The performance of your model looks good. Now the thing is how to understand residuals of a logistic regression. Actually, there many residual types that were defined, such as "deviance", "pearson", "working", "response", "partial". I think your residuals are deviance residuals. Here is the code to calculate these residuals, which may help you to understand the residuals.

# sample data

y = c(0,0,0,0,1,1,1,1,1)

x1 = c(1,2,3,1,2,2,3,3,3)

x2 = c(1,0,0,1,0,0,0,0,0)

fit = glm(y ~ x1 + x2, family = 'binomial')

lp = predict(fit)

mu = exp(lp)/(1+exp(lp))

# manually calculating response residuals

resid(fit, type="response")

response_residual = y - mu

# manually calculating the pearson residuals

resid(fit, type="pearson")

pearson_residual = (y-mu) / sqrt(mu*(1-mu))

# manually calculating the deviance residuals

resid(fit, type="deviance")

deviance_residual = sqrt(-2*log(1-mu))*sign(y-mu)

# manually calculating the 1st working residual

resid(fit, type="working")

working_residual = (y-mu) / (mu*(1-mu))

# manually calculating the partial residuals

resid(fit, type="partial")[,1]

(y-mu) / (mu*(1-mu)) + fit$coefficients[2]*(x1 - mean(x1))

resid(fit, type="partial")[,2]

(y-mu) / (mu*(1-mu)) + fit$coefficients[3]*(x2 - mean(x2))

Xinhai Li

Thank you for your answer :)

I am happy you think my model looks good, but could you please explain how you got from my plot to that conclusion?

I am happy to have found out, that the residuals below zero represent my pseudo absence data and the residuals above zero represent the pseudo presence data. But i do not understand why...?

Or maybe you can anser me that question: How can I reach residuals, that are bigger than 1 or lower than -1 if my predictor Data is normalized?

Guten Tag Matthias,

Assessing the goodness-of-fit of a binomial model is not as straightforward as a linear or log-linear model. Basically Hosmer et al. (1997) have recommended to look at two essential components of fit: 1) whether the fitted linear predictors are the appropriate ones to statistically explain the observed variance in the investigated probability, and (2) if the logit (or another link like the probit or cloglog) transformation is the correct function linking the covariates with the conditional mean.

For the first component, the Osius and Rojek (1992) test allows you to detect a lack-of-fit. For the second, Stukel (1988) has proposed a test to look for link misspecification, but just for the logit link. McCullagh & Nelder (1989) have proposed a more general test that does not only apply to the logit, but any link fittes in a GLM.

I would not personnally look at residual plots to assess the fit of a binomial model.

Viele Glück,

Julien