MATLAB: How to get R-square (goodness of fit) when using MNRFIT for logistic regression in Statistics Toolbox 7.1 (R2009a)

Statistics and Machine Learning Toolbox

I am using MNRFIT for logistic regression. I want to know how to get R-square values from MNRFIT.

Best Answer

There is no equivalent of R-square for logistic regression. Note that the output parameter "dev" from MNRFIT is the deviance of the fit, and it can be used to compare models. Deviance is the difference between the log-likelihood of the fitted model and the maximum possible log-likelihood.

Some statisticians have proposed some pseudo R-square values but those are still debatable. If you are interested in just goodness of fit, you should consider 'Pearson residuals' and 'Deviance residuals' in the output structure 'stats' of the function MNRFIT.

Related Solutions

MATLAB: Are there functions in the Statistics Toolbox for survival analysis or multinomial linear models

There are several functions in the Statistics Toolbox for use with survival analysis. To get started, take a look at the demos "Analyzing survival or reliability data" for an overview, and "Fitting custom univariate distributions, part 2" for some more advanced information. You can find both demos under "Fitting Distributions to Data" in the Statistics Toolbox demos.

Functions useful with survival analysis include the following functions that allow data to be censored:

DFITTOOL - Distribution fitting tool

ECDF - Empirical cumulative distribution function, computes the Kaplan-Meier estimate of the cumulative distribution function

ECDFHIST - Histogram from ecdf output

EVFIT, EXPFIT, GAMFIT, LOGNFIT, MLE, MLECOV, NORMFIT, WBLFIT

- Distribution parameter estimation

KSDENSITY - Kernel-smoothing density estimate

PROBPLOT - Probability plot

There is a GLMFIT function for fitting generalized linear models, including ones with a binomial response variable.

As of MATLAB (7.3) R2006b, the function MNRFIT performs multinomial logistic regression.

There are various models used for multinomial response variables when the response categories are ordered. Some of these can be fit as a series of binomial fits. For example, one model calls for a series of binomial fits for ordered category j+1 or higher, given that you are in category j or higher. These types of models can be fit using the GLMFIT function.

MATLAB: Log-likelihoods from mnrfit; testing proportional-odds model

You are correct about the "dev" output. Here's an illustration using the "help mnrfit" example. I can calculate the binomial log likelihood using the fitted probabilities from the model, and again using the sample proportions, and see that -2 times their difference matches the deviance:

>> xx = linspace(-4,4)';
>> Y = [1 11 13; 2 9 14; 6 14 5; 5 10 10; 5 14 6; 7 13 5; 8 11 6];
>> [betaHatNom,dev] = mnrfit(x,Y,'model','nominal','interactions','on'); dev
dev =
    8.4767
>> -2*(sum(sum(Y.*log(pHatNom))) - sum(sum(Y.*log(Y/25))))
ans =
    8.4767

Best Answer

Related Solutions

MATLAB: Are there functions in the Statistics Toolbox for survival analysis or multinomial linear models

MATLAB: Log-likelihoods from mnrfit; testing proportional-odds model

Related Question