LSMEANS stand for least squares means, while quantile regression uses check loss (which is piecewise linear) but not square loss. In this sense, LSMEANS do not directly apply for quantile regression.
However, the goal of least squares means is to estimate the marginal means for a balanced population. Similarly, we can estimate balanced quantile effects by (1) balancing the data and (2) fitting a quantile regression model on the balanced data.
(Mimicing the example from http://dawg.utk.edu/glossary/g_least_squares_means.htm🙂
"Suppose you have a treatment applied to 3 trees (experimental unit), and 2 observations (samples) are collected on each. However, one observation is missing, giving values of (45, 36), (56, ), and (37, 41), where parentheses are around each tree. The raw average is simply (45+36+56+37+41)/5 = 43, and note the reduced influence of the second tree since it has fewer values. The least squares mean would be based on a model u + T + S(T), resulting in an average of the tree averages, as follows.
Least squares mean =[ (45+36)/2 + 56 + (37+41)/2 ] / 3 = 45.17 This more accurately reflects the average of the 3 trees, and is less affected by the missing value."
For quantile regression, the balanced data can be (45, 36), (56, 56 ), and (37, 41), where 56 for the second obs is for balance purposes. Then, we can compute balanced quantiles on this balanced data. However, this data-balancing method is still an open-question and can be very difficult for more complicated cases.
The current QUANTREG procedure does not provide this functionality. Wish that some researchers can publish a paper for solving this problem.
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