# [R] Design matrix for species mixture

Jim Lemon drjimlemon at gmail.com
Fri May 12 02:53:44 CEST 2017

```Hi Margot,
I'm not sure I understand your model, but if I make up some data in
which the response variable is vegetation cover and the three species
are:

A - eats one type of plant
B - eats another type of plant
C - preys on herbivorous insects

1,1,0,0,1
2,0.3,1,1,1
3,0.6,0,1,1
4,0.2,1,1,1
5,0.7,1,0,1
6,0.8,0,0,0
7,0.3,1,0,0
8,0.4,0,1,0
9,0.1,1,1,0
10,0.5,0,1,0
11,0.5,1,0,1
12,0.1,1,1,0
13,0.6,0,1,1
14,0,1,1,0",
print(summary(lm(propveg~A+B+C+A:B+A:C+B:C,df)))

Is that something like what you want?

Jim

On Fri, May 12, 2017 at 12:40 AM, Margot Neyret <margotneyret at gmail.com> wrote:
> Hello,
>
> I have fields with species mixtures (for instance, species a, b, c, a+b, a+c, b+c), and I look at the effect of each species on a response Y. More specifically, I would like to compare the effect of individual species, either alone or in mixture.
>
>>Y = rnorm(18,0,1)
>>mixture= rep(c('a','b', 'c', 'a+b', 'a+c', 'b+c'), each = 3)
>
> Thus I create variables A, B and C with :
> - A = 1 when the mixture contains a (ie mixture = a or a+b or a+c); and 0 otherwise.
> - Idem for variables C and B.
>
>>A = ifelse(mixture %in% c('a', 'a+b', 'a+c'), 1, 0)
>>B = ifelse(mixture %in% c('b', 'a+b', 'b+c'), 1, 0)
>>C = ifelse(mixture %in% c('c', 'a+c', 'b+c'), 1, 0)
>
> My plan was to build a design matrix from these 3 variables, that would then allow me to compare the effects of each species.
>
>> mm = model.matrix(~A+B+C+0)
>> summary(lm(Y~mm))
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) -0.8301 0.6221 -1.334 0.203
> mmA 1.1636 0.4819 2.415 0.030 *
> mmB 0.8452 0.4819 1.754 0.101
> mmC -0.1005 0.4819 -0.208 0.838
> ---
> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> Residual standard error: 0.8347 on 14 degrees of freedom
> Multiple R-squared: 0.4181, Adjusted R-squared: 0.2934
> F-statistic: 3.353 on 3 and 14 DF, p-value: 0.04964
>
> My questions :
> 1. Does this approach make any sense ? I have a feeling I am doing something strange but I cannot put my finger on it.
> 1. My ddl are wrong, I should not have an intercept here, or at least my intercept should be one of my species. Should I just remove one species form the design matrix ?
> 2. Is there any way to do post-hoc tests on my species now, as I would have done with Tukey test or lsmeans ?
>
> My objective afterwards is to add other explanatory variables and interactions in the model.
>
>
> M. N.
>
>
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>
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