ENBIS-18 in Nancy

2 – 25 September 2018; Ecoles des Mines, Nancy (France) Abstract submission: 20 December 2017 – 4 June 2018

Analysis of Designed Experiments with Functional Responses

4 September 2018, 14:10 – 14:30

Abstract

Submitted by
Chris Gotwalt
Authors
Chris Gotwalt (JMP Division of SAS Institute), Phil Kay (JMP Division of SAS Institute)
Abstract
Designed experiments with a functional responses are now quite common in science and industry. Examples are easy to come by: repeated measurements in time, experiments that study behavior over a range of temperature settings, machines that output shear/viscosity curves or spectral curves, dissolution profiles. A variety of techniques have been developed to model such data, such as partial least squares, linear mixed models with time series errors, and many ad-hoc approaches where one extracts features from the response curves like the overall mean or time where a peak occurs. All of these methods encounter substantial difficulty when one wants a simple prediction equation for the response curve as a function of the longitudinal variable (time, shear, temperature, etc.) and the other experimental factors. We will introduce and demonstrate a two-step approach that simplifies the process substantially. First the functional responses are fit with splines and a functional principal components analysis extracts the principal eigenfunctions and scalar scores for each function. This is a dimension reduction step that solves out the longitudinal variables. Then the leading functional principal component scores, which a just scalars, are modeled using the factors as inputs least squares and a variable selection procedure such as forward selection. Combining the results leads to a single expression that shows how the functional response changes as a function of the longitudinal variable and the experimental factors. We will review the statistical methodology and then use case studies to demonstrate the simplicity and effectiveness of the approach as it is implemented in JMP Pro 14.

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