A protocol for modelling generalised biological responses using latent variables in structural equation models

Abstract

In this paper, we consider the problem of how to quantitatively characterise the degree to which a study object exhibits a generalised response. By generalised response, we mean a multivariate response where numerous individual properties change in concerted fashion due to some internal integration. In latent variable structural equation modelling (LVSEM), we would typically approach this situation using a latent variable to represent a general property of interest (e.g. performance) and multiple observed indicator variables that reflect the specific features associated with that general property. While ecologists have used LVSEM in a number of cases, there is substantial potential for its wider application. One obstacle is that LV models can be complex and easily over-specified, degrading their value as a means of generalisation. It can also be challenging to diagnose causes of misspecification and understand which model modifications are sensible. In this paper, we present a protocol, consisting of a series of questions, designed to guide the researchers through the evaluation process. These questions address: (1) theoretical development, (2) data requirements, (3) whether responses to perturbation are general, (4) unique reactions by individual measures and (5) how far generality can be extended. For this illustration, we reference a recent study considering the potential consequences of maintaining biodiversity as part of agricultural management on the overall quality of grapes used for wine-making. We extend our presentation to include the complexities that occur when there are multiple species with unique reactions.