| Correlated parameters are often expected when modeling a natural system. However, correlation among the variables often blurs the model uncertainty and makes it difficult to determine parameter sensitivity. In simple systems, model structure and uncertainty can be explained directly; however, uncertainty and parameter relationships in model structures of complex systems, such as process models and spatial models, are not usually straightforward. A common data examination method used to identify the variable relationships is a variable correlation matrix or covariance matrix. A variable covariance matrix is a composite of variable causality, correlation, and other interactions. In other words, the variable covariance matrix contains information about the relationship of variables in a system. Therefore, the variable covariance matrix in a model is expected to match the natural system being modeled. However, the true covariance matrix of the natural system is not always known. A covariance structure analysis, based on structural equation modeling, is a potential way to search for explanation of the covariance related to the modeled system. The main subject in this study is to investigate the use of covariance structure analysis of covariance matrices among variables (both independent and dependent) in a system to explain the parameter causal relationships and sensitivities. Three case studies, including two simple nonlinear regression models, a forest process model, and a spatial dynamic host-parasitoid interaction model, will be used to illustrate this application. |
