how to calculate aic in matlab

To calculate Akaike Information Criteria (AIC) in Matlab, we can use the built-in function aicbic.

The formula for AIC is AIC = 2k - 2ln(L), where k is the number of parameters in the model and L is the likelihood function of the model. The aicbic function takes in the number of observations, the negative log-likelihood, and the number of parameters in the model as input arguments, and returns the AIC value.

Here's an example code snippet:

main.m
% generate some data
x = randn(100,1);
y = 2*x + randn(100,1);

% fit a linear regression model
mdl = fitlm(x,y);

% calculate the negative log-likelihood
negLogLikelihood = -loglik(mdl);

% get the number of parameters in the model
numParams = length(mdl.Coefficients.Estimate);

% get the number of observations
numObs = length(y);

% calculate AIC using aicbic function
aic = aicbic(negLogLikelihood,numParams,numObs);

% display AIC value
disp(['AIC: ' num2str(aic)]);
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In this example, we first generate some data, and then fit a linear regression model using fitlm. We then calculate the negative log-likelihood using the loglik function from the Statistics and Machine Learning Toolbox. Next, we get the number of parameters and observations from the model and data, respectively. Finally, we use the aicbic function to calculate the AIC value, and display the result using disp.

Note that the aicbic function also returns the Bayesian Information Criteria (BIC) value, which can be useful for model selection.