Dear Idzhar,

It is not mandatory, especially in your case. You could use calibration plots and Nagelkrke's R2 instead.

Best,

Wadie

Hi Idzhar Arbarizq , please share more information on the pattern/structure of the repeated values - as well as your research design, and main your research objective: what is your study/analysis is addressing. This information can better inform the response to your question above.

The Hosmer and Lameshow test is conducted to evaluate model fit and significance, specifically assessing whether the model with a predictor provides a better fit than the null model.

No, the Hosmer-Lemeshow test is not mandatory in binary logistic regression. While it's commonly used to assess goodness-of-fit, its use is not required. Some statisticians argue against its use due to limitations and sensitivity to sample size and grouping method. Other goodness-of-fit tests like the Pearson Chi-Square test, Deviance test, and Likelihood Ratio test are also commonly used alternatives. The choice of which test to use depends on the specific context and goals of the analysis.

Goodness-of-fit tests in binary logistic regression are applied to assess how well the model fits the observed data. Here are some common tests and when they're typically applied:

1. Hosmer-Lemeshow Test: Usually applied after fitting the logistic regression model to the data. It assesses whether there is a significant difference between observed and expected outcomes across different groups defined by predicted probabilities. This test helps to evaluate the calibration of the model.

However, it has some limitations, such as sensitivity to sample size and grouping method.

2. Pearson Chi-Square Test: Applied to assess the overall fit of the model by comparing observed and expected frequencies in each category of the binary outcome variable. It tests the null hypothesis that there is no difference between observed and expected frequencies.

3. Deviance Test: Comparing the fit of the full model with a model containing only an intercept term. It's used to assess whether adding predictors significantly improves the fit of the model.

4. Likelihood Ratio Test (LRT): Applied to compare the fit of the current model with a null model (usually a model with only an intercept term). It evaluates whether adding predictors improves model fit significantly.

5. Pseudo R-squared: Calculated to measure the proportion of variance explained by the model. It's typically applied to understand the overall goodness of fit of the model, though it's less commonly used for model comparison due to its limitations.

6. Area Under the ROC Curve (AUC): Used to evaluate the discriminatory power of the model by measuring its ability to distinguish between the two outcome categories. It's commonly applied in classification tasks to assess model performance.

In general, these tests are applied after fitting the logistic regression model to the data to evaluate different aspects of model performance, such as calibration, overall fit, improvement in fit with added predictors, and discriminatory power.