Suppose I fit a quantile regression model with BMI as a response and gender as a predictor. Now, How can I interpret the estimated coefficient for gender.
Note that :gender 1=male , 0=female.
Quantile Regression – How to Interpret Categorical Variables
quantile regression
Related Solutions
Yes, that is the interpretation. One way in which you can see this is by predicting the median for different values of your standardized, each 1 unit (in this case standard deviation) appart. Than you can look at how much these predicted medians differ, and you will see that that is exactly the same number as your standardized quantile regression coefficient. Here is an example:
. sysuse auto, clear
(1978 Automobile Data)
.
. // standardize variables
. sum price if !missing(price,weight)
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
price | 74 6165.257 2949.496 3291 15906
. gen double z_price = ( price - r(mean) ) / r(sd)
.
. sum weight if !missing(price,weight)
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
weight | 74 3019.459 777.1936 1760 4840
. gen double z_weight = ( weight - r(mean) ) / r(sd)
.
. // estimate the quartile regression
. qreg z_price z_weight
Iteration 1: WLS sum of weighted deviations = 47.263794
Iteration 1: sum of abs. weighted deviations = 54.018868
Iteration 2: sum of abs. weighted deviations = 43.851751
Median regression Number of obs = 74
Raw sum of deviations 48.21332 (about -.41744651)
Min sum of deviations 43.85175 Pseudo R2 = 0.0905
------------------------------------------------------------------------------
z_price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
z_weight | .2552875 .1368752 1.87 0.066 -.0175682 .5281432
_cons | -.3415908 .1359472 -2.51 0.014 -.6125966 -.070585
------------------------------------------------------------------------------
.
. // predict the predicted median for z_weight
. // is -2, -1, 0, 1, 2
. drop _all
. set obs 5
obs was 0, now 5
. gen z_weight = _n - 3
. predict med
(option xb assumed; fitted values)
. list
+----------------------+
| z_weight med |
|----------------------|
1. | -2 -.8521658 |
2. | -1 -.5968783 |
3. | 0 -.3415908 |
4. | 1 -.0863033 |
5. | 2 .1689841 |
+----------------------+
.
. // compute how much the predicted median
. // differs between cars 1 standard deviation
. // weight apart
. gen diff = med - med[_n - 1]
(1 missing value generated)
. list
+---------------------------------+
| z_weight med diff |
|---------------------------------|
1. | -2 -.8521658 . |
2. | -1 -.5968783 .2552875 |
3. | 0 -.3415908 .2552875 |
4. | 1 -.0863033 .2552875 |
5. | 2 .1689841 .2552875 |
+---------------------------------+
I suspect you mistake Quantile Regression for some sort of piece-wise linear regression, where a normal OLS line is fitted to subsets of the observation space (note that if you think about this, it can be quite complicated to determine how to subset this data in a multivariate case if you only have a single parameter $\tau$).
Quantile regression is something different, where the conditional median is estimated (for $\tau = 0.5$) or at any other percentile of interest. Which percentile depends on the value of $\tau$ you specify: you specifically are calculating the conditional median at every percentile. It is usually applied in cases where certain assumptions do not hold (for example if there is a multimodal structure to your data and a conditional mean is not very informative). It is not re-estimating the OLS line based on bins of your independent variable (as you seem to suspect). Note also that if it was doing this, you would have a single observation in every bin and it would not even be possible to estimate a slope $\hat{\beta}$. In other words: Quantile Regression does not subset the number of observations used or anything like that.
Best Answer
First, let's streamline the complexity. Quantilte regression is no different from linear regression, except that it centers it on the Median instead of the Mean. In other words, quantile regression is a nifty type of regression that reduces the impact of outliers on the regression coefficients.
So, how would you interpret the coefficient for male in your regression. Let's say your regression equation looks like this:
BMI = 25 + 1(Gender with Male = 1 and Female = 0)
We could rewrite this regression as follows:
BMI = 25 + 1 if Gender is Male.
As depicted, just writing the regression equation out perfectly explains the interpretation of the Gender coefficient. In this case, if Gender is Male the estimated BMI will be greater by one unit than if it is not Male.
Note that this coefficient does not necessarily have to be positive. This will very much depend on your actual sample.
Dr. Halls, a source on the Internet posted this relevant information: Are men heavier than women? Normally, Yes. What about their Body Mass Index (BMI)?
Usually, BMI values of girls are slightly higher than boys (from age 7 to 16). As long as men and women are not overweight, BMI values of men are also slightly higher than for women( after age 18).