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# Question about significance testing of a break-point in a piecewise model

Using proc mixed I have created a two segment piecewise regression line with a known break-point. Is there a way to determine if the change in slope across the break-point, (the difference in slope between segment 1 and segment 2) is statistically significant?

Posts: 5,056

## Re: Question about significance testing of a break-point in a piecewise model

We would have to see your model formulation to be more specific. But the idea is to include in your model a common slope for both segments and a difference in slope that applies to segment 2 only. That way, you automatically get the test for the significance of the difference in slopes.

PG

PG
Posts: 5,056

## Re: Question about significance testing of a break-point in a piecewise model

For a specialized tool addressing this problem (non SAS), take a look at Joinpoint from the National Cancer Institute :

Joinpoint Regression Program - Surveillance Research Program

PG

PG
Posts: 5,056

## Re: Question about significance testing of a break-point in a piecewise model

If it can be of some inspiration, run the following simulation :

data have;
do x = 0 to 10 by 0.1;
y = x + 0.7*max(0, x - 5) + rannor(1234);
output;
end;
run;

proc sgplot data=have;
scatter x=x y=y;
series x=x y=x;
run;

%let break_X=5;

data tmp;
set have;
xp = max(0, x - &break_X);
run;

proc reg data=tmp;
model y = x xp;
run;

The xp term in the model tests the difference in slopes.

PG

PG
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