Collects the usual model-comparison statistics into one tidy data frame, one row per model. These comprise the number of observations, the degrees of freedom, AIC, BIC, the log-likelihood, an R-squared and the root-mean-square error.
Details
The R-squared depends on the kind of model. An lm reports the ordinary
coefficient of determination. Every glm, including quasi-likelihood
families and negative binomial fits from MASS::glm.nb(), reports the
deviance R-squared, \(1 - D/D_0\). Here \(D\) is the residual deviance
of the model and \(D_0\) the deviance of the null model, which
stats::glm() fits to the same rows with the same prior weights and
offset. The null model has an intercept only if the model has one. Both
deviances are stored with the fit, so nothing is refitted. The value is the
share of the null deviance that the predictors explain, the
Kullback-Leibler R-squared of Cameron and Windmeijer (1997). It equals the
ordinary R-squared for a Gaussian model with the identity link and
McFadden's (1974) pseudo-R-squared for binary logistic regression. For
Poisson, grouped binomial, Gamma and other models, the two measures differ.
Mixed models (merMod) report an R-squared of NA, since no single
definition is standard for them.
A linear mixed model fitted with lme4::lmer() by restricted maximum
likelihood (REML, its default) is refitted by maximum likelihood with
lme4::refitML(). Its AIC, BIC and log-likelihood come from the refit, and
a message says so. A REML likelihood is the likelihood of the residuals left
once the fixed effects are removed. Two models with different fixed effects
therefore have REML likelihoods of different data, and their criteria cannot
be compared. The anova() method for lme4 fits refits them by maximum
likelihood for the same reason. If a refit fails, a warning says so, and
that model's df, AIC, BIC and logLik are NA. The other columns
describe the model as supplied.
References
Cameron AC, Windmeijer FAG (1997). “An R-squared measure of goodness of fit for some common nonlinear regression models.” Journal of Econometrics, 77(2), 329–342. doi:10.1016/S0304-4076(96)01818-0 .
McFadden D (1974). “Conditional logit analysis of qualitative choice behavior.” In Zarembka P (ed.), Frontiers in econometrics, 105–142. Academic Press, New York, NY.
Examples
m1 <- lm(yield ~ rainfall, data = crop_yield)
m2 <- lm(yield ~ rainfall + fertiliser, data = crop_yield)
m3 <- lm(yield ~ rainfall + fertiliser + soil_ph + treatment,
data = crop_yield)
model_fit_table(simple = m1, medium = m2, full = m3)
#> model n df AIC BIC logLik R2 RMSE
#> 1 simple 200 3 640.110 650.005 -317.055 0.097 1.181
#> 2 medium 200 4 591.636 604.829 -291.818 0.299 1.041
#> 3 full 200 6 422.174 441.964 -205.087 0.705 0.675