Python : How to interpret the result of logistic regression by sm.Logit

Question

When I run a logistic regression by sm.Logit (in the statsmodel library), part of the result is like this:

Pseudo R-squ.: 0.4335

Log-Likelihood: -291.08

LL-Null: -513.87

LLR p-value: 2.978e-96

How could I explain the significance of the model? Or say, the ability of explaining? Which indicator should I use? I have searched online and there isn't much information about Pseudo R2 and LLR pvalue. I'm confused that how I can say that my model is good.

Answer 1

From Hands-On Machine Learning for Algorithmic Trading:

• Log-Likelihood: this is the maximized value of the log-likelihood function.
• LL-Null: this is the result of the maximized log-likelihood function when only an intercept is included. It forms the basis for the pseudo- statistic and the Log-Likelihood Ratio (LRR) test (see below)
• pseudo-: this is a substitute of the familiar available under least squares. It is computed based on the ratio of the maximized log-likelihood function for the null model m0 and the full model m1 as follows:

_{(source: googleapis.com)}

The values vary from 0 (when the model does not improve the likelihood) to 1 (where the model fits perfectly and the log-likelihood is maximized at 0). Consquently, higher values indicate a better fit.

• LLR: The LLR test generally compares a more restricted model and is computed as:

The null hypothesis is that the restricted model performs better but a low p-value suggests that we can reject this hypothesis and prefer the full model over the null model. This is similar to the F-test for linear regression (where can also use the LLR test when we estimate the model using MLE).

• z-statistic: plays the same role as the t-statistic in the linear regression output and is equally computed as the ratio of the coefficient estimate and its standard error.

• p-values: these indicate the probability of observing the test statistic assuming the null hypothesis that the population coefficient is zero.

As you can see (and the way I understand it), many of these metrics are counterparts to those of the linear regression case. Furthermore, as Rose already point out, I would recommend checking the statsmodel documentation.