Error Covariance Penalized Regression: A novel multivariate model combining penalized regression with multivariate error structure

Franco Allegrini; Jez W B Braga; Alessandro C O Moreira; Alejandro C Olivieri

doi:10.1016/j.aca.2018.02.002

Error Covariance Penalized Regression: A novel multivariate model combining penalized regression with multivariate error structure

Anal Chim Acta. 2018 Jun 29:1011:20-27. doi: 10.1016/j.aca.2018.02.002. Epub 2018 Feb 9.

Authors

Franco Allegrini¹, Jez W B Braga², Alessandro C O Moreira³, Alejandro C Olivieri⁴

Affiliations

¹ Departamento de Química Analítica, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Instituto de Química de Rosario (IQUIR-CONICET), Suipacha 531, Rosario, S2002LRK, Argentina.
² Departamento de Química Analítica, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Instituto de Química de Rosario (IQUIR-CONICET), Suipacha 531, Rosario, S2002LRK, Argentina; Laboratório de Automação, Quimiometria e Química Ambiental, Instituto de Química, Universidade de Brasília, CEP 70904-970, Brasília, DF, Brazil.
³ Laboratório de Automação, Quimiometria e Química Ambiental, Instituto de Química, Universidade de Brasília, CEP 70904-970, Brasília, DF, Brazil; Laboratório de Produtos Florestais, Serviço Florestal Brasileiro, CEP 70818-900, Brasília, DF, Brazil.
⁴ Departamento de Química Analítica, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Instituto de Química de Rosario (IQUIR-CONICET), Suipacha 531, Rosario, S2002LRK, Argentina. Electronic address: olivieri@iquir-conicet.gov.ar.

PMID: 29475481
DOI: 10.1016/j.aca.2018.02.002

Abstract

A new multivariate regression model, named Error Covariance Penalized Regression (ECPR) is presented. Following a penalized regression strategy, the proposed model incorporates information about the measurement error structure of the system, using the error covariance matrix (ECM) as a penalization term. Results are reported from both simulations and experimental data based on replicate mid and near infrared (MIR and NIR) spectral measurements. The results for ECPR are better under non-iid conditions when compared with traditional first-order multivariate methods such as ridge regression (RR), principal component regression (PCR) and partial least-squares regression (PLS).

Keywords: Error covariance matrix; Multivariate calibration; Penalized regression.