Calculate MID Importance

mid.importance() calculates the MID importance of a fitted MID model. This is a measure of feature importance that quantifies the average contribution of each component function across a dataset.

Usage

mid.importance(
  object,
  data = NULL,
  weights = NULL,
  sort = TRUE,
  measure = 1L,
  max.nsamples = 10000L,
  seed = NULL
)

Arguments

object

a "mid" object.

data

a data frame containing the observations to calculate the importance. If not provided, data is automatically extracted based on the function call.

weights

an optional numeric vector of sample weights.

sort

logical. If TRUE, the output data frame is sorted by importance in descending order.

measure

an integer specifying the measure of importance. Possible alternatives are 1 for the mean absolute effect, 2 for the root mean square effect, and 3 for the median absolute effect.

max.nsamples

an integer specifying the maximum number of samples to retain in the predictions component of the returned object. If the number of observations exceeds this value, a weighted random sample is taken.

seed

an integer seed for random sampling. Default is NULL.

Value

mid.importance() returns an object of class "midimp". This is a list containing the following components:

importance

a data frame with the calculated importance values, sorted by default.

predictions

the matrix of the fitted or predicted MID values. If the number of observations exceeds max.nsamples, this matrix contains a sampled subset.

measure

a character string describing the type of the importance measure used.

For a "mids" collection object, mid.importance() returns a collection object of class "midimps"-"midlist".

Details

The MID importance of a component function \(g_S\), where \(S\) represents a single feature \(\{j\}\) or a feature pair \(\{j, k\}\), is defined as the mean absolute effect on the predictions within the given data:

$$\mathbf{I}(g_S) = \frac{1}{n} \sum_{i=1}^n |g_S(\mathbf{x}_{i,S})|$$

Terms with higher importance values have a larger average impact on the model's overall predictions. Because all components (main effects and interactions) are measured on the same scale as the response variable, these values provide a direct and comparable measure of each term's contribution to the model.

See also

interpret, plot.midimp, ggmid.midimp

Examples

data(airquality, package = "datasets")
mid <- interpret(Ozone ~ .^2, data = airquality, lambda = 1)
#> 'model' not passed: response variable in 'data' is used

# Calculate MID importance using median absolute contribution
imp <- mid.importance(mid, data = airquality)
print(imp)
#> 
#> MID Importance based on 153 Observations
#> 
#> Measure: Mean Absolute Contribution
#> 
#> Importance:
#>             term importance order
#> 1           Temp   13.87964     1
#> 2           Wind   10.33988     1
#> 3        Solar.R    5.02987     1
#> 4            Day    4.89338     1
#> 5          Month    2.15840     1
#> 6   Solar.R:Wind    0.45055     2
#> 7       Temp:Day    0.40191     2
#> 8       Wind:Day    0.38748     2
#> 9  Solar.R:Month    0.38573     2
#> 10    Wind:Month    0.38059     2
#> 11     Month:Day    0.31367     2
#> 12     Wind:Temp    0.29737     2
#> 13   Solar.R:Day    0.28360     2
#> 14  Solar.R:Temp    0.21667     2
#> 15    Temp:Month    0.14529     2

# Calculate MID importance using root mean square contribution
imp <- mid.importance(mid, measure = 2)
print(imp)
#> 
#> MID Importance based on 111 Observations
#> 
#> Measure: Root Mean Square Contribution
#> 
#> Importance:
#>             term importance order
#> 1           Temp   16.23318     1
#> 2           Wind   14.77135     1
#> 3        Solar.R    7.25789     1
#> 4            Day    5.69615     1
#> 5          Month    2.66095     1
#> 6     Wind:Month    0.56416     2
#> 7   Solar.R:Wind    0.55387     2
#> 8  Solar.R:Month    0.51838     2
#> 9       Wind:Day    0.51729     2
#> 10      Temp:Day    0.48825     2
#> 11     Month:Day    0.47409     2
#> 12     Wind:Temp    0.41887     2
#> 13   Solar.R:Day    0.32822     2
#> 14  Solar.R:Temp    0.30586     2
#> 15    Temp:Month    0.20071     2