Piecewise regression

[LOLO12]

Hello,
I have a math problem that is not straight forward. I have data where the slope is not increasing or decreasing. It is flat some time and then increasing or decreasing. This type of data called piecewise linear regression. I suppose to calculate the slopes and only keep the slope where it is significant change and not flat. The issue all solutions online present some codes that I suppose to decide manually.
I need to decide in the slope automatically bc I have 20 subjects and they have 5 treatments and 3 conditions. Please let me know if you can help I can send a dummy data.

[PaigeMiller]

Example of piecewise regression in SAS

https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_nlin_examples01.htm

[sbxkoenk]

Your question is also known as

• segmented regression
• change point models

Segmented regression models in SAS
By Rick Wicklin on The DO Loop December 14, 2020
https://blogs.sas.com/content/iml/2020/12/14/segmented-regression-sas.html

A segmented regression model is a piecewise regression model that has two or more sub-models, each defined on a separate domain for the explanatory variables.

SAS/STAT User's Guide
The MCMC Procedure
Example 80.12 Change Point Models
https://go.documentation.sas.com/doc/en/pgmsascdc/v_037/statug/statug_mcmc_examples18.htm

Koen

[LOLO12]

these only demonstrate if the model is quadratic and not linear. I need it for a linear equation. 

[sbxkoenk]

Do you have many repeated measurements for your patients?

Are the repeated measurements equally spaced and forming a time series?
You could also work with so-called "structural break detection"-methods in time series analysis.

You can detect changing level , changing slope , changing regressor influence , changing variability , changing seasonality , ...

Koen

[LOLO12]

it is equally spaced and structured. 

I'm not familiar with Time series. Do you have an example? 

[sbxkoenk]

SAS® 9.4 and SAS® Viya® 3.5 Programming Documentation
SAS/ETS 15.3 User's Guide
The UCM Procedure
Example 42.7 Detection of Level Shift
https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/etsug/etsug_ucm_examples07.htm

(checkbreak option in LEVEL statement of PROC UCM)

The UCM procedure analyzes and forecasts equally spaced univariate time series data by using an unobserved components model (UCM). The UCMs are also called structural models in the time series literature.

Koen

[LOLO12]

I don't have time value for the interval= option!!

[sbxkoenk]

You can make a row number and use interval=day (space between adjacent observations = 1) :

Like here :

data work.class; set sashelp.class; rownum=_N_; run;

proc ucm data=work.class;
   id rownum interval=day;
   model height;
   irregular;
   level plot=smooth checkbreak;
   estimate;
  *forecast plot=decomp;
run;
/* end of program */

[EDIT]
Do you have a datetime variable for your measurements? 
In that case, and if the (equal) interval in-between measurements is not a typical one (like day, week, 10-days, month, ...), then you can make a custom interval and specify that one in interval= option.

Koen