how to use aic in matlab

May I ask how can I use aicbic in matlab for user defined functions? I tried to fit a set of data using different combinations of functions (sine, polynomial), I wanted to use aic/bic to test which one is a better function to model the data. From https://jp.mathworks.com/help/econ/aicbic.html, I need to provide the log-likelihood of the models. How can we calculate the log-likelihood?

Refer to https://jp.mathworks.com/help/ident/ref/idgrey.aic.html#buy65_c-model, it seems that the models are the ones defined by the matlab, such as

• idtf
• idgrey
• idpoly
• ..

Is there a way to use aic/bic for the models defined by the user (e.g,, y1= ax+bx^2+c, y2=ax+dx^3+sin(x))? Many thanks in advance!

Answer 1

[Moksh]

Hi Jing,

As per my understanding, you are trying to calculate aic/bic scores for custom-designed functions. It is accurate that the ‘aic’ function in MATLAB restricts the input to a specific set of models, so it cannot be used for every case.

You can use the ‘aicbic’ function on any model if you have the following data:

1. Log-likelihood values derived from fitting the model on data
2. Corresponding number of estimated model parameters

You can try using the ‘fitdist’ function in MATLAB, which creates a ‘pdf’ of the specified distribution for input data. Log-likelihood then can be calculated using this pdf distribution.

Here is an example code using Rayleigh distribution:

% Generating random data through Rayleigh distribution
x = raylrnd(2, 20, 1);

% Fitting the data on Rayleigh distribution and getting the log-likelihood
pd = fitdist(x, 'Rayleigh');
logL = pd.NLogL;

% Computing aic and bic scores from the log-likelihood values and number of
% estimated parameters (Assuming 39 model parameters)
[aic_score, bic_score] = aicbic(logL, 39);

Given that you have not provided the specific model, it is recommended to attempt fitting the data to various distributions based on your model and obtain the corresponding Log-likelihood values.

Refer to the following documents for further understanding of the specified functions.

• aicbic - https://in.mathworks.com/help/econ/aicbic.html
• fitdist - https://in.mathworks.com/help/stats/fitdist.html
• rayrnd - https://in.mathworks.com/help/stats/raylrnd.html