This example uses elastic net, a combination of the ridge and LASSO methods.
Input
The input table, glm2_elastic_net, contains a set of U. S. macroeconomic variables for the years 1947 through 1962. The response variable is the number of people employed (in millions).
id | gnp_deflator | gnp | unemployed | armed_forces | population | year | employed |
---|---|---|---|---|---|---|---|
1 | 83 | 234.289 | 235.6 | 159 | 107.608 | 1947 | 60.323 |
2 | 88.5 | 259.426 | 232.5 | 145.6 | 108.632 | 1948 | 61.122 |
3 | 88.2 | 258.054 | 368.2 | 161.6 | 109.773 | 1949 | 60.171 |
4 | 89.5 | 284.599 | 335.1 | 165 | 110.929 | 1950 | 61.187 |
5 | 96.2 | 328.975 | 209.9 | 309.9 | 112.075 | 1951 | 63.221 |
6 | 98.1 | 346.999 | 193.2 | 359.4 | 113.27 | 1952 | 63.639 |
7 | 99 | 365.385 | 187 | 354.7 | 115.094 | 1953 | 64.989 |
8 | 100 | 363.112 | 357.8 | 335 | 116.219 | 1954 | 63.761 |
9 | 101.2 | 397.469 | 290.4 | 304.8 | 117.388 | 1955 | 66.019 |
10 | 104.6 | 419.18 | 282.2 | 285.7 | 118.734 | 1956 | 67.857 |
11 | 108.4 | 442.769 | 293.6 | 279.8 | 120.445 | 1957 | 68.169 |
12 | 110.8 | 444.546 | 468.1 | 263.7 | 121.95 | 1958 | 66.513 |
13 | 112.6 | 482.704 | 381.3 | 255.2 | 123.366 | 1959 | 68.655 |
14 | 114.2 | 502.601 | 393.1 | 251.4 | 125.368 | 1960 | 69.564 |
15 | 115.7 | 518.173 | 480.6 | 257.2 | 127.852 | 1961 | 69.331 |
16 | 116.9 | 554.894 | 400.7 | 282.7 | 130.081 | 1962 | 70.551 |
SQL Call
Because the response variable has a normal distribution, the Family is Gaussian. The Alpha value, 0.1, specifies an elastic net model.
SELECT * FROM GLM2 ( ON glm2_elastic_net AS InputTable OUT TABLE ModelTable (glm2_elastic_net_model) OUT TABLE RegularizationTable (glm2_3regularization) USING InputColumns ('gnp_deflator','gnp','armed_forces','population') ResponseColumn ('employed') Family ('GAUSSIAN') Intercept ('TRUE') NumLambdas (10) Alpha (0.1) ) AS dt;
Output
dfDevRatio | devRatio | dfDev | deviance | lambda |
---|---|---|---|---|
0 | 0 | 15 | 185.008826 | 33.4451683575075 |
3 | 0.495555028370924 | 12 | 93.3267719826986 | 12.0195703031457 |
4 | 0.825255933667388 | 11 | 32.3291945626626 | 4.31960959885052 |
4 | 0.930305894169471 | 11 | 12.8940246988259 | 1.55238719986506 |
4 | 0.951974575788374 | 11 | 8.88512735154485 | 0.557899033039046 |
4 | 0.957608388774071 | 11 | 7.84282222515759 | 0.200498516795911 |
4 | 0.963457573112318 | 11 | 6.76067149768095 | 0.0720554309233708 |
4 | 0.971089487544852 | 11 | 5.34869996838526 | 0.0258953792203741 |
4 | 0.980005044362085 | 11 | 3.69924326849269 | 0.00930631676715827 |
4 | 0.984687706599481 | 11 | 2.83290942539757 | 0.00334451683575075 |
df_dev_ratio | deviance_ratio | df_dev | deviance | lambda | intercept | armed_forces | gnp | gnp_deflator | population |
---|---|---|---|---|---|---|---|---|---|
0 | 0 | 15 | 185.008826 | 33.4451683575075 | 65.317 | 0 | 0 | 0 | 0 |
3 | 0.495555028370924 | 12 | 93.3267719826986 | 12.0195703031457 | 54.8218575447 | 0 | 0.0036713396 | 0.0326415425 | 0.0489911516 |
4 | 0.825255933667388 | 11 | 32.3291945626626 | 4.31960959885052 | 43.8369917073 | 0.0017090903 | 0.0074174574 | 0.0652234077 | 0.0981636428 |
4 | 0.930305894169471 | 11 | 12.8940246988259 | 1.55238719986506 | 37.154679985 | 0.0024827573 | 0.0101765417 | 0.0856518657 | 0.126554407 |
4 | 0.951974575788374 | 11 | 8.88512735154485 | 0.557899033039046 | 35.1825736622 | 0.0024452942 | 0.0125438456 | 0.093815729 | 0.1285468441 |
4 | 0.957608388774071 | 11 | 7.84282222515759 | 0.200498516795911 | 37.4679867235 | 0.0020860735 | 0.0163287498 | 0.0905074779 | 0.1002494791 |
4 | 0.963457573112318 | 11 | 6.76067149768095 | 0.0720554309233708 | 45.5465937467 | 0.0013152824 | 0.0244413997 | 0.0730722137 | 0.0214742023 |
4 | 0.971089487544852 | 11 | 5.34869996838526 | 0.0258953792203741 | 58.8296374248 | 0.0002910015 | 0.0379400515 | 0.0279059919 | -0.0948299091 |
4 | 0.980005044362085 | 11 | 3.69924326849269 | 0.00930631676715827 | 81.0307817472 | -0.0015741337 | 0.0585698986 | -0.0217865608 | -0.3048408138 |
4 | 0.984687706599481 | 11 | 2.83290942539757 | 0.00334451683575075 | 100.3707843847 | -0.0030991548 | 0.0773443707 | -0.0790919789 | -0.4785227208 |
The function also outputs a model table, which is not shown here.