This pages holds the details for the formula preprocessing blueprint. This is the blueprint used by default from mold() if x is a formula.

## Usage

default_formula_blueprint(
intercept = FALSE,
allow_novel_levels = FALSE,
composition = "tibble"
)

# S3 method for formula
mold(formula, data, ..., blueprint = NULL)

## Arguments

intercept

A logical. Should an intercept be included in the processed data? This information is used by the process function in the mold and forge function list.

allow_novel_levels

A logical. Should novel factor levels be allowed at prediction time? This information is used by the clean function in the forge function list, and is passed on to scream().

indicators

A single character string. Control how factors are expanded into dummy variable indicator columns. One of:

• "traditional" - The default. Create dummy variables using the traditional model.matrix() infrastructure. Generally this creates K - 1 indicator columns for each factor, where K is the number of levels in that factor.

• "none" - Leave factor variables alone. No expansion is done.

• "one_hot" - Create dummy variables using a one-hot encoding approach that expands unordered factors into all K indicator columns, rather than K - 1.

composition

Either "tibble", "matrix", or "dgCMatrix" for the format of the processed predictors. If "matrix" or "dgCMatrix" are chosen, all of the predictors must be numeric after the preprocessing method has been applied; otherwise an error is thrown.

formula

A formula specifying the predictors and the outcomes.

data

A data frame or matrix containing the outcomes and predictors.

...

Not used.

blueprint

A preprocessing blueprint. If left as NULL, then a default_formula_blueprint() is used.

## Value

For default_formula_blueprint(), a formula blueprint.

## Details

While not different from base R, the behavior of expanding factors into dummy variables when indicators = "traditional" and an intercept is not present is not always intuitive and should be documented.

• When an intercept is present, factors are expanded into K-1 new columns, where K is the number of levels in the factor.

• When an intercept is not present, the first factor is expanded into all K columns (one-hot encoding), and the remaining factors are expanded into K-1 columns. This behavior ensures that meaningful predictions can be made for the reference level of the first factor, but is not the exact "no intercept" model that was requested. Without this behavior, predictions for the reference level of the first factor would always be forced to 0 when there is no intercept.

Offsets can be included in the formula method through the use of the inline function stats::offset(). These are returned as a tibble with 1 column named ".offset" in the $extras$offset slot of the return value.

## Mold

When mold() is used with the default formula blueprint:

• Predictors

• The RHS of the formula is isolated, and converted to its own 1 sided formula: ~ RHS.

• Runs stats::model.frame() on the RHS formula and uses data.

• If indicators = "traditional", it then runs stats::model.matrix() on the result.

• If indicators = "none", factors are removed before model.matrix() is run, and then added back afterwards. No interactions or inline functions involving factors are allowed.

• If indicators = "one_hot", it then runs stats::model.matrix() on the result using a contrast function that creates indicator columns for all levels of all factors.

• If any offsets are present from using offset(), then they are extracted with model_offset().

• If intercept = TRUE, adds an intercept column.

• Coerces the result of the above steps to a tibble.

• Outcomes

• The LHS of the formula is isolated, and converted to its own 1 sided formula: ~ LHS.

• Runs stats::model.frame() on the LHS formula and uses data.

• Coerces the result of the above steps to a tibble.

## Forge

When forge() is used with the default formula blueprint:

• It calls shrink() to trim new_data to only the required columns and coerce new_data to a tibble.

• It calls scream() to perform validation on the structure of the columns of new_data.

• Predictors

• It runs stats::model.frame() on new_data using the stored terms object corresponding to the predictors.

• If, in the original mold() call, indicators = "traditional" was set, it then runs stats::model.matrix() on the result.

• If, in the original mold() call, indicators = "none" was set, it runs stats::model.matrix() on the result without the factor columns, and then adds them on afterwards.

• If, in the original mold() call, indicators = "one_hot" was set, it runs stats::model.matrix() on the result with a contrast function that includes indicators for all levels of all factor columns.

• If any offsets are present from using offset() in the original call to mold(), then they are extracted with model_offset().

