40.5 Model Comparison

Compare nested models via ANOVA (F-test), and non-nested via AIC/BIC, cross-validation, or predictive performance metrics. jtools::export_summs() offers attractive comparison tables.

fit_a <- lm(metascore ~ log1p(budget), data = movies_small)
fit_b <- lm(metascore ~ log1p(budget) + log1p(us_gross), data = movies_small)
fit_c <- lm(metascore ~ log1p(budget) + log1p(us_gross) + runtime, data = movies_small)

coef_names <- c("Budget" = "log1p(budget)",
                "US Gross" = "log1p(us_gross)",
                "Runtime (Hours)" = "runtime",
                "Constant" = "(Intercept)")

export_summs(fit_a, fit_b, fit_c, robust = "HC3", coefs = coef_names)
Model 1Model 2Model 3
Budget-2.43 ***-5.16 ***-6.70 ***
(0.44)   (0.62)   (0.67)   
US Gross       3.96 ***3.85 ***
       (0.51)   (0.48)   
Runtime (Hours)              14.29 ***
              (1.63)   
Constant105.29 ***81.84 ***83.35 ***
(7.65)   (8.66)   (8.82)   
N831       831       831       
R20.03    0.09    0.17    
Standard errors are heteroskedasticity robust. *** p < 0.001; ** p < 0.01; * p < 0.05.
 
# AIC/BIC comparison
broom::glance(fit_a) %>% select(AIC, BIC, adj.r.squared) %>% mutate(model = "fit_a")
#> # A tibble: 1 × 4
#>     AIC   BIC adj.r.squared model
#>   <dbl> <dbl>         <dbl> <chr>
#> 1 7039. 7053.        0.0271 fit_a
broom::glance(fit_b) %>% select(AIC, BIC, adj.r.squared) %>% mutate(model = "fit_b")
#> # A tibble: 1 × 4
#>     AIC   BIC adj.r.squared model
#>   <dbl> <dbl>         <dbl> <chr>
#> 1 6984. 7003.        0.0910 fit_b
broom::glance(fit_c) %>% select(AIC, BIC, adj.r.squared) %>% mutate(model = "fit_c")
#> # A tibble: 1 × 4
#>     AIC   BIC adj.r.squared model
#>   <dbl> <dbl>         <dbl> <chr>
#> 1 6913. 6937.         0.166 fit_c
# Nested model ANOVA (fit_a ⊂ fit_b ⊂ fit_c)
anova(fit_a, fit_b, fit_c)
#> Analysis of Variance Table
#> 
#> Model 1: metascore ~ log1p(budget)
#> Model 2: metascore ~ log1p(budget) + log1p(us_gross)
#> Model 3: metascore ~ log1p(budget) + log1p(us_gross) + runtime
#>   Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
#> 1    829 230545                                  
#> 2    828 215136  1     15409 64.634  3.11e-15 ***
#> 3    827 197160  1     17976 75.401 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1