This paper presents a model for constructing complex visualization instances by describing them as a set of smaller interconnected modules. The module-relationship structure of the model allows users to explore a given visualization instance a piece at a time, and then to relate modules to ne another to explore the data more deeply. This is known as compositional visualization. Each model is a visualization in itself and represent some aspect or view of the data. When a number of such smaller visualization views are considered conjunctively the result is a broader view of the data that includes the aspects provided by each module. Compositional visualization is one technique for dealing with data that is too large or complex to visualize using a single visualization. The model first decomposes data into a collection of simpler data modules. The data modules are then mapped to simple visualization models. The visualization modules are combined to form larger visualization instances. However, the decomposition of data is not necessarily equivalent to the composition of visualization, thus a visualization may give a false impression of data if poorly constructed. The reasons for this and ways to overcome it are presented.