Calculate MID Conditional Expectation

mid.conditional() calculates the data required to draw Individual Conditional Expectation (ICE) curves from a fitted MID model. ICE curves visualize how a single observation's prediction changes as a specified variable's value varies, while all other variable are held constant.

Usage

mid.conditional(
  object,
  variable,
  data = NULL,
  resolution = 100L,
  max.nsamples = 500L,
  seed = NULL,
  type = c("response", "link"),
  keep.effects = TRUE
)

Arguments

object

a "mid" object.

variable

a character string or expression specifying the single predictor variable for which to calculate ICE curves.

data

a data frame containing the observations to be used for the ICE calculations. If not provided, data is automatically extracted based on the function call.

resolution

an integer specifying the number of evaluation points for the variable's range.

max.nsamples

an integer specifying the maximum number of samples. If the number of observations exceeds this limit, the data is randomly sampled.

seed

an integer seed for random sampling. Default is NULL.

type

the type of prediction to return. "response" (default) for the original scale or "link" for the scale of the linear predictor.

keep.effects

logical. If TRUE, the effects of individual component functions are stored in the output object.

Value

mid.conditional() returns an object of class "midcon". This is a list with the following components:

observed

a data frame of the original observations used, along with their predictions.

conditional

a data frame of the hypothetical observations and their corresponding predictions.

variable

name of the target variable.

values

a vector of the sample points for the variable used in the ICE calculation.

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

Details

This function generates Individual Conditional Expectation (ICE) data by evaluating the MID model over a range of values for a specific variable. For a given observation \(\mathbf{x}_i\), the ICE value at \(X_j = x'\) is computed by replacing the value \(x_{i,j}\) with \(x'\) while keeping all other features \(\mathbf{x}_{i,\setminus j}\) fixed:

$$f_{\text{ICE}}(x') = g(x', \mathbf{x}_{i,\setminus j})$$

The function creates a set of hypothetical observations across a grid of evaluation points for the specified variable. The resulting object can be plotted to visualize how the prediction changes for individuals as a specific feature varies, revealing both global trends and local departures (heterogeneity).

See also

interpret, plot.midcon, ggmid.midcon

Examples

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

# Calculate the ICE values for a fitted MID model
con <- mid.conditional(mid, variable = "Wind", data = airquality)
print(con)
#> 
#> Individual Conditional Expectation for 153 Observations
#> 
#> Variable: Wind
#> 
#> Sample Points:  2.3000, 2.4859, 2.6717, ... 
#> 
#> Conditional Expectations:
#>    .id Wind   yhat
#> 1    1  2.3 93.187
#> 2    2  2.3 80.733
#> 3    3  2.3 75.251
#> 4    4  2.3 80.683
#> 5    5  2.3 77.034
#> 6    6  2.3 80.108
#> 7    7  2.3 84.101
#> 8    8  2.3 76.878
#> 9    9  2.3 72.084
#> 10  10  2.3 86.434
#> 11  11  2.3 83.927
#> 12  12  2.3 90.309
#> 13  13  2.3 83.397
#> 14  14  2.3 87.020
#> 15  15  2.3 70.543
#> 16  16  2.3 88.585
#> 17  17  2.3 92.022
#> 18  18  2.3 72.778
#> 19  19  2.3 89.513
#> 20  20  2.3 70.525