Lets say I have a predictor variable with the following values:
x <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
I want a piecewise linear model with breakpoints at 3, 5, and 7, so I construct 3 new variables:
x1 <- pmax(x – 3) # 0 0 0 0 1 2 3 4 5 6
x2 <- pmax(x – 5) # 0 0 0 0 0 0 1 2 3 4
x3 <- pmax(x – 7) # 0 0 0 0 0 0 0 0 1 2
I then use lrm:
fit <- lrm(y ~ x + x1 + x2 + x3)
(this is just a simple example, my predictor variable has many more values)
Here are actual results:
Coef S.E. Wald Z Pr(>|Z|)
y>=2 3.2585 0.2496 13.06 <0.0001
y>=3 1.9381 0.2118 9.15 <0.0001
y>=4 0.7775 0.1980 3.93 <0.0001
y>=5 -0.2087 0.1978 -1.05 0.2914
y>=6 -1.4611 0.2058 -7.10 <0.0001
y>=7 -3.2949 0.2213 -14.89 <0.0001
x 4.2534 0.9371 4.54 <0.0001
x1 11.1903 2.9621 3.78 0.0002
x2 29.9125 5.5337 5.41 <0.0001
x3 -36.5740 6.3731 -5.74 <0.0001
It is easiest to explain what I would want if this were simple OLS. Basically I want to report the difference in slopes between the second to last segment and the last segment.
In OLS, these slopes would be x+x1+x2 and x+x1+x2+x3. Given that the coefficient on x3 is significant, I can say that the two slopes differ.
Now I know that ordered logit is quite different. Taking the exponential of the coefficients gives me the odds ratio, or how much the odds of moving up a category in y is influenced by a one unit change in x.
Can I just take the ratio of the “slopes?” (x+x1+x2)/(x+x1+x2+x3) What would be the correct interpretation here?
What I think I really want here is the log odds of moving up a category when x, x1 and x2 all increase by one unit, compared with the log odds of moving up a category when x, x1, x2, AND x3 all increase by one unit. Any help here?
