[R-lang] Re: 3 Level IV

[Peter Graff]

Dear Florian, dear Roger,

Thank you very much for your help.

The design is basically a regular 2x2 with one cell missing due to linguistic impossibility.

> Level 1: A C
> Level 2: A D
> Level 3: B D

The question is whether 1=3>2. I turns out, that when I code collinearly (AvB, CvD; Coding 1), I get 2 significant effects, which practically cancel each other out.

CODING 1

Level 1:	-.25	.5
Level 2:	-.25	-.25
Level 3:	.5	-.25

But when I code orthogonally, I only get one (3>2).

CODING 2

Level 1:	-.25	.5
Level 2:	-.25	-.5
Level 3:	.5	0

It is also clear from the data, that the result is 1=3>2. It thus seems like the collinearity is producing a spurious significance, even though the collinear coding more straightforwardly mirrors the theoretical motivation.

Best,

Peter

On Feb 19, 2011, at 7:33 PM, T. Florian Jaeger wrote:

> Hi Peter,
> 
> that depends on your question (the hypothesis that you wish to test). Multi-collinearity is a consideration that should come in AFTER you've decided what question to test. 
> 
> HTH,
> Florian
> 
> On Sat, Feb 12, 2011 at 8:35 PM, Peter Graff <graff@mit.edu> wrote:
> Dear R-Lang,
> 
> I have a question about how to code a 3-level IV in a regression.
> 
> The 3 levels are motivated by 2 2-level predictors of theoretical interest (A/B and C/D):
> 
> Level 1: A C
> Level 2: A D
> Level 3: B D
> 
> Is it reasonable to code:
> 
> A versus B, C versus D, Interaction
> 
> Or ist it better to code:
> 
> A v B, AC v AD
> 
> The first coding reflects the theoretical interest more directly, the second coding has considerably less collinearity.
> 
> Thank you very much,
> 
> Peter Graff
> 

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