Choosing linear trend coefficients

[rogersaj]

A few days ago, I asked for help interpeting a linear trend here:  http://support.sas.com/kb/22/912.html 

It turns out my analysis was wrong because of my categories were unevenly spaced (in addition to not being sorted, which they are now). @sld pointed me to this resource to deal with unequally spaced treatments: http://support.sas.com/kb/22/912.html 

But I can't seem to figure out how to use PROC IML to find my coefficients for the linear trend. 

First, since my categories are distances, do I use the midpoint?

• Distance le 5km; midpoint = 2.5
• Distance between 6 to 15km; midpoint = 10.5
• Distance between 16 to 30km; midpoint = 23
• Distance beween 31 to 100km; midpoint = 75

proc iml;
	distcat={2.5,10.5,23,75};
	contrL=orpol(distcat,4);
	print contrL;
quit;

Output: 

If my code is right, how do I interpet the output to create my dose levels to test for linear trend with PROC GLM "Estimate"?

Thanks!

[Rick_SAS · Accepted solution]

I assume you only have the categories of distance? If you know the actual distances, you could use DISTANCE as a covariate.

I don't think it matters too much how you set up the reference values. Using the midpoint seems reasonable because it is the expected value of the distance traveled under the assumption of uniformly distributed villages. 

As to the interpretation, the columns of the matrix represent polynomials of degree 0 (intercept), 1, 2, 3, and 4. So the elements of the second column (-0.447 ... 0.8365) are the values to use for the linear trend. The elements of the third column (0.598 ... 0.223) are the values to use for the quadratic trend.