Sample of a Conceptual Framework

 

Conceptual Framework

This paper shall utilize the mathematical modelling by Arbia, G., Griffith, D. and Haining, R. (1999). The purpose of adopting this approach using maps and error processes with simple but well-defined properties is to understand better how different elements of the situation, individually and together, contribute to the final propagated error. The problem with using real maps (rather than artificially generated maps) is that real maps usually have complex structures so that it may not be clear the extent to which aggregate statistics computed to measure the severity of the error problem are an aggregation across many types of quite different map segments with different structures. Usually, real errors are not known for any data set, and unless their structure is uniform across the map, the same problem for interpreting aggregate statistics could arise.

Using formal mathematical modeling, rather than just simulation, means that where theoretical results can be obtained they can be used to check simulation output before the simulation is used to obtain properties that are not accessible to mathematical analysis. Furthermore it is only through formal mathematical modeling, leading to closed-form expressions, that a rigorous study can be undertaken that yields quantitative and qualitative insights as to how different elements contribute individually or interactively to error propagation. The formal expressions make the contributions explicit, and regression (adding maps) and ANOVA (ratioing) are used to quantify the relative contributions of each term in the expression. Where theoretical results have not been obtained, as in the case of ratioing, simulation alone, even with regression analysis of the outputs cannot produce the same quality of evidence because of the dangers of model misspecification in using regression. (Arbia, G., Griffith, D. and Haining, R., 1999)