This function discretizes a training set using the user provided method(s) among the three topdown methods from the discretization package. Depending on the user providing a test and/or a validation set, the function returns the best discretization for logistic regression.

topdown_iter(
predictors,
labels,
test = F,
validation = F,
proportions = c(0.3, 0.3),
criterion = "gini",
param = list(1, 2, 3)
)

## Arguments

predictors The matrix array containing the numeric attributes to discretize. The actual labels of the provided predictors (0/1). Boolean : True if the algorithm should use predictors to construct a test set on which to search for the best discretization scheme using the provided criterion (default: TRUE). Boolean : True if the algorithm should use predictors to construct a validation set on which to calculate the provided criterion using the best discretization scheme (chosen thanks to the provided criterion on either the test set (if true) or the training set (otherwise)) (default: TRUE). The list of the (2) proportions wanted for test and validation set. Only the first is used when there is only one of either test or validation that is set to TRUE. Produces an error when the sum is greater to one. Useless if both test and validation are set to FALSE. Default: list(0.2,0.2). The criterion ('gini','aic','bic') to use to choose the best discretization scheme among the generated ones (default: 'gini'). Nota Bene: it is best to use 'gini' only when test is set to TRUE and 'aic' or 'bic' when it is not. When using 'aic' or 'bic' with a test set, the likelihood is returned as there is no need to penalize for generalization purposes. List providing the methods to test (from 1, 2 and 3, default: list(1,2,3)).

## Details

This function discretizes a dataset containing continuous features $$X$$ in a supervised way, i.e. knowing observations of a binomial random variable $$Y$$ which we would like to predict based on the discretization of $$X$$. To do so, the Topdown alorithms ... In the context of Credit Scoring, a logistic regression is fitted between the ‘‘discretized'' features $$E$$ and the response feature $$Y$$. As a consequence, the output of this function is the discretized features $$E$$, the logistic regression model of $$E$$ on $$Y$$ and the parameters used to get this fit.

## References

Enea, M. (2015), speedglm: Fitting Linear and Generalized Linear Models to Large Data Sets, https://CRAN.R-project.org/package=speedglm

HyunJi Kim (2012). discretization: Data preprocessing, discretization for classification. R package version 1.0-1. https://CRAN.R-project.org/package=discretization

Gonzalez-Abril, L., Cuberos, F. J., Velasco, F. and Ortega, J. A. (2009) Ameva: An autonomous discretization algorithm, Expert Systems with Applications, 36, 5327–5332.

Kurgan, L. A. and Cios, K. J. (2004). CAIM Discretization Algorithm, IEEE Transactions on knowledge and data engineering, 16, 145–153.

Tsai, C. J., Lee, C. I. and Yang, W. P. (2008). A discretization algorithm based on Class-Attribute Contingency Coefficient, Information Sciences, 178, 714–731.

glm, speedglm, discretization

## Examples

# Simulation of a discretized logit model
x <- matrix(runif(300), nrow = 100, ncol = 3)
cuts <- seq(0, 1, length.out = 4)
xd <- apply(x, 2, function(col) as.numeric(cut(col, cuts)))
theta <- t(matrix(c(0, 0, 0, 2, 2, 2, -2, -2, -2), ncol = 3, nrow = 3))
log_odd <- rowSums(t(sapply(seq_along(xd[, 1]), function(row_id) {
sapply(
seq_along(xd[row_id, ]),
function(element) theta[xd[row_id, element], element]
)
})))
y <- stats::rbinom(100, 1, 1 / (1 + exp(-log_odd)))

topdown_iter(x, y)
#> New names:
#> *  -> ...1
#> *  -> ...2
#> *  -> ...3#> New names:
#> *  -> ...1
#> *  -> ...2
#> *  -> ...3#> New names:
#> *  -> ...1
#> *  -> ...2
#> *  -> ...3#> Generalized Linear Model of class 'speedglm':
#>
#> Call:  speedglm::speedglm(formula = stats::formula("labels ~ ."), data = Filter(function(x) (length(unique(x)) >      1), cbind(data.frame(sapply(disc\$Disc.data, as.factor), stringsAsFactors = TRUE),      data_train[, sapply(data_train, is.factor), drop = FALSE])),      family = stats::binomial(link = "logit"), weights = NULL,      fitted = TRUE)
#>
#> Coefficients:
#> (Intercept)          X12          X22          X32
#>      -14.31        16.09        -2.08        -1.98
#>