how to calculate aicc in matlab

To calculate the Akaike Information Criterion with a correction for finite sample sizes (AICC) in Matlab, you can use the following code:

main.m
% load data
load('mydata.mat');

% specify your candidate models and evaluate them using your chosen metric (e.g., likelihood)
model1 = fitlm(X, Y, 'linear');
model2 = fitlm(X, Y, 'quadratic');
likelihood1 = model1.LogLikelihood;
likelihood2 = model2.LogLikelihood;

% calculate the number of model parameters (k) for each model
k1 = size(model1.Coefficients, 1)-1; % subtract 1 for the intercept term
k2 = size(model2.Coefficients, 1)-1; % subtract 1 for the intercept term

% calculate the sample size (n)
n = size(X, 1);

% calculate AICC for each model
AICC1 = -2 * likelihood1 + 2*k1 + 2*k1*(k1+1)/(n-k1-1);
AICC2 = -2 * likelihood2 + 2*k2 + 2*k2*(k2+1)/(n-k2-1);
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In this code, I assumed that you have loaded your data into X and Y matrices or tables (replace mydata.mat with your data file name if needed). You can define your candidate models using the fitlm function, which estimates a linear (or quadratic, in this example) regression model. Then, you can compute the log-likelihood for each model using the LogLikelihood property of the model object. Next, you can compute the number of model parameters (k) based on the number of coefficients in the model object. Finally, you can calculate AICC for each model using the formula:

AICC = -2 * log-likelihood + 2k + 2k(k+1)/(n-k-1)

Note that the formula for AICC includes a correction factor that depends on k and n, which adjusts the penalty for model complexity based on the sample size. Lower AICC values indicate better model fit, with a penalty for model complexity.