Water quality in the River Clyde: a case study of additive and interaction models

Additive models are widely used to provide very flexible and effective descriptions of regression data where assumptions of linear relationships are too restrictive. However, these models usually assume independent errors and there are many applications where the data are correlated. This is often true in environmental settings and an application to water quality modelling in the River Clyde is described. Methods of fitting and analysing an additive model in this setting are discussed. An approach which fits an additive model in the usual way but incorporates the correlated error structure into the assessment of components is described. The methods are applied to the Clyde data to identify the factors which affect water quality, as well as spatial and temporal trends. Interaction terms, which allow the effects of explanatory variables to change smoothly with position down the river, are also explored. Particular emphasis is placed on approximate F tests to identify the most suitable models and the presence and nature of particular covariate effects.