In a regression model, the parameters do not all have the meaning. For
instance, the intercept has to be interpreted as theoretical outcome value
under some conditions (when predictors are set to 0), whereas other
coefficients are to be interpreted as amounts of change. Others, such as
interactions, represent changes in another of the parameter. The
parameters_type function attempts to retrieve information and meaning
of parameters. It outputs a dataframe of information for each parameters,
such as the Type (whether the parameter corresponds to a factor or a
numeric predictor, or whether it is a (regular) interaction or a nested
one), the Link (whether the parameter can be interpreted as a mean
value, the slope of an association or a difference between two levels) and,
in the case of interactions, which other parameters is impacted by which
parameter.
Examples
library(parameters)
model <- lm(Sepal.Length ~ Petal.Length + Species, data = iris)
parameters_type(model)
#> Parameter Type Link Term Variable
#> 1 (Intercept) intercept Mean (Intercept) <NA>
#> 2 Petal.Length numeric Association Petal.Length Petal.Length
#> 3 Speciesversicolor factor Difference Speciesversicolor Species
#> 4 Speciesvirginica factor Difference Speciesvirginica Species
#> Level Secondary_Parameter Secondary_Type Secondary_Link Secondary_Term
#> 1 <NA> <NA> NA NA NA
#> 2 <NA> <NA> NA NA NA
#> 3 versicolor <NA> NA NA NA
#> 4 virginica <NA> NA NA NA
#> Secondary_Variable Secondary_Level Tertiary_Parameter
#> 1 NA NA NA
#> 2 NA NA NA
#> 3 NA NA NA
#> 4 NA NA NA
model <- lm(Sepal.Length ~ Species + poly(Sepal.Width, 2), data = iris)
parameters_type(model)
#> Parameter Type Link Term Variable
#> 1 (Intercept) intercept Mean (Intercept) <NA>
#> 2 Speciesversicolor factor Difference Speciesversicolor Species
#> 3 Speciesvirginica factor Difference Speciesvirginica Species
#> 4 poly(Sepal.Width, 2)1 poly Association poly(Sepal.Width, 2)1 Sepal.Width
#> 5 poly(Sepal.Width, 2)2 poly Association poly(Sepal.Width, 2)2 Sepal.Width
#> Level Secondary_Parameter Secondary_Type Secondary_Link Secondary_Term
#> 1 <NA> <NA> NA NA NA
#> 2 versicolor <NA> NA NA NA
#> 3 virginica <NA> NA NA NA
#> 4 1 <NA> NA NA NA
#> 5 2 <NA> NA NA NA
#> Secondary_Variable Secondary_Level Tertiary_Parameter
#> 1 NA NA NA
#> 2 NA NA NA
#> 3 NA NA NA
#> 4 NA NA NA
#> 5 NA NA NA
model <- lm(Sepal.Length ~ Species + poly(Sepal.Width, 2, raw = TRUE), data = iris)
parameters_type(model)
#> Parameter Type Link Term
#> 1 (Intercept) intercept Mean (Intercept)
#> 2 Speciesversicolor factor Difference Speciesversicolor
#> 3 Speciesvirginica factor Difference Speciesvirginica
#> 4 poly(Sepal.Width, 2, raw = TRUE)1 poly_raw Association poly(Sepal.Width, 2)1
#> 5 poly(Sepal.Width, 2, raw = TRUE)2 poly_raw Association poly(Sepal.Width, 2)2
#> Variable Level Secondary_Parameter Secondary_Type Secondary_Link
#> 1 <NA> <NA> <NA> NA NA
#> 2 Species versicolor <NA> NA NA
#> 3 Species virginica <NA> NA NA
#> 4 Sepal.Width 1 <NA> NA NA
#> 5 Sepal.Width 2 <NA> NA NA
#> Secondary_Term Secondary_Variable Secondary_Level Tertiary_Parameter
#> 1 NA NA NA NA
#> 2 NA NA NA NA
#> 3 NA NA NA NA
#> 4 NA NA NA NA
#> 5 NA NA NA NA
