# [R] Nested ANOVA with covariate using Type III sums of squares in R

Anita Narwani anarwani at uvic.ca
Thu Jun 3 01:59:31 CEST 2010

```Hello,

I have been trying to get an ANOVA table for a linear model containing a
single nested factor, two fixed factors and a covariate:

carbonmean<-lm(C.Mean~ Mean.richness + Diversity + Zoop + Diversity/Phyto
+ Zoop*Diversity/Phyto)

where, Mean.richness is a covariate, Zoop is a categorical variable (the
species), Diversity is a categorical variable (Low or High), and Phyto
(community composition) is also categorical but is nested within the level
of Diversity. Quinn & Keough's statistics text recommends using Type III
SS for a nested ANOVA with a covariate.

I get the following output using the Type I SS ANOVA:

Analysis of Variance Table
Response: C.Mean
Df    	Sum Sq   	Mean Sq 	F value    	Pr(>F)
Mean.richness         		1  	56385326  	56385326 	23.5855 	3.239e-05 ***
Diversity             		1  	14476593  	14476593  	6.0554  	0.019634 *
Zoop                  		1  	13002135  	13002135  	5.4387  	0.026365 *
Diversity:Phyto       		6 	126089387  	21014898  	8.7904 	1.257e-05 ***
Diversity:Zoop        		1    	263036    	263036  	0.1100  	0.742347
Diversity:Zoop:Phyto  	6  	61710145  	10285024  	4.3021  	0.002879 **
Residuals            		31  	74110911   	2390675
I have tried using both the drop1() command and the Anova() command in the
car package.
When I use the Anova command I get the following error message:
>Anova(carbonmean,type="III")
“Error in linear.hypothesis.lm(mod, hyp.matrix, summary.model = sumry,:
One or more terms aliased in model.”

I am not sure why this is aliased. There are no missing cells, and the
cells are balanced (aside from for the covariate). Each Phyto by Zoop
cross is replicated 3 times, and there are four Phyto levels within each
level of Diversity. When I remove the nested factor (Phyto), I am able to
get the Type III SS output.

Then when I use drop1(carbonmean,.~.,Test=”F”) I get the following output:
> drop1(carbonmean,.~.,Test="F")
Single term deletions

Model:
C.Mean ~ Mean.richness + Diversity + Zoop + Diversity/Phyto + Zoop *
Diversity/Phyto
Df 	Sum of Sq       RSS       	AIC
<none>                             		74110911       718
Mean.richness         		1  	49790403 	123901314	741
Diversity             		0         	0  		74110911	718
Zoop                  		0         	0  		74110911	718
Diversity:Phyto       		6 	118553466	192664376	752
Diversity:Zoop        		0 	-1.49e-08	74110911       	718
Diversity:Zoop:Phyto  	6  	61710145 	135821055       735

There are zero degrees of freedom for Diversity, Zoop and their
interaction, and zero sums of sq for Diversity and Zoop. This cannot be
correct, however when I do the model simplification by dropping terms from
the models manually and comparing them using anova(), I get virtually the
same results.

I would appreciate any suggestions for things to try or pointers as to
what I may be doing incorrectly.

Thank you.
Anita Narwani.

PhD Candidate
Water & Aquatic Sciences Research Program
University of Victoria, Department of Biology

```