Hi all,
I would like to calculate the partial correlation coefficients (PCC) and Matlab provides the function of `partialcorr`. However, there is no way to set a confidence interval in Matlab, and I even do not know what that is in Matlab.
Therefore, how can I finish a PCC calculation with a custom confidence interval? If there exists some better way via other access or software. I can also abandon Matlab temporarily. Thank you so much!
Check this one (or some other similar links on the web)
https://www.researchgate.net/post/How_to_calculate_confidence_interval_for_partial_correlation
1. Function for Partial Correlation:
Matlab
function [partial_corr, conf_interval] = partialcorr(data, x, y, z) % This function calculates the partial correlation coefficient and its confidence interval. % Calculate linear regression coefficients beta_xy = regress(data(:, y), [ones(size(data,1),1) data(:, x)]); beta_yz = regress(data(:, z), [ones(size(data,1),1) data(:, y)]); % Calculate residuals res_x = data(:, x) - beta_xy(2)*data(:, y) - beta_xy(1); res_y = data(:, y) - beta_yz(2)*data(:, z) - beta_yz(1); % Calculate partial correlation coefficient partial_corr = corr(res_x, res_y); % Calculate standard error n = size(data, 1); se = sqrt((1 - partial_corr^2) / (n - 3)); % Calculate custom confidence interval (e.g., 95%) alpha = 0.05; t_stat = partial_corr / se; df = n - 3; conf_interval = tinv(1 - alpha/2, df) * se + partial_corr; end
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2. Usage Example:
Matlab
% Sample data data = [1 2 3; 4 5 6; 7 8 9; 10 11 12]; % Calculate partial correlation between x and y, controlling for z [partial_corr, conf_interval] = partialcorr(data, 1, 2, 3); % Display results fprintf('Partial correlation: %.4f\n', partial_corr); fprintf('Confidence interval: [%.4f, %.4f]\n', conf_interval(1), conf_interval(2));
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Explanation:
- This function first calculates the linear regression coefficients for both x and y variables, considering the third variable z.
- Then, it calculates the residuals for both x and y by removing the effects of the other variables using the regression coefficients.
- The partial correlation coefficient is then calculated using the correlation between the residuals of x and y.
- The custom confidence interval is calculated using the standard error and the desired confidence level (e.g., 95% using tinv).
Note:
- This code assumes normally distributed data and homoscedasticity. For non-normal data, consider non-parametric alternatives.
- This is a basic example, and you might need to modify it based on your specific data and analysis needs.