MATLAB: What’s the meaning of sfit when estimating an ordered probit model

MATLABordered probit statistics regression

I'm estimating an ordered probit model, and I'd like to have some parameter indicating the goodness of fit (unlike other regression models, there are many proposed indicators to evaluate this). So I'd like to know:

1) What's the meaning of stats.sfit? The matlab help states "the estimated dispersion parameter", but I don't know what do they mean with that.

2) If sfit is not indicating goodness of fit, is there some way to obtain it directly from Matlab?

Best Answer

Hi,

I cannot find stats.sfit function. So, I am giving general sfit function related to curve fitting overview.

Fit function : fits curve or surface to data

So, fit function will return surface object or curve object. Here surface object is considered as sfit.

confint funtion: Confidence intervals for fit coefficients of cfit or sfit object.

confint(sfit) returns 95% confidence bounds.for sfit or cfit object.

Refer to this documents for better understanding :

https://in.mathworks.com/help/curvefit/sfit.html

https://in.mathworks.com/help/curvefit/evaluate-a-surface-fit.html

https://in.mathworks.com/help/curvefit/cfit.confint.html

So, sfit is not totally related to goodness of fit. MATLAB has function

goodnessOfFit which you can use.

goodnessOfFit : returns fit values that represent the error norm between test and reference data sets.

Refer to this document and example for better understanding :

https://in.mathworks.com/help/ident/ref/goodnessoffit.html

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MATLAB: What is the difference between the LAR and Bisquare robust option in the Curve Fitting tool

'LAR' specifies the least absolute residual method.

'Bisquare' specifies the bisquare weights method.

For more detailed information on these two methods please see the following links:

Robust Lease Squares

MATLAB Answers post on the differences between the two

MATLAB Answers post on LAR method

Robustfit function from Stat Toolbox which gives more general info and references on rubust fitting

Wordpress article that discusses these methods

MATLAB: How to work with CFIT objects in curve fitting

You can use the function CONFINT to find confidence intervals. Full documentation on this function is available at

https://www.mathworks.com/help/curvefit/cfit.confint.html

Here is an example. Suppose that we have exported a fitted model from CFTOOL to the workspace.

fittedmodel1 =
     General model:
       fittedmodel1(x) = a*sin(x) + b
     Coefficients (with 95% confidence bounds):
       a =       1.018  (0.938, 1.097)
       b =    -0.03808  (-0.09455, 0.01839)

Now use CONFINT to get confidence intervals:

 confint(fittedmodel1)
ans =
    0.9380   -0.0946
    1.0973    0.0184

Here, the first column is the 95% confidence interval on the first parameter and the second column is the 95% confidence interval on the second parameter. A second input to CONFINT can give other levels of confidence.

To get the actual parameter values, use structure indexing. For example, parameter a could be found by typing

fittedmodel1.a

Another function of interest is PREDINT, to find prediction intervals. Full documentation for this function is available at

https://www.mathworks.com/help/curvefit/predint.html

Best Answer

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