Goodness-of-fit tests for Simple Binary Logistic Regression

Find definitions and interpretation guidance for every statistic in the Goodness-of-Fit Tests table.

Deviance Goodness-of-Fit Test

The deviance goodness-of-fit test assesses the discrepancy between the current model and the full model.

Interpretation

Use the goodness-of-fit tests to determine whether the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict. If the p-value for the goodness-of-fit test is lower than your chosen significance level, the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict. This list provides common reasons for the deviation:
  • Incorrect link function
  • Omitted higher-order term for variables in the model
  • Omitted predictor that is not in the model
  • Overdispersion

If the deviation is statistically significant, you can try a different link function or change the terms in the model. To use a different link function, you should use Binary Fitted Line Plot or Fit Binary Logistic Regression in Minitab Statistical Software.

For binary logistic regression, the format of the data affects the p-value because it changes the number of trials per row. The p-value for the deviance test usually decreases as the number of trials per row decreases.

Pearson Goodness-of-Fit Test

The Pearson goodness-of-fit test assesses the discrepancy between the current model and the full model.

Interpretation

Use the goodness-of-fit tests to determine whether the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict. If the p-value for the goodness-of-fit test is lower than your chosen significance level, the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict. This list provides common reasons for the deviation:
  • Incorrect link function
  • Omitted higher-order term for variables in the model
  • Omitted predictor that is not in the model
  • Overdispersion

If the deviation is statistically significant, you can try a different link function or change the terms in the model. To use a different link function, you should use Binary Fitted Line Plot or Fit Binary Logistic Regression in Minitab Statistical Software.

For binary logistic regression, the format of the data affects the p-value because it changes the number of trials per row. The approximation to the chi-square distribution that the Pearson test uses is inaccurate when the expected number of events per row in the data is small. Thus, the Pearson goodness-of-fit test is inaccurate when the data are in Binary Response/Frequency format.

Hosmer-Lemeshow

The Hosmer-Lemeshow goodness-of-fit test compares the observed and expected frequencies of events and non-events to assess how well th model fits the data.

Interpretation

Use the goodness-of-fit tests to determine whether the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict. If the p-value for the goodness-of-fit test is lower than your chosen significance level, the predicted probabilities deviate from the observed probabilities in a way that the binomial distribution does not predict. This list provides common reasons for the deviation:
  • Incorrect link function
  • Omitted higher-order term for variables in the model
  • Omitted predictor that is not in the model
  • Overdispersion

If the deviation is statistically significant, you can try a different link function or change the terms in the model. To use a different link function, you should use Binary Fitted Line Plot or Fit Binary Logistic Regression in Minitab Statistical Software.

The Hosmer-Lemeshow test does not depend on the number of trials per row in the data as the other goodness-of-fit tests do. When the data have few trials per row, the Hosmer-Lemeshow test is a more trustworthy indicator of how well the model fits the data.

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