# Interactions
model <- lm(Sepal.Length ~ Sepal.Width * Species, data = iris)
parameters_type(model)
#> Parameter Type Link Term
#> 1 (Intercept) intercept Mean (Intercept)
#> 2 Sepal.Width numeric Association Sepal.Width
#> 3 Speciesversicolor factor Difference Speciesversicolor
#> 4 Speciesvirginica factor Difference Speciesvirginica
#> 5 Sepal.Width:Speciesversicolor interaction Difference Speciesversicolor
#> 6 Sepal.Width:Speciesvirginica interaction Difference Speciesvirginica
#> Variable Level Secondary_Parameter Secondary_Type Secondary_Link
#> 1 <NA> <NA> <NA> <NA> <NA>
#> 2 Sepal.Width <NA> <NA> <NA> <NA>
#> 3 Species versicolor <NA> <NA> <NA>
#> 4 Species virginica <NA> <NA> <NA>
#> 5 Species versicolor Sepal.Width numeric Association
#> 6 Species virginica Sepal.Width numeric Association
#> Secondary_Term Secondary_Variable Secondary_Level Tertiary_Parameter
#> 1 <NA> <NA> <NA> <NA>
#> 2 <NA> <NA> <NA> <NA>
#> 3 <NA> <NA> <NA> <NA>
#> 4 <NA> <NA> <NA> <NA>
#> 5 Sepal.Width Sepal.Width <NA> <NA>
#> 6 Sepal.Width Sepal.Width <NA> <NA>
model <- lm(Sepal.Length ~ Sepal.Width * Species * Petal.Length, data = iris)
parameters_type(model)
#> Parameter Type Link
#> 1 (Intercept) intercept Mean
#> 2 Sepal.Width numeric Association
#> 3 Speciesversicolor factor Difference
#> 4 Speciesvirginica factor Difference
#> 5 Petal.Length numeric Association
#> 6 Sepal.Width:Speciesversicolor interaction Difference
#> 7 Sepal.Width:Speciesvirginica interaction Difference
#> 8 Sepal.Width:Petal.Length interaction Association
#> 9 Speciesversicolor:Petal.Length interaction Difference
#> 10 Speciesvirginica:Petal.Length interaction Difference
#> 11 Sepal.Width:Speciesversicolor:Petal.Length interaction Association
#> 12 Sepal.Width:Speciesvirginica:Petal.Length interaction Association
#> Term Variable Level Secondary_Parameter
#> 1 (Intercept) <NA> <NA> <NA>
#> 2 Sepal.Width Sepal.Width <NA> <NA>
#> 3 Speciesversicolor Species versicolor <NA>
#> 4 Speciesvirginica Species virginica <NA>
#> 5 Petal.Length Petal.Length <NA> <NA>
#> 6 Speciesversicolor Species versicolor Sepal.Width
#> 7 Speciesvirginica Species virginica Sepal.Width
#> 8 Petal.Length Petal.Length <NA> Sepal.Width
#> 9 Petal.Length Petal.Length <NA> Speciesversicolor
#> 10 Petal.Length Petal.Length <NA> Speciesvirginica
#> 11 Petal.Length Petal.Length <NA> Sepal.Width:Speciesversicolor
#> 12 Petal.Length Petal.Length <NA> Sepal.Width:Speciesvirginica
#> Secondary_Type Secondary_Link Secondary_Term Secondary_Variable
#> 1 <NA> <NA> <NA> <NA>
#> 2 <NA> <NA> <NA> <NA>
#> 3 <NA> <NA> <NA> <NA>
#> 4 <NA> <NA> <NA> <NA>
#> 5 <NA> <NA> <NA> <NA>
#> 6 numeric Association Sepal.Width Sepal.Width
#> 7 numeric Association Sepal.Width Sepal.Width
#> 8 numeric Association Sepal.Width Sepal.Width
#> 9 factor Difference Speciesversicolor Species
#> 10 factor Difference Speciesvirginica Species
#> 11 interaction Difference Speciesversicolor Species
#> 12 interaction Difference Speciesvirginica Species
#> Secondary_Level Tertiary_Parameter
#> 1 <NA> <NA>
#> 2 <NA> <NA>
#> 3 <NA> <NA>
#> 4 <NA> <NA>
#> 5 <NA> <NA>
#> 6 <NA> <NA>
#> 7 <NA> <NA>
#> 8 <NA> <NA>
#> 9 versicolor <NA>
#> 10 virginica <NA>
#> 11 versicolor Sepal.Width
#> 12 virginica Sepal.Width
