93 L1.01: Overview
Automated Fitting of Models, Comparative Goodness of Fit, and Outliers
Objectives:
- Be able to adapt a modeling worksheet to compute a goodness-of-fit indicator from the deviation values between the data and the model.
- Be able to use the Solver add-in with to automatically find the model parameters which minimize the indicator, and thus fit the data as well as possible as measured by that indicator.
- Derive the standard deviation around the model from the sum of squared deviations, the number of deviation used in the sum, and the number of parameters in the model.
- Be able to use alternative goodness-of-fit measures such as maximum deviation.
- Select between different kinds of model by comparing best-fit standard deviations.
- Be able to use relative deviation to compute an alternative form of standard deviation
- Be able to identify data points that are outliers to the model implied by most of the data points, and to remove identified outliers from the model-fitting process when appropriate.
- Be able to make and use a modeling spreadsheet to fit any specified function to a dataset.
Overview—getting the computer to do the tedious part so that models can be applied more easily
Splitting the work of modeling. The modeling process has two parts, one requiring thought and the other just requiring patience. The thoughtful part is deciding what model makes sense to use, looking at the graphs to see if a better model is needed of if some data points should be handled specially, and interpreting what the final parameter values imply about the situation in which the data was taken. The second part of fitting is the tedious process of adjusting each parameter in turn until you find the best parameter values for the chosen kind of model.
Tedious tasks are what computers do best. In this topic you will learn to use Solver tool that can makes the computer quickly find the best-fit parameter values for a model. Choosing which kind of model to fit is still your job, but automation will give you more time to do it. Using an automated fitting process will also make it easier to use models that have more parameters, permitting models that are more realistic and can solve a wider range of problems.
What is the “best” fit? So far, we have relied on a person looking at the graph to decide when the parameter settings for a model gave a good fit. People are good at this kind of visual assessment, but computers are not — they are much better at dealing with numbers. So to automate the fitting task we will compute a number that measures how well a particular model fits the data we are working with.
Handling stray data points. It sometimes happens that a small subset of the points in a data set deviate substantially from the overall pattern. These “outlier” points sometimes convey important information, but other times simply reflect bad measurements. In either case, it is usually best to exclude them from the model-fitting process and report the