Deviance compares a fitted model to a saturated model (perfect fit). Smaller deviance generally indicates better fit, and differences in deviance can be used for likelihood ratio tests.
fit_null <- glm(am ~ 1, data = mtcars, family = binomial)
fit_full <- glm(am ~ wt + hp + factor(cyl), data = mtcars, family = binomial)
anova(fit_null, fit_full, test = "Chisq")Analysis of Deviance Table
Model 1: am ~ 1
Model 2: am ~ wt + hp + factor(cyl)
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1 31 43.230
2 27 7.255 4 35.974 2.929e-07 ***
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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Logistic regression does not use R-squared in the same way as linear regression. Model comparison is typically done with likelihood-based tools (deviance, likelihood ratio tests) and information criteria (AIC).
Some goodness-of-fit tests (e.g., Hosmer–Lemeshow) require additional packages and choices about grouping. In practice, you should combine multiple checks:
Pseudo R-squared measures (e.g., McFadden’s) are based on likelihoods and are best used for rough comparisons rather than as a direct analogue of linear-model R-squared.
fit_null <- glm(am ~ 1, data = mtcars, family = binomial)
fit_full <- glm(am ~ wt + hp + factor(cyl), data = mtcars, family = binomial)
mcfadden_r2 <- 1 - as.numeric(logLik(fit_full) / logLik(fit_null))
mcfadden_r2[1] 0.8321671AIC(fit_null, fit_full) df AIC
fit_null 1 45.22973
fit_full 5 17.25537