qda models

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qda models

Function	Works
`tidypredict_fit()`, `tidypredict_sql()`, `parse_model()`	✔
`tidypredict_to_column()`	✗
`tidypredict_test()`	✗
`tidypredict_interval()`, `tidypredict_sql_interval()`	✗
`parsnip`	✔

MASS::qda() fits quadratic discriminant analysis models. Unlike MASS::lda(), each class gets its own covariance estimate, so the class scores are quadratic rather than linear in the predictors: one intercept, one coefficient per predictor, and one coefficient per pair of predictors. The posterior probabilities are the softmax of those class scores.

Because these models predict one probability per outcome class, tidypredict_fit() returns a named list of expressions, one for each class, rather than a single expression. Since the output is a list, tidypredict_to_column() and tidypredict_test() are not supported.

`tidypredict_` functions

Note that MASS is used with :: below rather than attached, because attaching it would mask dplyr::select().

model <- MASS::qda(Species ~ ., data = iris)

Create the R formulas, one per class

fit <- tidypredict_fit(model)
names(fit)
#> [1] "setosa"     "versicolor" "virginica"
fit[["setosa"]]
#> 1/(1 + exp(-68.4372876863761 + (Sepal.Length * 18.0128645045465) + 
#>     (Sepal.Width * 15.9607000492876) + (Petal.Length * 3.26878502392697) + 
#>     (Petal.Width * -14.7125574674066) + (Sepal.Length * Sepal.Length * 
#>     -4.75138188253319) + (Sepal.Length * Sepal.Width * 3.67621661105371) + 
#>     (Sepal.Length * Petal.Length * 8.63171191375034) + (Sepal.Length * 
#>     Petal.Width * -6.45450343914607) + (Sepal.Width * Sepal.Width * 
#>     -9.85548321295217) + (Sepal.Width * Petal.Length * -2.11602239677401) + 
#>     (Sepal.Width * Petal.Width * 19.4803247040045) + (Petal.Length * 
#>     Petal.Length * -9.90187886398409) + (Petal.Length * Petal.Width * 
#>     26.9372270107537) + (Petal.Width * Petal.Width * -43.6223969131695) - 
#>     (-113.714590795937 + (Sepal.Length * 44.5528812152965) + 
#>         (Sepal.Width * -7.61595839316372) + (Petal.Length * 33.559537097271) + 
#>         (Petal.Width * -31.2558694597319) + (Sepal.Length * Sepal.Length * 
#>         -9.47171939291025) + (Sepal.Length * Sepal.Width * 12.4048261564855) + 
#>         (Sepal.Length * Petal.Length * 4.50020653857198) + (Sepal.Length * 
#>         Petal.Width * 4.77612732803424) + (Sepal.Width * Sepal.Width * 
#>         -7.78527008659406) + (Sepal.Width * Petal.Length * -1.1110791368753) + 
#>         (Sepal.Width * Petal.Width * 2.1040978276337) + (Petal.Length * 
#>         Petal.Length * -19.3881020632003) + (Petal.Length * Petal.Width * 
#>         17.9350353034303) + (Petal.Width * Petal.Width * -53.0229530714453))) + 
#>     exp(-67.7090772023948 + (Sepal.Length * 7.37247478397159) + 
#>         (Sepal.Width * 13.2452613006359) + (Petal.Length * 6.23406948373775) + 
#>         (Petal.Width * 9.66197608445426) + (Sepal.Length * Sepal.Length * 
#>         -5.26693339970327) + (Sepal.Length * Sepal.Width * 3.47972623582808) + 
#>         (Sepal.Length * Petal.Length * 9.96014594453995) + (Sepal.Length * 
#>         Petal.Width * -1.78815223046388) + (Sepal.Width * Sepal.Width * 
#>         -7.93772112409139) + (Sepal.Width * Petal.Length * -1.10268870214298) + 
#>         (Sepal.Width * Petal.Width * 8.47285053214324) + (Petal.Length * 
#>         Petal.Length * -6.70291026519806) + (Petal.Length * Petal.Width * 
#>         2.8909184691834) + (Petal.Width * Petal.Width * -9.65702517612499) - 
#>         (-113.714590795937 + (Sepal.Length * 44.5528812152965) + 
#>             (Sepal.Width * -7.61595839316372) + (Petal.Length * 
#>             33.559537097271) + (Petal.Width * -31.2558694597319) + 
#>             (Sepal.Length * Sepal.Length * -9.47171939291025) + 
#>             (Sepal.Length * Sepal.Width * 12.4048261564855) + 
#>             (Sepal.Length * Petal.Length * 4.50020653857198) + 
#>             (Sepal.Length * Petal.Width * 4.77612732803424) + 
#>             (Sepal.Width * Sepal.Width * -7.78527008659406) + 
#>             (Sepal.Width * Petal.Length * -1.1110791368753) + 
#>             (Sepal.Width * Petal.Width * 2.1040978276337) + (Petal.Length * 
#>             Petal.Length * -19.3881020632003) + (Petal.Length * 
#>             Petal.Width * 17.9350353034303) + (Petal.Width * 
#>             Petal.Width * -53.0229530714453))))

