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

From: Anita Narwani <anarwani_at_uvic.ca>
Date: Wed, 02 Jun 2010 16:59:31 -0700

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

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