What is the formula for pseudo R-squared?

What is the formula for pseudo R-squared?

• A. 1 - l(beta_hat) / l(null)
• B. l(null) / l(beta_hat)
• C. ln(l(beta_hat)) - ln(l(null))
• D. (l(null) - l(beta_hat)) / l(null)

Answer: (A)

Pseudo R-squared is a relative measure of model fit for likelihood-based models, comparing how well the full model with predictors explains the data versus a simple baseline (the null model). The version most commonly used is McFadden's R-squared, which is defined as one minus the ratio of the fitted model’s log-likelihood to the null model’s log-likelihood. Since log-likelihoods tend to be negative, the fitted model should have a higher (less negative) log-likelihood than the null model, making the ratio between 0 and 1. Subtracting that ratio from one yields a value between 0 and 1 that increases as the model fit improves. This is the standard way to quantify improvement in fit when moving from the null model to a model with predictors.

Pseudo R-squared is a relative measure of model fit for likelihood-based models, comparing how well the full model with predictors explains the data versus a simple baseline (the null model). The version most commonly used is McFadden's R-squared, which is defined as one minus the ratio of the fitted model’s log-likelihood to the null model’s log-likelihood. Since log-likelihoods tend to be negative, the fitted model should have a higher (less negative) log-likelihood than the null model, making the ratio between 0 and 1. Subtracting that ratio from one yields a value between 0 and 1 that increases as the model fit improves. This is the standard way to quantify improvement in fit when moving from the null model to a model with predictors.