LISREL: an Alternative to MANOVA and Principal Components in Designed Experiments when the Response is Multidimensional

Abstract

In designed industrial experiments, the response is often multidimensional. There may be different responses and/or responses of equal kind that are correlated. The usual analysis is by a separate ANOVA (Analysis of Variance) for each response or by MANOVA (Multivariate Analysis of Variance) of all responses simultaneously. However, ANOVA/MANOVA techniques do not fully address the multivariate situation. In this paper, MANOVA, principal components analysis, and LISREL (Linear Structural Relationship), are applied to the results of an experiment concerning high-precision breathing apparatus to be used by firefighters. The experimental design is a 25−1V, having seven response measurements and five replicates. We address both establishing a cause–effect relation, and the estimation of the impact size. The multivariate techniques strongly reduce the number of tests to be performed. MANOVA and LISREL provide standard errors of every parameter of interest. The LISREL model is very flexible in model building and parameter testing, and it gives enhanced insight into the experimental results. Its use in industrial experiments has not been fully exploited; one possible explanation is that such experiments often have too few runs. Copyright © 2005 John Wiley & Sons, Ltd.