Assess regression model fit using residuals
When assessing overall model fit (or error) of both multiple regression and logistic regression models, plot the raw residuals on the y-axis against the estimated outcomes on the x-axis. The value should be close to zero,"0." This means that the predicted values are relatively similar to the observed values.
Assessing overall model fit with proportional odds regression and multinomial logistic regression is a tedious and time-consuming process. Essentially, researchers choose a reference category within the categorical outcome or ordinal outcome and create "a-1" (where "a" is the number of independent categories or ordinal ranks in the outcome) logistic regression models and repeat residual analyses for each. Plot the raw residuals against the estimated outcomes for all models. If all models have a value close to "0," then model fit can be assumed.
With Cox regression, Cox-Snell residuals should be calculated. These residuals are then used as the time signature variable in a Kaplan-Meier curve predicting for the outcome. This curve is then compared to a survival function where the outcome has been modeled using a unit exponential distribution.* If the curves are similar, then model fit can be assumed.
Finally, for Poisson regression, plot the standardized residuals on the y-axis against the expected rate of outcome on the x-axis. Evidence of model fit is assumed when 95% of the residuals are between 2 and -2.*
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