Which proc reg statement is correct when doing segmented regression?

[JennMills]

I’m doing segmented regression.  I understand the theory behind it, but I can’t figure out which is the correct SAS model/output.  I found 2 different models in 2 books and they give slightly different results.  Any help is appreciated.

Example data:

Month    Mar    Apr    May    Jun    Jul (bp)    Aug    Sep    Oct    Nov

rate       55     51     48      49      150           156    165     172   180

X           1      2       3        4         5              6       7         8       9

X2        -4      -3     -2       -1         0              1       2         3       4

X3        -4      -3     -2       -1         0              0       0         0       0

X4         0       0       0       0         0              1       2         3       4

Which of these three models is correct?

Model 1: Proc reg; model rate = X   X4; run; (from Biostatistics for Animal Science)

Model 2: Proc reg; model rate = X2  X4;run;

Model 3: Proc reg; model rate = X3  X4;run; (from Draper and Smith, Applied reg analysis text book)

Model 2 output is the exact same at model 1 except the intercept parameters are more meaningful.

Model 3 is the same output as Model 2 except the slope after the break point (bp) is larger, and I don’t know why.

[SteveDenham · Accepted solution]

I would certainly expect models 1 and 2 to give the same output, as X2 is a centered version of X1.

The slope in Model 3 after the break is larger as it is the deviation from a plateau starting in July, as opposed to an additional increase over the linear trend modeled by X2.

Steve Denham

[JennMills]

Thanks, Steve.

Yes, I just figured out the slope after the break point reported by model 3 is the sum of the slope pre break point + the change in slope post break point.  I was not realizing models 1 and 2 were showing the change in slope rather than the new slope.