Erdogan CEVHER - 1 month ago 15

R Question

I wonder the real reason behind the difference in results of the two

`anova`

`library(PASWR2)`

head(HSWRESTLER); tail(HSWRESTLER)

# age ht wt abs triceps subscap hwfat tanfat skfat

# 1 18 65.75 133.6 8 6 10.5 10.71 11.9 9.80

# 2 15 65.50 129.0 10 8 9.0 8.53 10.0 10.56

# ...

# 77 15 68 153.8 13 7 11 10.07 16.7 11.77

# 78 15 66 258.6 45 37 43 33.75 34.5 38.93

mod1.HSW <- lm(hwfat ~ abs + triceps + subscap, data = HSWRESTLER)

anova(mod1.HSW)

# Analysis of Variance Table

# Response: hwfat

# Df Sum Sq Mean Sq F value Pr(>F)

# abs 1 5072.8 5072.8 535.858 < 2.2e-16 ***

# triceps 1 242.2 242.2 25.581 2.984e-06 ***

# subscap 1 2.2 2.2 0.237 0.6278

# Residuals 74 700.5 9.5

# ---

# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

mod2.HSW <- lm(hwfat ~ subscap + triceps + abs, data = HSWRESTLER)

anova(mod2.HSW) # ANOVA

# Analysis of Variance Table

# Response: hwfat

# Df Sum Sq Mean Sq F value Pr(>F)

# subscap 1 4939.0 4939.0 521.720 < 2.2e-16 ***

# triceps 1 204.6 204.6 21.616 1.422e-05 ***

# abs 1 173.6 173.6 18.341 5.473e-05 ***

# Residuals 74 700.5 9.5

# ---

# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

`?anova`

`anova`

Answer

When you call `anova`

on an `lm`

model fit, under the hood you are really using `?anova.lm`

, which according to the documentation *"gives a sequential analysis of variance table for that fit."* This is a `type I`

ANOVA, where order of the variables matter.The term `abs`

in your second example only represents the unique portion of the regression explained **given the previous two variables**.

You can perform `type II`

ANOVA using `drop1()`

. Here order doesn't matter, thus each main effect can be understood as the individual contribution of that predictor:

```
> drop1(mod1.HSW)
#Single term deletions
#
#Model:
#hwfat ~ abs + triceps + subscap
# Df Sum of Sq RSS AIC
#<none> 700.54 179.22
#abs 1 173.629 874.17 194.49
#triceps 1 111.837 812.38 188.77
#subscap 1 2.244 702.78 177.47
> drop1(mod2.HSW)
#Single term deletions
#
#Model:
#hwfat ~ subscap + triceps + abs
# Df Sum of Sq RSS AIC
#<none> 700.54 179.22
#subscap 1 2.244 702.78 177.47
#triceps 1 111.837 812.38 188.77
#abs 1 173.629 874.17 194.49
```