model <- lm(Sepal.Length ~ Species * Sepal.Width, data = iris)
parameters_type(model)
#> Parameter Type Link Term
#> 1 (Intercept) intercept Mean (Intercept)
#> 2 Speciesversicolor factor Difference Speciesversicolor
#> 3 Speciesvirginica factor Difference Speciesvirginica
#> 4 Sepal.Width numeric Association Sepal.Width
#> 5 Speciesversicolor:Sepal.Width interaction Difference Sepal.Width
#> 6 Speciesvirginica:Sepal.Width interaction Difference Sepal.Width
#> Variable Level Secondary_Parameter Secondary_Type Secondary_Link
#> 1 <NA> <NA> <NA> <NA> <NA>
#> 2 Species versicolor <NA> <NA> <NA>
#> 3 Species virginica <NA> <NA> <NA>
#> 4 Sepal.Width <NA> <NA> <NA> <NA>
#> 5 Sepal.Width <NA> Speciesversicolor factor Difference
#> 6 Sepal.Width <NA> Speciesvirginica factor Difference
#> Secondary_Term Secondary_Variable Secondary_Level Tertiary_Parameter
#> 1 <NA> <NA> <NA> <NA>
#> 2 <NA> <NA> <NA> <NA>
#> 3 <NA> <NA> <NA> <NA>
#> 4 <NA> <NA> <NA> <NA>
#> 5 Speciesversicolor Species versicolor <NA>
#> 6 Speciesvirginica Species virginica <NA>
model <- lm(Sepal.Length ~ Species / Sepal.Width, data = iris)
parameters_type(model)
#> Parameter Type Link Term
#> 1 (Intercept) intercept Mean (Intercept)
#> 2 Speciesversicolor factor Difference Speciesversicolor
#> 3 Speciesvirginica factor Difference Speciesvirginica
#> 4 Speciessetosa:Sepal.Width nested Difference Sepal.Width
#> 5 Speciesversicolor:Sepal.Width nested Difference Sepal.Width
#> 6 Speciesvirginica:Sepal.Width nested Difference Sepal.Width
#> Variable Level Secondary_Parameter Secondary_Type Secondary_Link
#> 1 <NA> <NA> <NA> <NA> <NA>
#> 2 Species versicolor <NA> <NA> <NA>
#> 3 Species virginica <NA> <NA> <NA>
#> 4 Sepal.Width <NA> Speciessetosa factor Difference
#> 5 Sepal.Width <NA> Speciesversicolor factor Difference
#> 6 Sepal.Width <NA> Speciesvirginica factor Difference
#> Secondary_Term Secondary_Variable Secondary_Level Tertiary_Parameter
#> 1 <NA> <NA> <NA> <NA>
#> 2 <NA> <NA> <NA> <NA>
#> 3 <NA> <NA> <NA> <NA>
#> 4 Speciessetosa Species setosa <NA>
#> 5 Speciesversicolor Species versicolor <NA>
#> 6 Speciesvirginica Species virginica <NA>
# Complex interactions
data <- iris
data$fac2 <- ifelse(data$Sepal.Width > mean(data$Sepal.Width), "A", "B")
model <- lm(Sepal.Length ~ Species / fac2 / Petal.Length, data = data)
parameters_type(model)
#> Parameter Type Link Term
#> 1 (Intercept) intercept Mean (Intercept)
#> 2 Speciesversicolor factor Difference Speciesversicolor
#> 3 Speciesvirginica factor Difference Speciesvirginica
#> 4 Speciessetosa:fac2B nested Difference fac2B
#> 5 Speciesversicolor:fac2B nested Difference fac2B
#> 6 Speciesvirginica:fac2B nested Difference fac2B
#> 7 Speciessetosa:fac2A:Petal.Length nested Association Petal.Length
#> 8 Speciesversicolor:fac2A:Petal.Length nested Association Petal.Length
#> 9 Speciesvirginica:fac2A:Petal.Length nested Association Petal.Length
#> 10 Speciessetosa:fac2B:Petal.Length nested Association Petal.Length
#> 11 Speciesversicolor:fac2B:Petal.Length nested Association Petal.Length
#> 12 Speciesvirginica:fac2B:Petal.Length nested Association Petal.Length
#> Variable Level Secondary_Parameter Secondary_Type
#> 1 <NA> <NA> <NA> <NA>
#> 2 Species versicolor <NA> <NA>