• If intercept = TRUE in the original call to mold(), then an intercept column is added.

• It coerces the result of the above steps to a tibble.

• Outcomes

• It runs stats::model.frame() on new_data using the stored terms object corresponding to the outcomes.

• Coerces the result to a tibble.

## Differences From Base R

There are a number of differences from base R regarding how formulas are processed by mold() that require some explanation.

Multivariate outcomes can be specified on the LHS using syntax that is similar to the RHS (i.e. outcome_1 + outcome_2 ~ predictors). If any complex calculations are done on the LHS and they return matrices (like stats::poly()), then those matrices are flattened into multiple columns of the tibble after the call to model.frame(). While this is possible, it is not recommended, and if a large amount of preprocessing is required on the outcomes, then you are better off using a recipes::recipe().

Global variables are not allowed in the formula. An error will be thrown if they are included. All terms in the formula should come from data. If you need to use inline functions in the formula, the safest way to do so is to prefix them with their package name, like pkg::fn(). This ensures that the function will always be available at mold() (fit) and forge() (prediction) time. That said, if the package is attached (i.e. with library()), then you should be able to use the inline function without the prefix.

By default, intercepts are not included in the predictor output from the formula. To include an intercept, set blueprint = default_formula_blueprint(intercept = TRUE). The rationale for this is that many packages either always require or never allow an intercept (for example, the earth package), and they do a large amount of extra work to keep the user from supplying one or removing it. This interface standardizes all of that flexibility in one place.

## Examples

# ---------------------------------------------------------------------------

data("hardhat-example-data")

# ---------------------------------------------------------------------------
# Formula Example

# Call mold() with the training data
processed <- mold(
log(num_1) ~ num_2 + fac_1,
example_train,
blueprint = default_formula_blueprint(intercept = TRUE)
)

# Then, call forge() with the blueprint and the test data
# to have it preprocess the test data in the same way
forge(example_test, processed$blueprint) #>$predictors
#> # A tibble: 2 × 4
#>   (Intercept) num_2 fac_1b fac_1c
#>           <dbl> <dbl>  <dbl>  <dbl>
#> 1             1 0.967      0      0
#> 2             1 0.761      0      1
#>
#> $outcomes #> NULL #> #>$extras
#> $extras$offset
#> NULL
#>
#>

# Use outcomes = TRUE to also extract the preprocessed outcome
forge(example_test, processed$blueprint, outcomes = TRUE) #>$predictors
#> # A tibble: 2 × 4
#>   (Intercept) num_2 fac_1b fac_1c
#>           <dbl> <dbl>  <dbl>  <dbl>
#> 1             1 0.967      0      0
#> 2             1 0.761      0      1
#>
#> $outcomes #> # A tibble: 2 × 1 #> log(num_1) #> <dbl> #> 1 3.00 #> 2 3.04 #> #>$extras
#> $extras$offset
#> NULL
#>
#>

# ---------------------------------------------------------------------------
# Factors without an intercept

# No intercept is added by default
processed <- mold(num_1 ~ fac_1 + fac_2, example_train)

# So, for factor columns, the first factor is completely expanded into all
# K columns (the number of levels), and the subsequent factors are expanded
# into K - 1 columns.
processed$predictors #> # A tibble: 12 × 4 #> fac_1a fac_1b fac_1c fac_2B #> <dbl> <dbl> <dbl> <dbl> #> 1 1 0 0 0 #> 2 1 0 0 1 #> 3 1 0 0 0 #> 4 1 0 0 1 #> 5 0 1 0 0 #> 6 0 1 0 1 #> 7 0 1 0 0 #> 8 0 1 0 1 #> 9 0 0 1 0 #> 10 0 0 1 1 #> 11 0 0 1 0 #> 12 0 0 1 1 # In the above example, fac_1 is expanded into all three columns, # fac_2 is not. This behavior comes from model.matrix(), and is somewhat # known in the R community, but can lead to a model that is difficult to # interpret since the corresponding p-values are testing wildly different # hypotheses. # To get all indicators for all columns (irrespective of the intercept), # use the indicators = "one_hot" option processed <- mold( num_1 ~ fac_1 + fac_2, example_train, blueprint = default_formula_blueprint(indicators = "one_hot") ) processed$predictors
#> # A tibble: 12 × 5
#>    fac_1a fac_1b fac_1c fac_2A fac_2B
#>     <dbl>  <dbl>  <dbl>  <dbl>  <dbl>
#>  1      1      0      0      1      0
#>  2      1      0      0      0      1
#>  3      1      0      0      1      0
#>  4      1      0      0      0      1
#>  5      0      1      0      1      0
#>  6      0      1      0      0      1
#>  7      0      1      0      1      0
#>  8      0      1      0      0      1
#>  9      0      0      1      1      0
#> 10      0      0      1      0      1
#> 11      0      0      1      1      0
#> 12      0      0      1      0      1

