A Lasso-Type Penalized Spline for Smoothing Under Generalized Linear Mixed Model (GLMM) Framework

• Activity Number: 656
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Muhammad Mullah*+ and Andrea Benedetti
• Companies: McGill University and McGill University
• Keywords: Smoothing ; Penalised Spline Regression ; Generalized Linear Mixed Models ; LASSO ; Ridge Regression ; Gibbs Sampling

Abstract

Generalized linear mixed models (GLMM), mostly used for analysing correlated data, can also be used for smoothing. To achieve a smooth function, we can use the GLMM to shrink the regression coefficients of knot points from a regression spline towards zero, by including them as random effects. Allowing the random effects to follow a normal distribution with mean zero and a constant variance is equivalent to using a penalized spline by imposing a ridge type penalty that is constraining the sum of squares of the spline coefficients at knot points to be less than a judiciously selected constant. In the present study, we consider the coefficients at knots to follow a Laplace double exponential distribution with mean zero, which gives rise to a LASSO type sum of absolute values penalty in the penalized spline setting. Through a number of simulations, we compare the performance of smoothing in a GLMM using LASSO type penalty to that of using a ridge penalty by calculating the average squared error distance between the fitted and true curves. We then apply these techniques to obtain smooth curves in two real life datasets.