Why are there no R ^ 2 in GLM statistical models?

Question

I did a simple experiment with GLM in statsmodels and was puzzled by the search, why the GLM results do not contain any R ^ 2 attributes?

I feel that there is something very simple about why GLM does not have R ^ 2 computation and the ways that I can calculate it myself.

Thanks!

In [1]: import pandas as np In [2]: import pandas as pd In [3]: import numpy as np In [4]: import statsmodels.api as sm In [5]: data = pd.DataFrame({'col1':np.arange(10),'col2':np.arange( KeyboardInterrupt In [5]: x = np.arange(0,10,0.5) In [6]: In [6]: y = np.zeros(len(x)) In [7]: y[0] = 0 In [8]: for i in range(1,len(x)): ...: y[i] = 0.5*x[i] + 2.5*y[i-1] + 10*np.random.rand() ...: In [9]: print y [ 0.00000000e+00 9.35177024e-01 8.18487881e+00 2.95126464e+01 8.08584645e+01 2.11423251e+02 5.38685230e+02 1.35653420e+03 3.39564225e+03 8.49234338e+03 2.12377817e+04 5.31015961e+04 1.32764789e+05 3.31924691e+05 8.29818265e+05 2.07455796e+06 5.18640343e+06 1.29660216e+07 3.24150658e+07 8.10376747e+07] In [10]: X = pd.DataFrame({'x1':x[1:],'y-Lag1':y[:-1]}) In [11]: m1 = sm.GLM(y[1:],X).fit() In [12]: m1.summary() Out[12]: <class 'statsmodels.iolib.summary.Summary'> """ Generalized Linear Model Regression Results ============================================================================== Dep. Variable: y No. Observations: 19 Model: GLM Df Residuals: 17 Model Family: Gaussian Df Model: 1 Link Function: identity Scale: 12.9022715725 Method: IRLS Log-Likelihood: -50.199 Date: Thu, 23 Oct 2014 Deviance: 219.34 Time: 13:44:22 Pearson chi2: 219. No. Iterations: 3 ============================================================================== coef std err t P>|t| [95.0% Conf. Int.] ------------------------------------------------------------------------------ x1 1.5746 0.175 8.999 0.000 1.232 1.918 y-Lag1 2.5000 1.23e-07 2.03e+07 0.000 2.500 2.500 ============================================================================== """ In [13]: m1. m1.aic m1.llf m1.remove_data m1.bic m1.load m1.resid_anscombe m1.bse m1.model m1.resid_deviance m1.conf_int m1.mu m1.resid_pearson m1.cov_params m1.nobs m1.resid_response m1.deviance m1.norm_resid m1.resid_working m1.df_model m1.normalized_cov_params m1.save m1.df_resid m1.null m1.scale m1.f_test m1.null_deviance m1.summary m1.family m1.params m1.summary2 m1.fit_history m1.pearson_chi2 m1.t_test m1.fittedvalues m1.pinv_wexog m1.tvalues m1.initialize m1.predict m1.k_constant m1.pvalues 

Answer 1

For GLMs with Gaussian errors and an identical relationship, R ^ 2 makes sense (if the model has a constant), but it does not make sense as the general quality factor of the correspondence measure for GLM. You can submit an improvement request (or, even better, a transfer request) to include in the GLM results the better, more general benefit of compliance statistics.

You can read more about this in the context of R here .

Answer 2

Not sure why this is implemented this way, but the SO answer above and some wikipedias made it easy for me to calculate R ^ 2 manually:

 sst_val = sum(map(lambda x: np.power(x,2),y-np.mean(y))) sse_val = sum(map(lambda x: np.power(x,2),m1.resid_response)) r2 = 1.0 - sse_val/sst_val