Add the predictions to the original table

library(dplyr)

iris %>%
  mutate(!!!tidypredict_fit(model)) %>%
  glimpse()
#> Rows: 150
#> Columns: 8
#> $ Sepal.Length <dbl> 5.1, 4.9, 4.7, 4.6, 5.0, 5.4, 4.6, 5.0, 4.4, 4.9, 5.4, 4.…
#> $ Sepal.Width  <dbl> 3.5, 3.0, 3.2, 3.1, 3.6, 3.9, 3.4, 3.4, 2.9, 3.1, 3.7, 3.…
#> $ Petal.Length <dbl> 1.4, 1.4, 1.3, 1.5, 1.4, 1.7, 1.4, 1.5, 1.4, 1.5, 1.5, 1.…
#> $ Petal.Width  <dbl> 0.2, 0.2, 0.2, 0.2, 0.2, 0.4, 0.3, 0.2, 0.2, 0.1, 0.2, 0.…
#> $ Species      <fct> setosa, setosa, setosa, setosa, setosa, setosa, setosa, s…
#> $ setosa       <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
#> $ versicolor   <dbl> 4.918517e-26, 7.655808e-19, 1.552279e-21, 8.300396e-19, 3…
#> $ virginica    <dbl> 2.981541e-41, 1.311032e-34, 3.380440e-36, 8.541858e-32, 2…

Confirm that the results match the model’s predict() results

probs <- sapply(fit, \(f) rlang::eval_tidy(f, iris))
all.equal(unname(probs), unname(predict(model, iris)$posterior))
#> [1] TRUE

parsnip

parsnip fitted models are also supported by tidypredict:

library(parsnip)
library(discrim)

p_model <- discrim_quad() %>%
  set_engine("MASS") %>%
  fit(Species ~ ., data = iris)

