Hi all,
I am trying to fit a linear model (using lm) with 3 predictors (2
continuous and 1 factor) for a response variable. I have no
interaction terms nor missing values (though I do not have the same
sample size in all factor cells), so I thought the results would be
pretty straightforward, with no differences due to the "type" of Sum-
of-Sqares employed. However, I am getting somewhat conflicting results
(especially for the variable "IMC", see below) when I use anova, Anova
(from car package), and drop1. Actually, drop1(), Anova(type="II") and
Anova(type="III") all give the same results, only anova() yields a
different one.
Due to "consistency" of results I am imagining i should ignore R
standard anova's results, but I'd like to understand why and the
implications this would have to any other test I conduct.
Any comments would be welcome...
Best,
Rafael Maia
> m1<-lm(PC1~IMC+ResPlum+factor(Year),data=dados)
> summary(m1)
Call:
lm(formula = PC1 ~ IMC + ResPlum + factor(Year), data = dados)
Residuals:
Min 1Q Median 3Q Max
-4.0212 -0.8983 0.1623 1.2623 2.7767
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -5.1260 3.9075 -1.312 0.196080
IMC 8.8518 6.1188 1.447 0.154777
ResPlum 3.0034 0.7625 3.939 0.000276 ***
factor(Year)2 -1.2602 0.5186 -2.430 0.019069 *
factor(Year)3 0.6307 0.9014 0.700 0.487675
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Residual standard error: 1.659 on 46 degrees of freedom
Multiple R-squared: 0.4001, Adjusted R-squared: 0.3479
F-statistic: 7.669 on 4 and 46 DF, p-value: 8.033e-05
> anova(m1)
Analysis of Variance Table
Response: PC1
Df Sum Sq Mean Sq F value Pr(>F)
IMC 1 16.844 16.844 6.1204 0.0171142 *
ResPlum 1 44.860 44.860 16.3003 0.0002027 ***
factor(Year) 2 22.720 11.360 4.1278 0.0224493 *
Residuals 46 126.596 2.752
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
> drop1(m1, test="F")
Single term deletions
Model:
PC1 ~ IMC + ResPlum + factor(Year)
Df Sum of Sq RSS AIC F value Pr(F)
<none> 126.596 56.368
IMC 1 5.759 132.355 56.637 2.0928 0.1547766
ResPlum 1 42.700 169.295 69.191 15.5155 0.0002757 ***
factor(Year) 2 22.720 149.316 60.786 4.1278 0.0224493 *
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
> Anova(m1)
Anova Table (Type II tests)
Response: PC1
Sum Sq Df F value Pr(>F)
IMC 5.759 1 2.0928 0.1547766
ResPlum 42.700 1 15.5155 0.0002757 ***
factor(Year) 22.720 2 4.1278 0.0224493 *
Residuals 126.596 46
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
> Anova(m1, type="III")
Anova Table (Type III tests)
Response: PC1
Sum Sq Df F value Pr(>F)
(Intercept) 4.736 1 1.7210 0.1960800
IMC 5.759 1 2.0928 0.1547766
ResPlum 42.700 1 15.5155 0.0002757 ***
factor(Year) 22.720 2 4.1278 0.0224493 *
Residuals 126.596 46
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1