Contents |
Compare Models
Compare two fit models to the same dataset
It is not accessible from script. This feature is for OriginPro only.
Fit Result1 & Fit Result2
Specifies fit report sheets fitting with same datasets and different model. Click browse button to bring up Report Tree Browser and select related report sheets.
Comparison Method
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F-test |
Select to decide whether to output result of F-test for comparison. Please note that F-test only makes sense for nested models |
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Akaike's Information Criteria (AIC) |
Select to decide whether to output result of Akaike's Information Creiteria (AIC) for comparison. The method has less limitation for model comparison |
Additional Outputs
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Fit Parameters |
Select to decide whether to output Fit Parameter table for each dataset |
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Fit Statistics |
Select to decide whether to output Fit Statistics table for each dataset |
Results
The output report worksheet.
This tool helps to find out which model is the best fit for the same dataset.
Usually we have learned to compare values of Reduced Chi-Square to select the best fit model. It is a useful measure of goodness-of-fit. The more it is close to 1.0, the better model describes our data. But, since variance of each point which enters in the calculation of Chi-Square is not sufficiently known, Chi-Square criteria is not significant in a statistical sense.
So, we adopt the following 2 methods in model comparison.
F-test
F-test takes advantage of difference of the sum square of residuals of each fit to find out which model is the best. F-test is to compare the sum of square of residuals into a component removed by the simpler model and into a component additionally removed by the more complex model. So, it only makes sense when two models are nested. We recommend users to use this method in following situation
1. Equation of 2 models should be in similar structure , such as:
vs. 
2. Model with some parameter fixed vs. Model with no parameter fixed
Akaike's Information Criteria (AIC)
Akaike's Information Criteria is to find which model would best approximate reality given the data we have recorded. It can simultaneously compare nested or non-nested models. Not relying on concept of significance, AIC is founded on maximum likelihood to rank models. So robust and precise estimates can be obtained by incorporating model uncertainty based on AIC.
To use this tool, please pay attention to following
Suppose we have a dataset and want to see which model is the best fit model for it.
Candidate models are:
ExpDec1: 
ExpDec2: 
Operation
1.Import Exponential Growth.dat on \Samples\Curve Fitting folder
2.Highlight Col(B), select Analysis: Fitting: Nonlinear Curve Fit to open dialog. Set Function as ExpDec1. Click OK to get result sheet
3.Open Nonlinear Curve fit dialog again, Set Function as ExpDec2 this time. Click OK to get result sheet
4.Select Analysis: Fitting: Compare Models to open dialog
5.Click browse button to open Report Tree Browser and select 1 item for Fit Result1
6.Repeat same operation to select another item for Fit Result2
7. Select all options in GUI and click OK
8.From F-test table and AIC result table, we can draw conclusion that ExpDec1 function is the best fit model
1. F-test
F Statistic:
Prob:
2. Akaike's Information Criteria (AIC)
AIC:
Weight:
is the deference between two AIC values
1. Akaike, Hirotsugu (1974). "A new look at the statistical model identification". IEEE Transactions on Automatic Control19 (6): 716-723
2. Burnham, K. R. and D. R. Anderson. 2002. Model Selection and Multimodel Inference. Springer, New York.