# What are delta statistics for generalized linear models?

Generalized linear models include binary regression and Poisson regression. Delta is the overall change in a value. For example, if the low temperature on a particular day was 55 degrees and the high temperature was 75 degrees, this would give a delta of 20 degrees. Often, delta is considered the difference between a start and end value, irrespective of fluctuations that can occur between these points. For example, on the first day of the month, a bank account contains a certain amount of money. Though numerous deposits and withdrawals are made as the month progresses, if on the last day of the month the balance is the same as it was on the first day of the month, the bank could claim a balance delta of 0.
Delta beta
The delta beta measures the change in the regression coefficients (using the Pearson residuals) because of deleting a specific factor/covariate pattern. Minitab calculates a value for each distinct factor/covariate pattern. Use delta beta to detect factor/covariate patterns that have a strong effect on the estimated coefficients.
Delta beta (standardized)
The delta beta (standardized) measures the change in the regression coefficients (using the Pearson standardized residuals) because of deleting a specific factor/covariate pattern. Minitab calculates a value for each distinct factor/covariate pattern. Use standardized delta beta to detect factor/covariate patterns that have a strong effect on the standardized estimated coefficients.
Delta chi-square
The delta chi-square is the change in Pearson chi-square because of deleting all the observations with the jth factor/covariate pattern. Minitab calculates a delta chi-square value for each distinct factor/covariate pattern. Observations that are not fit well by the model. have high delta chi-square values.
Delta deviance
The delta deviance measures the change in the deviance goodness-of-fit statistic because of deleting a specific factor/covariate pattern. Delta deviance can be large because of a large residual (deviance or Pearson) and/or a large leverage. Minitab calculates a value for each distinct factor/covariate pattern.
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