1.4.3 A Gaussian fit🔗ℹ

formula-fit resolves the formula against the table and fits the family that #:family names, the Gaussian by default, with the same keywords as that family’s fit procedure. The model prints as the fit does, with the formula after the family:

> (define bp-fit (formula-fit (~ bp age dose marker) patients #:lambda 0.5))

> bp-fit

#<glmnet:gaussian (~ bp age dose marker) λ=0.5 dev=0.9137 nz=2/3>

coef returns an association list keyed by name, with the intercept first under R’s name for it, "(Intercept)". The lasso has found the two predictors that blood pressure depends on:

> (coef bp-fit)

'(("(Intercept)" . 93.51132211478343)   ("age" . 0.5139586017419673)   ("dose" . -1.7735029027253124)   ("marker" . 0.0))

> (cdr (assoc "dose" (coef bp-fit)))

-1.7735029027253124

predict takes a new table and reads the predictors from it by name. The columns can come in any order, and other columns are ignored; a missing predictor is an error that names it:

> (define new-patients     (list (cons "id" '(101 102))           (cons "marker" '(0.5 -0.5))           (cons "dose" '(2.0 8.0))           (cons "age" '(40 70))))

> (predict bp-fit new-patients)

'(110.52266037901148 115.30040101491863)

> (predict bp-fit (list (cons "age" '(40)) (cons "dose" '(2.0))))

predict: the table has no column with this name

column: "marker"

columns of the table: '("age" "dose")

formula-path fits a regularization path, and formula-cv cross-validates one, with the keywords of the family’s path fitter and cross-validation procedure. Both keep the names:

> (formula-path (~ bp age dose marker) patients #:lambda '(4.0 1.0 0.25))

#<glmnet-path:gaussian (~ bp age dose marker)   Df  %Dev Lambda 1  2 59.39   4.00 2  2 89.85   1.00 3  2 91.75   0.25>

> (define bp-cv (formula-cv (~ bp age dose marker) patients))

> bp-cv

#<glmnet-cv:gaussian (~ bp age dose marker) Mean-Squared Error        Lambda  Index  Measure     SE  Nonzero   min  0.2724     36    9.255  1.138        2   1se  0.7579     25    10.19  1.374        2>

> (coef bp-cv)

'(("(Intercept)" . 94.09234504611852)   ("age" . 0.49554398525920623)   ("dose" . -1.6834215534687091)   ("marker" . 0.0))

> (coef bp-cv #:lambda 'lambda-min)

'(("(Intercept)" . 92.99845164212019)   ("age" . 0.530213232303164)   ("dose" . -1.8530179478570004)   ("marker" . 0.0))

The model is a formula-model. formula-model-fit returns the result it holds, which is exactly what the family’s procedure returns for the same columns as a matrix:

> (formula-model-fit bp-fit)

#<glmnet:gaussian λ=0.5 dev=0.9137 nz=2/3>

> (equal? (formula-model-fit bp-fit)           (lasso (map list age dose marker) bp #:lambda 0.5))

#t