Multivariate Modelling with Latent Variables in Experimental Designs with an Application to Forestry Data
Dario Cziraky, Tugomir Filipan, and Anamarija Pisarovič
The classical experimental design approach to testing for treatment effects in forestry research applies ANOVA and dummy-variable regression techniques to the individual tree development indicators such as total tree height or trunk diameter. An alternative to standard techniques is provided by a more general framework of structural equation modelling, which encompasses most of the classical techniques and additionally allows estimation of a richer class of models. This includes latent variable models that enable simultaneous incorporation of multiple tree development indicators into a single model treating tree development as a latent variable imperfectly measured by the observable tree measures. A problem in classical experimental design is that we can either test for the treatment effects on separate tree development indicators (e.g., height or diameter), or make an attempt to combine multiple indicators into a single (latent) variable and then test for treatment effects on the composite tree development variable. In this paper we apply structural equations methods to experimental forestry data comparing several approaches to treatment effect testing.