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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?

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