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Generating the Constraint Matrix for Abundance-Based Constraints (ABCs)

Source: R/getConstraints.R
getConstraints.Rd

getConstraints is used to generate the constraint matrix for linear regression with ABCs.

Usage

getConstraints(formula, data, props = NULL)

Arguments

formula

an object of class "formula()" (or one that can be coerced to that class); a symbolic description of the model to be fitted.

data

an optional data frame (or object coercible by as.data.frame to a data frame) containing the variables in the model.

props

an optional named list with an entry for each named categorical variable in the model, specifying the proportions of each category. By default, props will be calculated from the empirical proportions in the data.

Details

For linear regression with categorical covariates (and interactions, etc.), constraints are needed for model identifiability. getConstraints() incorporates all the necessary constraints for a given formula statement within a single matrix.

props must include every level for all categorical covariates and all interactions that include at least one categorical covariate. It should be a named list of named vectors. It provides several useful options, including alternatives to ABCs:

  • ABCs using the sample proportions of each category (default);

  • ABCs using population proportions of each category (if known);

  • Reference group encoding (RGE), which fixes a reference category proportion at 1 and all others at 0 (default in lm());

  • Sum-to-zero (STZ) constraints, which use the same proportions for every category level.

This method is called by lmabc().

Value

getConstraints returns a matrix of constraints based on the given model formula.

See also

lmabc() for a use case of getConstraints.

Examples

getConstraints(Sepal.Length ~ Petal.Length + Species + Petal.Length*Species, data = iris)
#>          (Intercept) Petal.Length Speciessetosa Speciesversicolor
#> Species1           0            0     0.3333333         0.3333333
#> Species2           0            0     0.0000000         0.0000000
#>          Speciesvirginica Petal.Length:Speciessetosa
#> Species1        0.3333333                  0.0000000
#> Species2        0.0000000                  0.3333333
#>          Petal.Length:Speciesversicolor Petal.Length:Speciesvirginica
#> Species1                      0.0000000                     0.0000000
#> Species2                      0.3333333                     0.3333333
#> attr(,"pi_hat")
#> attr(,"pi_hat")$Species
#>     setosa versicolor  virginica 
#>  0.3333333  0.3333333  0.3333333 
#>