Variable selection in Functional Additive Regression Models

Abstract

This paper considers the problem of variable selection in regression models in the case of functional variables that may be mixed with other type of variables (scalar, multivariate, directional, etc.). Our proposal begins with a simple null model and sequentially selects a new variable to be incorporated into the model based on the use of distance correlation proposed by Székely et al. [2007]. For the sake of simplicity, this paper only uses additive models. However, the proposed algorithm may assess the type of contribution (linear, non linear, ...) of each variable. The algorithm has shown quite promising results when applied to simulations and real data sets.

Multi-Output Conditional Inference Trees Applied to the Electricity Market: Variable Importance Analysis

“…Comparing our results (multivariate response variable importance analysis, Figure 17), to those achieved in the univariate response case, papers [23,31,32], we can see that by using the new proposed algorithm EPD we can extract relevant information about variable importance, while also considering the possible interrelationships among the response variables in the analysis. This allows for a more effective analysis as there is no need to perform separate univariate studies, creating a more efficient analysis.…”

“…Most recently, Febrero et al [32], motivated by the problem of identifying the most relevant predictors for the demand and price of the Spanish electricity market and using a general additive regression model, proposed an algorithm based on the computation of distance correlations. With their variable selection solution, they were able to measure the level of redundancy among predictors of different scales.…”

“…As previously mentioned, in general, there is no direct competitor to our solution. However, Febrero et al [32] proposed a new variable selection framework for the univariate response scenario. In their study, they selected significant predictors for the price and demand of electricity individually for the Iberian market.…”

Predicting Malaria Transmission Dynamics in Dangassa, Mali: A Novel Approach Using Functional Generalized Additive Models

“…In any case, higher values of the distance correlation mean higher dependence, and the same authors that proposed the distance correlation have proposed an independence test for distance correlation [ 21 ]. The selection of the covariates was done using the algorithm described in the novel variable selection approach [ 19 ], which seems to select non-sparse models. To assess the performance of the algorithms related to the previous models in our data set, we have proposed a comparison based on some common characteristics of those models, such as the R-sq.…”

“…In this case, past meteorological information (previous 18 weeks to week of interest) was considered as a function for finding the patterns that have influenced an increase in malaria cases. This novel variable selection approach [ 19 ] makes intensive use of the distance correlation [ 20 ] and is implemented in the R package fda.usc [ 21 ]. We can also notice that this new variable selection approach allows the building of more efficient models based on historical data, which fully accounts for uncertainty associated with the model selection process.…”