#> 3 Species virginica <NA> <NA>
#> 4 fac2 B Speciessetosa factor
#> 5 fac2 B Speciesversicolor factor
#> 6 fac2 B Speciesvirginica factor
#> 7 Petal.Length <NA> Speciessetosa:fac2A interaction
#> 8 Petal.Length <NA> Speciesversicolor:fac2A interaction
#> 9 Petal.Length <NA> Speciesvirginica:fac2A interaction
#> 10 Petal.Length <NA> Speciessetosa:fac2B nested
#> 11 Petal.Length <NA> Speciesversicolor:fac2B nested
#> 12 Petal.Length <NA> Speciesvirginica:fac2B nested
#> Secondary_Link Secondary_Term Secondary_Variable Secondary_Level
#> 1 <NA> <NA> <NA> <NA>
#> 2 <NA> <NA> <NA> <NA>
#> 3 <NA> <NA> <NA> <NA>
#> 4 Difference Speciessetosa Species setosa
#> 5 Difference Speciesversicolor Species versicolor
#> 6 Difference Speciesvirginica Species virginica
#> 7 Difference fac2A fac2 A
#> 8 Difference fac2A fac2 A
#> 9 Difference fac2A fac2 A
#> 10 Difference fac2B fac2 B
#> 11 Difference fac2B fac2 B
#> 12 Difference fac2B fac2 B
#> Tertiary_Parameter
#> 1 <NA>
#> 2 <NA>
#> 3 <NA>
#> 4 <NA>
#> 5 <NA>
#> 6 <NA>
#> 7 Speciessetosa
#> 8 Speciesversicolor
#> 9 Speciesvirginica
#> 10 Speciessetosa
#> 11 Speciesversicolor
#> 12 Speciesvirginica
model <- lm(Sepal.Length ~ Species / fac2 * Petal.Length, data = data)
parameters_type(model)
#> Parameter Type Link
#> 1 (Intercept) intercept Mean
#> 2 Speciesversicolor factor Difference
#> 3 Speciesvirginica factor Difference
#> 4 Petal.Length numeric Association
#> 5 Speciessetosa:fac2B nested Difference
#> 6 Speciesversicolor:fac2B nested Difference
#> 7 Speciesvirginica:fac2B nested Difference
#> 8 Speciesversicolor:Petal.Length interaction Difference
#> 9 Speciesvirginica:Petal.Length interaction Difference
#> 10 Speciessetosa:fac2B:Petal.Length simple Association
#> 11 Speciesversicolor:fac2B:Petal.Length simple Association
#> 12 Speciesvirginica:fac2B:Petal.Length simple Association
#> Term Variable Level Secondary_Parameter
#> 1 (Intercept) <NA> <NA> <NA>
#> 2 Speciesversicolor Species versicolor <NA>
#> 3 Speciesvirginica Species virginica <NA>
#> 4 Petal.Length Petal.Length <NA> <NA>
#> 5 fac2B fac2 B Speciessetosa
#> 6 fac2B fac2 B Speciesversicolor
#> 7 fac2B fac2 B Speciesvirginica
#> 8 Petal.Length Petal.Length <NA> Speciesversicolor
#> 9 Petal.Length Petal.Length <NA> Speciesvirginica
#> 10 Petal.Length Petal.Length <NA> Speciessetosa:fac2B
#> 11 Petal.Length Petal.Length <NA> Speciesversicolor:fac2B
#> 12 Petal.Length Petal.Length <NA> Speciesvirginica:fac2B
#> Secondary_Type Secondary_Link Secondary_Term Secondary_Variable
#> 1 <NA> <NA> <NA> <NA>
#> 2 <NA> <NA> <NA> <NA>
#> 3 <NA> <NA> <NA> <NA>
#> 4 <NA> <NA> <NA> <NA>
#> 5 factor Difference Speciessetosa Species
#> 6 factor Difference Speciesversicolor Species
#> 7 factor Difference Speciesvirginica Species
#> 8 factor Difference Speciesversicolor Species
#> 9 factor Difference Speciesvirginica Species
#> 10 nested Difference fac2B fac2
#> 11 nested Difference fac2B fac2
#> 12 nested Difference fac2B fac2
#> Secondary_Level Tertiary_Parameter
#> 1 <NA> <NA>
#> 2 <NA> <NA>
#> 3 <NA> <NA>
#> 4 <NA> <NA>
#> 5 setosa <NA>
#> 6 versicolor <NA>
#> 7 virginica <NA>
#> 8 versicolor <NA>
#> 9 virginica <NA>
#> 10 B Speciessetosa
#> 11 B Speciesversicolor
#> 12 B Speciesvirginica