LASSO type penalized spline regression for binary data
Abstract Background Generalized linear mixed models (GLMMs), typically used for analyzing correlated data, can also be used for smoothing by considering the knot coefficients from a regression spline as random effects. The resulting models are called semiparametric mixed models (SPMMs). Allowing the...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
BMC
2021-04-01
|
Series: | BMC Medical Research Methodology |
Subjects: | |
Online Access: | https://doi.org/10.1186/s12874-021-01234-9 |
id |
doaj-449b938f9b4e41cba21c0351ed624088 |
---|---|
record_format |
Article |
spelling |
doaj-449b938f9b4e41cba21c0351ed6240882021-04-25T11:03:06ZengBMCBMC Medical Research Methodology1471-22882021-04-0121111410.1186/s12874-021-01234-9LASSO type penalized spline regression for binary dataMuhammad Abu Shadeque Mullah0James A. Hanley1Andrea Benedetti2Department of Epidemiology, Biostatistics and Occupational Health, McGill UniversityDepartment of Epidemiology, Biostatistics and Occupational Health, McGill UniversityDepartment of Epidemiology, Biostatistics and Occupational Health, McGill UniversityAbstract Background Generalized linear mixed models (GLMMs), typically used for analyzing correlated data, can also be used for smoothing by considering the knot coefficients from a regression spline as random effects. The resulting models are called semiparametric mixed models (SPMMs). Allowing the random knot coefficients to follow a normal distribution with mean zero and a constant variance is equivalent to using a penalized spline with a ridge regression type penalty. We introduce the least absolute shrinkage and selection operator (LASSO) type penalty in the SPMM setting by considering the coefficients at the knots to follow a Laplace double exponential distribution with mean zero. Methods We adopt a Bayesian approach and use the Markov Chain Monte Carlo (MCMC) algorithm for model fitting. Through simulations, we compare the performance of curve fitting in a SPMM using a LASSO type penalty to that of using ridge penalty for binary data. We apply the proposed method to obtain smooth curves from data on the relationship between the amount of pack years of smoking and the risk of developing chronic obstructive pulmonary disease (COPD). Results The LASSO penalty performs as well as ridge penalty for simple shapes of association and outperforms the ridge penalty when the shape of association is complex or linear. Conclusion We demonstrated that LASSO penalty captured complex dose-response association better than the Ridge penalty in a SPMM.https://doi.org/10.1186/s12874-021-01234-9Penalized splinesGeneralized linear mixed modelsRidge regressionLeast absolute shrinkage and selection operator (LASSO)Markov chain Monte Carlo |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Muhammad Abu Shadeque Mullah James A. Hanley Andrea Benedetti |
spellingShingle |
Muhammad Abu Shadeque Mullah James A. Hanley Andrea Benedetti LASSO type penalized spline regression for binary data BMC Medical Research Methodology Penalized splines Generalized linear mixed models Ridge regression Least absolute shrinkage and selection operator (LASSO) Markov chain Monte Carlo |
author_facet |
Muhammad Abu Shadeque Mullah James A. Hanley Andrea Benedetti |
author_sort |
Muhammad Abu Shadeque Mullah |
title |
LASSO type penalized spline regression for binary data |
title_short |
LASSO type penalized spline regression for binary data |
title_full |
LASSO type penalized spline regression for binary data |
title_fullStr |
LASSO type penalized spline regression for binary data |
title_full_unstemmed |
LASSO type penalized spline regression for binary data |
title_sort |
lasso type penalized spline regression for binary data |
publisher |
BMC |
series |
BMC Medical Research Methodology |
issn |
1471-2288 |
publishDate |
2021-04-01 |
description |
Abstract Background Generalized linear mixed models (GLMMs), typically used for analyzing correlated data, can also be used for smoothing by considering the knot coefficients from a regression spline as random effects. The resulting models are called semiparametric mixed models (SPMMs). Allowing the random knot coefficients to follow a normal distribution with mean zero and a constant variance is equivalent to using a penalized spline with a ridge regression type penalty. We introduce the least absolute shrinkage and selection operator (LASSO) type penalty in the SPMM setting by considering the coefficients at the knots to follow a Laplace double exponential distribution with mean zero. Methods We adopt a Bayesian approach and use the Markov Chain Monte Carlo (MCMC) algorithm for model fitting. Through simulations, we compare the performance of curve fitting in a SPMM using a LASSO type penalty to that of using ridge penalty for binary data. We apply the proposed method to obtain smooth curves from data on the relationship between the amount of pack years of smoking and the risk of developing chronic obstructive pulmonary disease (COPD). Results The LASSO penalty performs as well as ridge penalty for simple shapes of association and outperforms the ridge penalty when the shape of association is complex or linear. Conclusion We demonstrated that LASSO penalty captured complex dose-response association better than the Ridge penalty in a SPMM. |
topic |
Penalized splines Generalized linear mixed models Ridge regression Least absolute shrinkage and selection operator (LASSO) Markov chain Monte Carlo |
url |
https://doi.org/10.1186/s12874-021-01234-9 |
work_keys_str_mv |
AT muhammadabushadequemullah lassotypepenalizedsplineregressionforbinarydata AT jamesahanley lassotypepenalizedsplineregressionforbinarydata AT andreabenedetti lassotypepenalizedsplineregressionforbinarydata |
_version_ |
1721510098805719040 |