# It is not possible to construct a no-intercept model that expands all
# factors into K - 1 columns using the formula method. If required, a
# recipe could be used to construct this model.

# ---------------------------------------------------------------------------
# Global variables

y <- rep(1, times = nrow(example_train))

# In base R, global variables are allowed in a model formula
frame <- model.frame(fac_1 ~ y + num_2, example_train)
#>   fac_1 y num_2
#> 1     a 1 0.579
#> 2     a 1 0.338
#> 3     a 1 0.206
#> 4     a 1 0.546
#> 5     b 1 0.964
#> 6     b 1 0.631

# mold() does not allow them, and throws an error
try(mold(fac_1 ~ y + num_2, example_train))
#> Error in get_all_predictors(formula, data) :
#>   The following predictors were not found in data: 'y'.

# ---------------------------------------------------------------------------
# Dummy variables and interactions

# By default, factor columns are expanded
# and interactions are created, both by
# calling model.matrix(). Some models (like
# tree based models) can take factors directly
# but still might want to use the formula method.
# In those cases, set indicators = "none" to not
# run model.matrix() on factor columns. Interactions
# are still allowed and are run on numeric columns.

bp_no_indicators <- default_formula_blueprint(indicators = "none")

processed <- mold(
~ fac_1 + num_1:num_2,
example_train,
blueprint = bp_no_indicators
)

processed$predictors #> # A tibble: 12 × 2 #> num_1:num_2 fac_1 #> <dbl> <fct> #> 1 0.579 a #> 2 0.676 a #> 3 0.618 a #> 4 2.18 a #> 5 4.82 b #> 6 3.79 b #> 7 5.66 b #> 8 1.66 b #> 9 2.84 c #> 10 0.83 c #> 11 6.81 c #> 12 7.42 c # An informative error is thrown when indicators = "none" and # factors are present in interaction terms or in inline functions try(mold(num_1 ~ num_2:fac_1, example_train, blueprint = bp_no_indicators)) #> Error in validate_no_factorish_in_interactions(formula, factorish_names) : #> Interaction terms involving factors or characters have been detected on the RHS of formula. These are not allowed when indicators = "none". Interactions involving factors were detected for the following columns: 'fac_1'. try(mold(num_1 ~ paste0(fac_1), example_train, blueprint = bp_no_indicators)) #> Error in validate_no_factorish_in_functions(formula, factorish_names) : #> Functions involving factors or characters have been detected on the RHS of formula. These are not allowed when indicators = "none". Functions involving factors were detected for the following columns: 'fac_1'. # --------------------------------------------------------------------------- # Multivariate outcomes # Multivariate formulas can be specified easily processed <- mold(num_1 + log(num_2) ~ fac_1, example_train) processed$outcomes
#> # A tibble: 12 × 2
#>    num_1 log(num_2)
#>    <int>        <dbl>
#>  1     1      -0.546
#>  2     2      -1.08
#>  3     3      -1.58
#>  4     4      -0.605
#>  5     5      -0.0367
#>  6     6      -0.460
#>  7     7      -0.213
#>  8     8      -1.57
#>  9     9      -1.15
#> 10    10      -2.49
#> 11    11      -0.480
#> 12    12      -0.481

