This function takes a fitted linear.logic model and independent test
data as input for testing if the included terms are influential with respect
to the outcome.
This hypothesis test is based on a likelihood-ratio test.
importance.test.boosting(model, X, y, Z, Z.interactions = TRUE)A data frame consisting of three columns,
varThe tested term,
vimThe associated variable importance, and
p.valueThe corresponding p-value for testing if the term is influential.
A fitted linear.logic model (i.e., a model created via
fitLinearLogicModel or fitLinearBoostingModel)
Matrix or data frame of binary input data. This object should correspond to the binary matrix for fitting the model.
Response vector. 0-1 coding for binary outcomes.
Optional quantitative covariables supplied as a matrix or data frame. Only used (and required) if the model was fitted using them.
A Boolean value determining whether interactions with
quantitative covaraible Z shall be taken into account
In detail, the null hypotheses
$$H_0: \beta_j = \delta_j = 0$$
using the linear model
$$g(E[Y]) = \beta_0 + \sum_{i=1}^B \beta_i \cdot 1[C_i] + \delta_0 \cdot E
+ \sum_{i=1}^B \delta_i \cdot 1[C_i] \cdot E$$
are tested for each \(j \in \lbrace 1,\ldots,B \rbrace\)
if Z.interactions is set to TRUE.
Otherwise, the null hypotheses
$$H_0: \beta_j = 0$$
using the linear model
$$g(E[Y]) = \beta_0 + \sum_{i=1}^B \beta_i \cdot 1[C_i] + \delta_0 \cdot E$$
are tested.