Input
This input is diabetes data from "Least Angle Regression," by Bradley Efron and others.
The InputTable, diabetes, has one response (vector y) and ten baseline predictors measured on 442 diabetes patients. The baseline predictors are age, sex, body mass index (bmi), mean arterial pressure (map) and six blood serum measurements (tc, ldl, hdl, tch, ltg, glu).
The column id is the row identifier, y is the response, and the other columns are predictors.
- The value of the Normalize syntax element is irrelevant.
- If the value of the Intercept syntax element is 'true', then the intercept is considered to be constant along the entire path (which is typically not true).
id | age | sex | bmi | map | tc | ldl | hdl | tch | ltg | glu | y |
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.0380759 | 0.0506801 | 0.0616962 | 0.0218724 | -0.0442235 | -0.0348208 | -0.0434008 | -0.00259226 | 0.0199084 | -0.0176461 | 151 |
2 | -0.00188202 | -0.0446416 | -0.0514741 | -0.0263278 | -0.00844872 | -0.0191633 | 0.0744116 | -0.0394934 | -0.0683297 | -0.092204 | 75 |
3 | 0.0852989 | 0.0506801 | 0.0444512 | -0.00567061 | -0.0455994 | -0.0341945 | -0.0323559 | -0.00259226 | 0.00286377 | -0.0259303 | 141 |
4 | -0.0890629 | -0.0446416 | -0.011595 | -0.0366564 | 0.0121906 | 0.0249906 | -0.0360376 | 0.0343089 | 0.022692 | -0.00936191 | 206 |
5 | 0.00538306 | -0.0446416 | -0.0363847 | 0.0218724 | 0.00393485 | 0.0155961 | 0.00814208 | -0.00259226 | -0.0319914 | -0.0466409 | 135 |
... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
SQL Call
SELECT * FROM LAR ( ON diabetes AS InputTable OUT TABLE OutputTable (diabetes_lars) USING TargetColumns ('y', 'age', 'sex', 'bmi', 'map', 'tc', 'ldl', 'hdl', 'tch', 'ltg', 'glu') FitMethod ('lar') Intercept ('true') L2Normalization ('true') MaxIterNum (20) ) AS dt;
Output
message -------------------------------------------------------------------------- Successful. Result has been stored in the table specified in the argument OutputTable.
SELECT * FROM diabetes_lars WHERE steps <> 0 ORDER BY steps;
steps var_id var_name max_abs_corr step_length intercept age sex bmi map1 tc ldl hdl tch ltg glu ----- ------ -------- ------------------ ------------------ ------------------ ------------------- ------------------- ------------------ ------------------ ------------------- ------------------ ------------------- ------------------ ------------------ ------------------ 1 3 bmi 949.4352416992188 60.11927032470703 152.13348388671875 0.0 0.0 60.11927032470703 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2 9 ltg 889.3159790039062 513.2236938476562 152.13348388671875 0.0 0.0 361.8946228027344 0.0 0.0 0.0 0.0 0.0 301.77532958984375 0.0 3 4 map1 452.9009704589844 175.55322265625 152.13348388671875 0.0 0.0 434.7579650878906 79.2364501953125 0.0 0.0 0.0 0.0 374.91583251953125 0.0 4 7 hdl 316.0740661621094 259.3674621582031 152.13348388671875 0.0 0.0 505.6595458984375 191.26988220214844 0.0 0.0 -114.10098266601562 0.0 439.6649475097656 0.0 5 2 sex 130.13084411621094 88.6591567993164 152.13348388671875 0.0 -74.91651153564453 511.34808349609375 234.1546173095703 0.0 0.0 -169.71139526367188 0.0 450.6674499511719 0.0 6 10 glu 88.78243255615234 43.67793273925781 152.13348388671875 0.0 -111.97855377197266 512.0440673828125 252.5270233154297 0.0 0.0 -196.04544067382812 0.0 452.3927307128906 12.078152656555176 7 5 tc 68.96521759033203 135.9840850830078 152.13348388671875 0.0 -197.75650024414062 522.2648315429688 297.15972900390625 -103.94625091552734 0.0 -223.92604064941406 0.0 514.7494506835938 54.76768112182617 8 8 tch 19.98125457763672 54.015602111816406 152.13348388671875 0.0 -226.1336669921875 526.8854370117188 314.3892822265625 -195.1058349609375 0.0 -152.47726440429688 106.34280395507812 529.916015625 64.48741912841797 9 6 ldl 5.47747278213501 5.56723165512085 152.13348388671875 0.0 -227.17579650878906 526.3905639648438 314.9504699707031 -237.34097290039062 33.628273010253906 -134.59934997558594 111.3841323852539 545.4826049804688 64.6066665649414 10 1 age 5.089179039001465 73.5290756225586 152.13348388671875 -10.012197494506836 -239.819091796875 519.8397827148438 324.39044189453125 -792.1841430664062 476.745849609375 101.04457092285156 177.06417846679688 751.279296875 67.6253890991211
The following figure represents the results and shows how the standardized coefficients evolved during the model-building process. The x-axis represents the ratio of the norm of the current beta to the full beta. The y-axis represents the standardized coefficients, which are estimated when standardized predictors are used. The numbers on the top of the graph represent the steps of the model-building process. The numbers on the right represent the predictor IDs.
Download a zip file of all examples and a SQL script file that creates their input tables from the attachment in the left sidebar.