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Predictive Modelling Using Logistic Regression

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Summary

Logistic regression is a type of regression used to predict an event which has a binary response. It is used to model the probability of an event occurring based on one or more nominal, ordinal, interval, or ratio-level independent variables. Logistic regression models the log of the odds ratio, which is the log of the probability of the event occurring, and estimates the probability that an event will occur for a randomly selected set of observations. An example of logistic regression is predicting customer churn in the telecom industry. After creating the model, it is important to validate the model by checking indicator statistics, such as K-S statistic, and Population Stability Index (PSI). If PSI is below 0.1, there is an insignificant change in the development and validation populations, and if PSI is above 0.25, there is a significant change in the population and the model should be re-calibrated or re-developed.

Q&As

What is logistic regression used for?
Logistic regression is used to describe data and to explain the relationship between one dependent binary variable and one or more nominal, ordinal, interval, or ratio-level independent variables.

What is the log odds of an event?
The log odds of an event is the ratio of likelihood of the event occurring to the likelihood of it not occurring, given by p/(1-p).

What are the steps to build a logistic regression model?
The steps to build a logistic regression model are to check if the right probability is modeled, check if the convergence is satisfied, test for the global null hypothesis, check the maximum likelihood estimates, remove insignificant variables, examine the odd-ratio estimates, check the concordance, check the Hosmer-Lemeshow test statistics, check the KS statistics, and check the rank ordering of the response variables at the decile level.

What is population stability index used for?
Population stability index is used to give a view if the target population for the model has remained “stable” over a period of time with respect to the model score.

What is the K-S statistic and how is it used to validate a predictive model?
The K-S statistic is a measure of the extent of differentiation between responders and non-responders based on a particular model. It is used to validate a predictive model by evaluating certain key indicator statistics for the validation sample and comparing it with the ones from development sample.

AI Comments

👍 This is an excellent article that explains logistic regression in a very clear and concise manner. It also provides practical examples and a step-by-step guide to model validation.

👎 This article is too technical and may be too difficult for readers who are not familiar with logistic regression and its applications.

AI Discussion

Me: It's about predictive modelling using logistic regression. It explains how logistic regression is used to predict a binary response variable using one or more independent variables. It also discusses the log odds, logistic regression model, and model validation.

Friend: Wow, that's interesting. What are the implications of this article?

Me: Well, the implications are that logistic regression is a powerful tool for predicting binary response variables. It's a useful method for making predictions about events and outcomes, as well as for classifying observations. It also provides insight into how different variables interact with one another to influence a prediction. Finally, it's important to validate your model to ensure its accuracy and effectiveness over time.

Action items

Research other methods of model validation and compare them to the Population Stability Index (PSI).
Practice building a logistic regression model using a dataset of your choice.
Experiment with different combinations of independent variables to determine which ones are most effective in predicting the target variable.

Technical terms

Predictive Modelling: A type of data analysis that uses existing data to make predictions about future outcomes.
Logistic Regression: A type of regression analysis used to predict a binary response variable (e.g. pass/fail) based on one or more independent variables.
Linear Regression: A type of regression analysis used to predict a continuous response variable (e.g. height) based on one or more independent variables.
Odds: The ratio of the likelihood of an event occurring to the likelihood of it not occurring.
Log Odds: The log of the odds ratio, which is the log (p/1-p) where p is the probability of the event occurring and 1-p is the probability of the non-occurrence of the event.
Logistic Regression Model: A model that estimates the probability of an event occurring by modeling the log of the odds ratio.
Logit Function: A link function used in logistic regression that is best suited for a binomial distribution.
Maximum Likelihood Estimates: The parameters chosen to maximize the likelihood of observing the sample values rather than minimizing the sum of squared errors.
Concordance: The percent concordant, percent discordant, and percent tied, which should be greater than 0.5 for a good model.
Hosmer-Lemeshow Test: A test used to measure the goodness of fit of a logistic model.
KS Statistics: A statistic used to measure the accuracy of a logistic model.
Predictive Model Validation: The process of evaluating the predictive power and effectiveness of a predictive model over a required target sample.
K-S Statistic: A statistic used to estimate the extent of differentiation between responders and non-responders based on a particular model.
Population Stability Index (PSI): A method used to quantify the stability of the target population for a model over a period of time.