Recent developments of multivariate smoothing methods provide a rich collection of feasible models for nonparametric multivariate data analysis. Among the most interpretable are those with smoothed additive terms. Construction of various methods and algorithms for computing the models have been the main concern in literature in this area. Less results are available on the validation of computed fit, instead, and many applications of nonparametric methods end up in computing and comparing the generalized validation error or related indexes. This article reviews the behavior of some of the best known multivariate nonparametric methods, based on subset selection and on projection, when (exact) collinearity or multicollinearity (near collinearity) is present in the input matrix. It shows the possible aliasing effects in computed fits of some selection methods and explores the properties of the projection spaces reached by projection methods in order to help data analysts to select the best model in case of ill conditioned input matrices. Two simulation studies and a real data set application are presented to illustrate further the effects of collinearity or multicollinearity in the fit.

On multicollinearity and concurvity in some nonlinear multivariate models / Morlini, Isabella. - In: STATISTICAL METHODS & APPLICATIONS. - ISSN 1618-2510. - STAMPA. - 15:1(2006), pp. 3-26. [10.1007/s10260-006-0005-9]

On multicollinearity and concurvity in some nonlinear multivariate models

MORLINI, Isabella
2006

Abstract

Recent developments of multivariate smoothing methods provide a rich collection of feasible models for nonparametric multivariate data analysis. Among the most interpretable are those with smoothed additive terms. Construction of various methods and algorithms for computing the models have been the main concern in literature in this area. Less results are available on the validation of computed fit, instead, and many applications of nonparametric methods end up in computing and comparing the generalized validation error or related indexes. This article reviews the behavior of some of the best known multivariate nonparametric methods, based on subset selection and on projection, when (exact) collinearity or multicollinearity (near collinearity) is present in the input matrix. It shows the possible aliasing effects in computed fits of some selection methods and explores the properties of the projection spaces reached by projection methods in order to help data analysts to select the best model in case of ill conditioned input matrices. Two simulation studies and a real data set application are presented to illustrate further the effects of collinearity or multicollinearity in the fit.
2006
15
1
3
26
On multicollinearity and concurvity in some nonlinear multivariate models / Morlini, Isabella. - In: STATISTICAL METHODS & APPLICATIONS. - ISSN 1618-2510. - STAMPA. - 15:1(2006), pp. 3-26. [10.1007/s10260-006-0005-9]
Morlini, Isabella
File in questo prodotto:
File Dimensione Formato  
2006 Sma.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 218.85 kB
Formato Adobe PDF
218.85 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/455562
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 40
  • ???jsp.display-item.citation.isi??? ND
social impact