Calculating Negative 2 Log Likelihood of Logistic Model Inr

The negative 2 log likelihood (N2LL) is a statistical measure used to evaluate the fit of a logistic regression model. For the International Normalized Ratio (INR), a common blood coagulation test, understanding N2LL helps assess how well the logistic model predicts INR values based on given predictors.

What is Negative 2 Log Likelihood?

The negative 2 log likelihood (N2LL) is a statistical measure that quantifies how well a model fits the observed data. In logistic regression, it measures the discrepancy between the predicted probabilities and the actual observed outcomes.

Lower N2LL values indicate a better fit of the model to the data. The N2LL is calculated by taking the negative log likelihood and multiplying it by 2, which simplifies comparisons between models.

Formula: N2LL = -2 * (log likelihood)

Logistic Model INR

The International Normalized Ratio (INR) is a measure of blood coagulation used to monitor warfarin therapy. A logistic model can predict INR values based on patient characteristics such as age, weight, and previous INR readings.

The logistic model for INR prediction typically includes predictors like age, weight, and previous INR values. The model outputs probabilities that can be converted to predicted INR values.

Calculating Negative 2 Log Likelihood

To calculate the N2LL for a logistic model predicting INR, follow these steps:

Fit the logistic regression model to your data, including predictors like age, weight, and previous INR values.
Calculate the log likelihood of the model.
Multiply the log likelihood by -2 to get the N2LL.

Example Calculation:

If the log likelihood of your logistic model is -150, then:

N2LL = -2 * (-150) = 300

This means the model has a negative 2 log likelihood of 300, indicating a reasonable fit to the data.

Interpretation

The N2LL value helps determine how well the logistic model fits the data. A lower N2LL indicates a better fit. However, it's important to compare N2LL values between different models to determine which one fits the data best.

For example, if you compare two models predicting INR, the model with the lower N2LL is the better fit.

Note: N2LL should be used in conjunction with other model evaluation metrics, such as AIC or BIC, for a comprehensive assessment of model performance.

FAQ

What does a low N2LL value mean?

A low N2LL value indicates that the model fits the data well. It means the predicted probabilities are close to the observed outcomes.

How is N2LL different from log likelihood?

N2LL is simply the negative log likelihood multiplied by 2. It's a scaled version of the log likelihood that makes comparisons between models easier.

Can N2LL be negative?

Yes, N2LL can be negative if the log likelihood is positive. However, in practice, N2LL is typically positive for well-fitting models.