AIC compares competing statistical models by balancing explained variation against model complexity. Lower values are preferred, but an isolated AIC score has little meaning. section 5.7.6 section 14.5.2
Use AIC with these practical rules:
- Compare models fitted to the same analytical problem rather than interpreting one score alone. section 5.7.6
- Prefer the model with the lower AIC when other evidence is comparable. section 14.5.2
- Treat a difference of two or more AIC units as a rule-of-thumb indication of a significantly better fit. section 5.7.6
NBA regression comparison
A reduced regression predicting wins from screen assists, deflections, and loose balls had AIC 514, versus 518 for the fuller model. The reduced model therefore compared favorably, alongside slightly better adjusted R² and cleaner diagnostics, although its average prediction error was marginally larger. section 5.7.6
fit2 <- lm(wins ~ screen_assists_pts + deflections + loose_balls,
data = train)
tidy(fit2)
## # A tibble: 4 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -56.1 25.5 -2.20 0.0317
## 2 screen_assists_pts 1.12 0.422 2.65 0.0101
## 3 deflections 2.35 0.859 2.74 0.00805
## 4 loose_balls 4.81 1.98 2.42 0.0182
augment(fit2) -> fit_tbl2
print(fit_tbl2)
# A tibble: 67 × 10
## wins screen_assists_pts deflections loose_balls .fitted .resid
## <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 49 20 14.1 8.3 39.3 9.66
## 2 42 26.2 12.1 8 40.1 1.85
## 3 39 25.7 12.6 8.1 41.2 -2.24
## 4 19 22.4 11.8 7.6 33.3 -14.3
## 5 33 20.1 11.5 8.4 33.8 -0.825
## 6 54 19.9 13.9 8.6 40.2 13.8
## 7 57 26.3 14.2 8.7 48.6 8.44
## 8 53 16.6 14.9 8.4 37.9 15.1
## 9 48 20.2 14.2 8.6 41.2 6.76
##10 37 20.1 11.9 8.5 35.2 1.75
## hat .sigma .cooksd .std.resid
## <dbl> <dbl> <dbl> <dbl>
## 1 0.0224 10.8 0.00472 0.907
## 2 0.0726 10.8 0.000626 0.179
## 3 0.0568 10.8 0.000691 -0.214
## 4 0.0647 10.7 0.0324 -1.37
## 5 0.0749 10.9 0.000128 -0.0797
## 6 0.0316 10.7 0.0138 1.30
## 7 0.0792 10.8 0.0144 0.817
## 8 0.0550 10.7 0.0303 1.44
## 9 0.0298 10.8 0.00312 0.637
##10 0.0632 10.9 0.000478 0.168
## # ... with 57 more rows
fit_tbl2 %>%
mutate(wins_dif = abs(wins - .fitted)) -> fit_tbl2
mean(fit_tbl2$wins_dif)
## [1] 8.427093
glance(fit2)
## # A tibble: 1 × 12
## r.squared adj.r.squared sigma statistic p.value df logLik
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0.194 0.156 10.8 5.06 0.00334 3 -252.
## AIC BIC deviance df.residual nobs
## dbl> <dbl> <dbl> <int> <int>
## 1 514. 525. 7302. 63 67
vif(fit2)
## screen_assists_pts deflections loose_balls
## 1.085184 1.031128 1.098619
par(mfrow = c(2,2))
plot(fit2)
Inspect the reduced regression, its coefficient output, and augmented predictions before comparing model diagnostics and AIC. section 5.7.6