tidypredict_fit(p_model)[["virginica"]]
#> 1/(exp(-113.714590795937 + (Sepal.Length * 44.5528812152965) + 
#>     (Sepal.Width * -7.61595839316372) + (Petal.Length * 33.559537097271) + 
#>     (Petal.Width * -31.2558694597319) + (Sepal.Length * Sepal.Length * 
#>     -9.47171939291025) + (Sepal.Length * Sepal.Width * 12.4048261564855) + 
#>     (Sepal.Length * Petal.Length * 4.50020653857198) + (Sepal.Length * 
#>     Petal.Width * 4.77612732803424) + (Sepal.Width * Sepal.Width * 
#>     -7.78527008659406) + (Sepal.Width * Petal.Length * -1.1110791368753) + 
#>     (Sepal.Width * Petal.Width * 2.1040978276337) + (Petal.Length * 
#>     Petal.Length * -19.3881020632003) + (Petal.Length * Petal.Width * 
#>     17.9350353034303) + (Petal.Width * Petal.Width * -53.0229530714453) - 
#>     (-67.7090772023948 + (Sepal.Length * 7.37247478397159) + 
#>         (Sepal.Width * 13.2452613006359) + (Petal.Length * 6.23406948373775) + 
#>         (Petal.Width * 9.66197608445426) + (Sepal.Length * Sepal.Length * 
#>         -5.26693339970327) + (Sepal.Length * Sepal.Width * 3.47972623582808) + 
#>         (Sepal.Length * Petal.Length * 9.96014594453995) + (Sepal.Length * 
#>         Petal.Width * -1.78815223046388) + (Sepal.Width * Sepal.Width * 
#>         -7.93772112409139) + (Sepal.Width * Petal.Length * -1.10268870214298) + 
#>         (Sepal.Width * Petal.Width * 8.47285053214324) + (Petal.Length * 
#>         Petal.Length * -6.70291026519806) + (Petal.Length * Petal.Width * 
#>         2.8909184691834) + (Petal.Width * Petal.Width * -9.65702517612499))) + 
#>     exp(-68.4372876863761 + (Sepal.Length * 18.0128645045465) + 
#>         (Sepal.Width * 15.9607000492876) + (Petal.Length * 3.26878502392697) + 
#>         (Petal.Width * -14.7125574674066) + (Sepal.Length * Sepal.Length * 
#>         -4.75138188253319) + (Sepal.Length * Sepal.Width * 3.67621661105371) + 
#>         (Sepal.Length * Petal.Length * 8.63171191375034) + (Sepal.Length * 
#>         Petal.Width * -6.45450343914607) + (Sepal.Width * Sepal.Width * 
#>         -9.85548321295217) + (Sepal.Width * Petal.Length * -2.11602239677401) + 
#>         (Sepal.Width * Petal.Width * 19.4803247040045) + (Petal.Length * 
#>         Petal.Length * -9.90187886398409) + (Petal.Length * Petal.Width * 
#>         26.9372270107537) + (Petal.Width * Petal.Width * -43.6223969131695) - 
#>         (-67.7090772023948 + (Sepal.Length * 7.37247478397159) + 
#>             (Sepal.Width * 13.2452613006359) + (Petal.Length * 
#>             6.23406948373775) + (Petal.Width * 9.66197608445426) + 
#>             (Sepal.Length * Sepal.Length * -5.26693339970327) + 
#>             (Sepal.Length * Sepal.Width * 3.47972623582808) + 
#>             (Sepal.Length * Petal.Length * 9.96014594453995) + 
#>             (Sepal.Length * Petal.Width * -1.78815223046388) + 
#>             (Sepal.Width * Sepal.Width * -7.93772112409139) + 
#>             (Sepal.Width * Petal.Length * -1.10268870214298) + 
#>             (Sepal.Width * Petal.Width * 8.47285053214324) + 
#>             (Petal.Length * Petal.Length * -6.70291026519806) + 
#>             (Petal.Length * Petal.Width * 2.8909184691834) + 
#>             (Petal.Width * Petal.Width * -9.65702517612499))) + 
#>     1)

Parse model spec

Here is an example of the model spec:

pm <- parse_model(model)
str(pm, 2)
#> List of 3
#>  $ general    :List of 4
#>   ..$ model  : chr "qda"
#>   ..$ version: num 2
#>   ..$ type   : chr "multiclass_regression"
#>   ..$ family : chr "multinomial"
#>  $ classes    : chr [1:3] "setosa" "versicolor" "virginica"
#>  $ class_terms:List of 3
#>   ..$ :List of 15
#>   ..$ :List of 15
#>   ..$ :List of 15
#>  - attr(*, "class")= chr [1:3] "parsed_model" "pm_multiclass_regression" "list"

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.

qda models

tidypredict_ functions

parsnip

Parse model spec

`tidypredict_` functions