Generalized Linear model

Highlights & Limitations

How it works

df <- mtcars %>%
  mutate(char_cyl = paste0("cyl", cyl)) %>%
  select(wt, char_cyl, am) 

model <- glm(am ~ wt + char_cyl, data = df, family = "binomial")

It returns a SQL query that contains the coefficients (model$coefficients) operated against the correct variable or categorical variable value. In most cases the resulting SQL is one short CASE WHEN statement per coefficient. It appends the offset field or value, if one is provided.

For binomial models, the sigmoid equation is applied. This means that the target SQL database type will need to support the exponent function.

library(tidypredict)

tidypredict_sql(model, dbplyr::simulate_mssql())
## <SQL> 1.0 - 1.0 / (1.0 + EXP((((20.8527831345691) + ((`wt`) * (-7.85934263583835))) + ((CASE WHEN (((`char_cyl`) = ('cyl6')) =  'TRUE') THEN (1.0) WHEN (((`char_cyl`) = ('cyl6')) =  'FALSE') THEN (0.0) END) * (3.10462643177453))) + ((CASE WHEN (((`char_cyl`) = ('cyl8')) =  'TRUE') THEN (1.0) WHEN (((`char_cyl`) = ('cyl8')) =  'FALSE') THEN (0.0) END) * (5.37942092366097))))

Alternatively, use tidypredict_to_column() if the results are the be used or previewed in dplyr.

df %>%
  tidypredict_to_column(model) %>%
  head(10) 
##       wt char_cyl am        fit
## 1  2.620     cyl6  1 0.96662269
## 2  2.875     cyl6  1 0.79605201
## 3  2.320     cyl4  1 0.93208127
## 4  3.215     cyl6  0 0.21242376
## 5  3.440     cyl8  0 0.30918450
## 6  3.460     cyl6  0 0.03783629
## 7  3.570     cyl8  0 0.13875740
## 8  3.190     cyl4  0 0.01450687
## 9  3.150     cyl4  0 0.01975984
## 10 3.440     cyl6  0 0.04399324

Under the hood

The parser reads several parts of the glm object to tabulate all of the needed variables. One entry per coefficient is added to the final table. Other variables are added at the end. Some variables are not required for every parsed model. For example, offset is listed because it’s part of the formula (call) of the model, if there were no offset in a given model, that line would not exist.

parse_model(model)
## # A tibble: 10 x 10
##    labels  estima… type   field… fiel…    qr_1   qr_2    qr_3   qr_4 vals 
##    <chr>     <dbl> <chr>  <chr>  <chr>   <dbl>  <dbl>   <dbl>  <dbl> <chr>
##  1 (Inter…   20.9  term   <NA>   <NA>  - 0.679 - 5.11 - 1.15    6.05 <NA> 
##  2 wt       - 7.86 term   <NA>   {{:}}   0       1.62   0.232 - 2.58 <NA> 
##  3 char_c…    3.10 term   cyl6   <NA>    0       0      1.56    1.86 <NA> 
##  4 char_c…    5.38 term   cyl8   <NA>    0       0      0       3.20 <NA> 
##  5 labels     0    varia… char_… wt     NA      NA     NA      NA    <NA> 
##  6 model     NA    varia… <NA>   <NA>   NA      NA     NA      NA    glm  
##  7 version   NA    varia… <NA>   <NA>   NA      NA     NA      NA    1.0  
##  8 residu…   NA    varia… <NA>   <NA>   NA      NA     NA      NA    28   
##  9 family    NA    varia… <NA>   <NA>   NA      NA     NA      NA    bino…
## 10 link      NA    varia… <NA>   <NA>   NA      NA     NA      NA    logit

The output from parse_model() is transformed into a dplyr, a.k.a Tidy Eval, formula. All categorical variables are operated using if_else().

tidypredict_fit(model)
## 1 - 1/(1 + exp((((20.8527831345691) + ((wt) * (-7.85934263583835))) + 
##     ((ifelse((char_cyl) == ("cyl6"), 1, 0)) * (3.10462643177453))) + 
##     ((ifelse((char_cyl) == ("cyl8"), 1, 0)) * (5.37942092366097))))

From there, the Tidy Eval formula can be used anywhere where it can be operated. tidypredict provides three paths:

The same applies to the prediction interval functions.

How it performs

Testing the tidypredict results is easy. The tidypredict_test() function automatically uses the lm model object’s data frame, to compare tidypredict_fit(), and tidypredict_interval() to the results given by predict()

tidypredict_test(model)
## tidypredict test results
## Difference threshold: 1e-12
## 
##  All results are within the difference threshold