, and depending on the problem you may have in hand (distribution of the underlying variables and number of observations), you may need a large number of repetitions to obtain the correct standard errors. Is it possible that you have few observations, or that you are running sqreg with the default number of repetitions (20)? Perhaps you can increase those to 200 or larger, and see how much of a discrepancy between qreg and sqreg remains.
I would also suggest to use qreg with robust standard errors, or look into the user written command -qreg2-.
Hope this helps.
Fernando

[Melissa Sherry]

Hi Fenando,

Thank you so much for the quick reply! I have 8,740 individuals in my sample. As an example, when I use qreg to calculate a coefficient for my neighborhood variable (3 levels, reference is 1, )I get the following for quantile .3:

	Coef.	Std. Err.	t	P>t	[95% Conf.	Interval]
2	49.20261	95.93139	0.51	0.608	-138.846	237.2508
3	75.16665	115.3681	0.65	0.515	-150.982	301.3154

When I use sqreg with the same list of variables and the same outcome, for quantile 0.3 I get:I was not specifying the number of bootstrap repetitions for sqreg, so I will try increasing that.

	Coef.	Std. Err.	t	P>t	[95% Conf.	Interval]
2	49.20261	34.46973	1.43	0.153	-18.3667	116.7719
3	75.16665	34.69137	2.17	0.03	7.163221	143.1701

I will also try using robust standard errors for the qreg. Any other thoughts you have on interpretation and choosing sqreg versus qreg results as more robust would be really helpful!

Thank you!

Melissa