# Inline functions on the LHS are run, but any matrix
# output is flattened (like what happens in model.matrix())
# (essentially this means you don't wind up with columns
# in the tibble that are matrices)
processed <- mold(poly(num_2, degree = 2) ~ fac_1, example_train)
processed$outcomes #> # A tibble: 12 × 2 #> poly(num_2, degree = 2).1 poly(num_2, degree = 2).2 #> <dbl> <dbl> #> 1 0.0981 -0.254 #> 2 -0.177 -0.157 #> 3 -0.327 0.108 #> 4 0.0604 -0.270 #> 5 0.537 0.634 #> 6 0.157 -0.209 #> 7 0.359 0.120 #> 8 -0.325 0.103 #> 9 -0.202 -0.124 #> 10 -0.468 0.492 #> 11 0.144 -0.221 #> 12 0.143 -0.222 # TRUE ncol(processed$outcomes) == 2
#> [1] TRUE

# Multivariate formulas specified in mold()
# carry over into forge()
forge(example_test, processed$blueprint, outcomes = TRUE) #>$predictors
#> # A tibble: 2 × 3
#>   fac_1a fac_1b fac_1c
#>    <dbl>  <dbl>  <dbl>
#> 1      1      0      0
#> 2      0      0      1
#>
#> $outcomes #> # A tibble: 2 × 2 #> poly(num_2, degree = 2).1 poly(num_2, degree = 2).2 #> <dbl> <dbl> #> 1 0.541 0.646 #> 2 0.306 0.00619 #> #>$extras
#> $extras$offset
#> NULL
#>
#>

# ---------------------------------------------------------------------------
# Offsets

# Offsets are handled specially in base R, so they deserve special
# treatment here as well. You can add offsets using the inline function
# offset()
processed <- mold(num_1 ~ offset(num_2) + fac_1, example_train)

processed$extras$offset
#> # A tibble: 12 × 1
#>    .offset
#>      <dbl>
#>  1   0.579
#>  2   0.338
#>  3   0.206
#>  4   0.546
#>  5   0.964
#>  6   0.631
#>  7   0.808
#>  8   0.208
#>  9   0.316
#> 10   0.083
#> 11   0.619
#> 12   0.618

# Multiple offsets can be included, and they get added together
processed <- mold(
num_1 ~ offset(num_2) + offset(num_3),
example_train
)

identical(
processed$extras$offset$.offset, example_train$num_2 + example_train$num_3 ) #> [1] TRUE # Forging test data will also require # and include the offset forge(example_test, processed$blueprint)
#> $predictors #> # A tibble: 2 × 0 #> #>$outcomes
#> NULL
#>
#> $extras #>$extras$offset #> # A tibble: 2 × 1 #> .offset #> <dbl> #> 1 1.06 #> 2 0.802 #> #> # --------------------------------------------------------------------------- # Intercept only # Because 1 and 0 are intercept modifying terms, they are # not allowed in the formula and are instead controlled by the # intercept argument of the blueprint. To use an intercept # only formula, you should supply NULL on the RHS of the formula. mold( ~NULL, example_train, blueprint = default_formula_blueprint(intercept = TRUE) ) #>$predictors
#> # A tibble: 12 × 1
#>    (Intercept)
#>            <dbl>
#>  1             1
#>  2             1
#>  3             1
#>  4             1
#>  5             1
#>  6             1
#>  7             1
#>  8             1
#>  9             1
#> 10             1
#> 11             1
#> 12             1
#>
#> $outcomes #> # A tibble: 12 × 0 #> #>$blueprint
#> Formula blueprint:
#>
#> # Predictors: 0
#>   # Outcomes: 0
#>    Intercept: TRUE
#> Novel Levels: FALSE
#>  Composition: tibble
#> $extras #>$extras$offset #> NULL #> #> # --------------------------------------------------------------------------- # Matrix output for predictors # You can change the composition of the predictor data set bp <- default_formula_blueprint(composition = "dgCMatrix") processed <- mold(log(num_1) ~ num_2 + fac_1, example_train, blueprint = bp) class(processed$predictors)