Assumption 5 - Independence of observations

[OskarBienko]

Hi @kennethleungty ,

In my opinion plotting residuals vs index (or time) is usually misleading. I prefer to check the independence assumption via Ljung-Box test of autocorrelation. I've writtten a function which do this for me.

from statsmodels.stats.diagnostic import acorr_ljungbox
import statsmodels as statsmodels


def check_independence(model:statsmodels.genmod.generalized_linear_model.GLMResultsWrapper, order:int):
    
    '''
    1. Perform the Ljung-Box test to check if residuals are autocorrelated
    2. Print both the null hypothesis and the p-values
    '''
    
    # If the lags parameter is an integer then this is taken to be the largest lag that is included, the test result is reported for all smaller lag length
    ljungbox_pvalues = acorr_ljungbox(x=model.resid_deviance.values, lags=order)['lb_pvalue'].round(2)
    boolean_mask = ljungbox_pvalues > 0.05
    
    if not ljungbox_pvalues.empty:
        print(f'The null hypothesis of Ljung-Box test is that there is autocorrelation in residuals of any order up to {order}.')
        print('p-value = P(reject H0|H0 true)')
        print(f'p-values of Ljung-Box test are: {[pvalue for pvalue in ljungbox_pvalues.values]}')
        print(f'p-values > 0.05, thus the residuals are uncorrelated at lags {[lag for lag in ljungbox_pvalues[boolean_mask].index]}')
        print(f'p-values < 0.05, thus the residuals are autocorrelated at lags {[lag for lag in ljungbox_pvalues[~boolean_mask].index]}')

In your example there is some autocorrelation - check out the output below.

check_independence(model=logit_results, order=10)

The null hypothesis of Ljung-Box test is that there is autocorrelation in residuals of any order up to 10.
p-value = P(reject H0|H0 true)
p-values of Ljung-Box test are: [0.36, 0.6, 0.62, 0.71, 0.02, 0.01, 0.02, 0.04, 0.04, 0.07]
p-values > 0.05, thus the residuals are uncorrelated at lags [1, 2, 3, 4, 10]
p-values < 0.05, thus the residuals are autocorrelated at lags [5, 6, 7, 8, 9]