Cross Validated Asked on November 2, 2021
I have performed logistic regression (using ‘LOGIT’) on variables from titanic dataset. The formula used is:
survived ~ age + sex + pclass
I have obtained results as follows:
==================== Summary() ====================
Logit Regression Results
==============================================================================
Dep. Variable: survived No. Observations: 714
Model: Logit Df Residuals: 710
Method: MLE Df Model: 3
Date: Mon, 20 Jul 2020 Pseudo R-squ.: 0.3289
Time: 14:29:27 Log-Likelihood: -323.65
converged: True LL-Null: -482.26
Covariance Type: nonrobust LLR p-value: 1.860e-68
===============================================================================
coef std err z P>|z| [0.025 0.975]
-------------------------------------------------------------------------------
Intercept 5.0560 0.502 10.069 0.000 4.072 6.040
sex[T.male] -2.5221 0.207 -12.168 0.000 -2.928 -2.116
age -0.3693 0.076 -4.841 0.000 -0.519 -0.220
pclass -1.2885 0.139 -9.253 0.000 -1.561 -1.016
===============================================================================
==================== Summary2() ====================
Results: Logit
=================================================================
Model: Logit Pseudo R-squared: 0.329
Dependent Variable: survived AIC: 655.2909
Date: 2020-07-20 14:29 BIC: 673.5745
No. Observations: 714 Log-Likelihood: -323.65
Df Model: 3 LL-Null: -482.26
Df Residuals: 710 LLR p-value: 1.8597e-68
Converged: 1.0000 Scale: 1.0000
No. Iterations: 6.0000
------------------------------------------------------------------
Coef. Std.Err. z P>|z| [0.025 0.975]
------------------------------------------------------------------
Intercept 5.0560 0.5021 10.0692 0.0000 4.0719 6.0402
sex[T.male] -2.5221 0.2073 -12.1676 0.0000 -2.9284 -2.1159
age -0.3693 0.0763 -4.8415 0.0000 -0.5188 -0.2198
pclass -1.2885 0.1393 -9.2528 0.0000 -1.5615 -1.0156
=================================================================
Edit: I want to explain results in lay terms. I want to determine how much odds of survival change with changes in each predictor variable. To clarify, I want to know:
What are the odds of a male surviving as compared to a female?
How do odds change for every 1 year increase in age of the person?
I understand it is a very basic question, but it is important to have reliable knowledge about it.
The question title is:
How to get log odds from these results of logistic regression
The estimates are already on the log-odds scale. All you have to do is read the relevant entry.
What are the odds of a male surviving as compared to a female?
The log-odds of a male surviving compared to a female is -2.5221, holding the other variables constant. If we exponentiate this we get
> exp(-2.5221)
[1] 0.0803
and this is the odds ratio of survival for males compared to females - that is the odds of survival for males is 92% lower than the odds of survival for females
How do odds change for every 1 year increase in age of the person?
Every 1 year increase in age
is associated with a 0.3693 decrease in log-odds of survival holding the other variables constant. If we exponentiate this:
> exp(-0.3693)
[1] 0.691
So every 1 unit increase in age
is associated with a decrease in the odds of survival of 31%, holding the other variables constant.
Answered by Robert Long on November 2, 2021
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