Logistic Regression and Model Fit Statistics Quiz

Study Notes

Logistic Regression and Model Fit Statistics

The lecture covers logistic regression and its application in modeling limited dependent variables.
The formula for calculating probabilities, odds, and ln(odds) is presented using an example of a binary dependent variable.
The statistical model for the example of whether households take or decline an offer of roof solar panels is presented, with family size and monthly mortgage as independent variables.
Linear regression and model fit statistics, such as R-squared and F-value, are discussed and compared to logistic regression.
Interpretation of logistic regression coefficients focuses on the change of one independent variable while keeping all others constant.
An example is presented to illustrate interpretation of the coefficients, with a 1 unit increase in family size resulting in an 11 times increase in the odds of taking up the offer of roof solar panels.
Model comparison is discussed, with specification 2 showing a better fit than specification 1 based on the model chi-square and Hosmer and Lemeshow test.
Pseudo R-squared is presented as an alternative to R-squared for logistic regression models.
The H-L Statistic is introduced as another measure of model fit, comparing observed and predicted values for different groups based on their estimated probability.
The lecture emphasizes the importance of assessing model fit statistics to ensure the validity of the logistic regression model.
The lecture notes that further topics, such as robust/clustered standard errors, identification strategies, and endogeneity, are still open for discussion.
The lecture concludes by summarizing the key points covered in the lecture.Advanced Statistical Analysis: Logistic Regression, Heteroskedasticity, and Cluster Standard Errors
Logistic regression is used to model binary outcomes and estimate the probability of an event occurring.
The logit function is used to transform the probability into a log-odds ratio, which is then used to estimate the coefficients of the model.
Model fit statistics, such as the deviance and AIC, can be used to evaluate the goodness of fit of the model.
Heteroskedasticity occurs when the variance of the errors is not constant across observations. This violates the assumptions of OLS regression and can lead to biased standard errors and significance tests.
The Breusch-Pagan test can be used to test for heteroskedasticity, and robust standard errors or clustered standard errors can be used to correct for it.
Clustered standard errors are used when the errors are correlated within groups or clusters of observations, such as in panel or survey data.
There is ongoing academic debate about the best way to adjust for clustering and whether it is necessary in certain cases.
The data and Stata code used in the lecture can be found on the course platform.
The goal of hypothesis testing is to reject the null hypothesis, which assumes that there is no relationship between the dependent and independent variables.
Interpretation of logistic regression coefficients depends on the scale of the outcome variable, which can be in terms of odds, odds ratios, or probabilities.
The lecture covered practical examples and calculations to illustrate the concepts of logistic regression, heteroskedasticity, and cluster standard errors.
The next lecture will cover remaining issues and include a Q&A session, and computer labs will provide hands-on practice with Stata.