Modelling
The target variable is the first variable. We use the out-of-sample AUC evaluation metric to find the best predicting model.
search_res <- search.bin(data = get.data(data, endogenous = 1, weights = data.berka$w),
combinations = get.combinations(sizes = c(1,2,3),
numTargets = 1),
metric <- get.search.metrics(typesIn = c(),
typesOut = c("auc"),
simFixSize = 20,
trainRatio = 0.8,
seed = 123),
items = get.search.items(bestK = 0,
inclusion = TRUE,
type1 = TRUE,
mixture4 = TRUE))
print(search_res)
#> LDT search result:
#> Method in the search process: Binary
#> Expected number of models: 29, searched: 29 , failed: 7 (24.1%)
#> Elapsed time: 0.01681293 minutes
#> Length of results: 2
#> --------
#> Failures:
#> 1. ldt::statistics->matrix singularity: 7 (24.1%)
#> --------
#> Target (label):
#> Evaluation (aucOut):
#> Inclusion weights average:
#> maximum value: 0.6738315
#> name: ln(payments)
#> count: 6
#> Mixture significant [mean-1.95*std, mean, mean+1.95*std]:
#> ln(amount): (3x1) 0.1843058, 0.6110107, 1.037716
#> ln(payments): (3x1) 0.7696544, 1.032932, 1.296209
#> --------The output of the search.bin() function does not contain
any estimation results, but only the information required to replicate
them. The summary() function returns a similar structure
but with the estimation results included.
While choosing an out-of-sample metric indicates our interest in the
predictive power of the best model, for presentation purposes, the
mixture4 = TRUE part is also included in the
searchItems argument. Therefore, we use the results to
study the coefficients uncertainty. In this regard, we select the first
four regressors with the highest inclusion weights (note the
inclusion = TRUE) and plot their combined weighted
distributions. Note that the parameters of the generalized lambda
distribution are estimated from the first four moments of the combined
distribution using the s.gld.from.moments()}` function in
this package, with the distribution restricted to be unimodal with a
continuous tail.
First, we prepare data for plot:
inclusion_mat <- search_res$results[sapply(search_res$results, function(a)a$typeName == "inclusion")][[1]]$value
inclusion_mat <- inclusion_mat[!(rownames(inclusion_mat) %in% c("label", "(Intercept)")), ]
sorted_inclusion_mat <- inclusion_mat[order(inclusion_mat[,1], decreasing = TRUE),]
selected_vars <- rownames(sorted_inclusion_mat)[1:4]
mixture_mat <- search_sum$results[sapply(search_sum$results, function(a)a$typeName == "mixture")][[1]]$value
moments <- lapply(selected_vars, function(v)mixture_mat[rownames(mixture_mat)==v,])
gld_parms <- lapply(moments, function(c) s.gld.from.moments(c[[1]], c[[2]],
c[[3]], c[[4]],
start = c(0.25, 0.25),
type = 4,
nelderMeadOptions = get.options.neldermead(100000,1e-6)))Then we plot the estimated distributions:
# plots
probs <- seq(0.01,0.99,0.01)
i <- 0
for (gld in gld_parms){
i <- i + 1
x <- s.gld.quantile(probs, gld[1],gld[2],gld[3],gld[4])
y <- s.gld.density.quantile(probs, gld[1],gld[2],gld[3],gld[4])
plot(x, y, type = "l", xaxt = "n", xlab = NA, ylab = NA, col = "blue", lwd = 2,
main = selected_vars[i])
lower <- x[abs(probs - 0.05)<1e-10]
upper <- x[abs(probs - 0.95)<1e-10]
axis(1, at = c(lower, 0, upper), labels = c(round(lower, 2), 0, round(upper, 2)))
xleft <- x[x <= lower]
xright <- x[x >= upper]
yleft <- y[x <= lower]
yright <- y[x >= upper]
polygon(c(min(x), xleft, lower), c(0, yleft, 0), col = "gray", density = 30, angle = 45)
polygon(c(max(x), upper, xright), c(0, 0, yright), col = "gray", density = 30, angle = -45)
text(mean(x), mean(y), "90%", col = "gray")
}
Determinants of Loan Default: Variables with the highest inclusion weights, automatically selected. Each plot presents a combined distribution of all estimated coefficients, estimated by generalized lambda distribution.