YO.FS and YO*FS - difference?

[tatos]

If we have 2 factors and we want to consider different models for the linear predictor, what is the difference between saying

YO.FS and YO*FS where YO and FS are the 2 factors..?

 

[John Potter]

Hi tatos,

YO.FS considers the just interaction between YO and FS whereas
YO*FS considers YO, FS and YO.FS
So, the linear predictor needs to record information about YO, information about FS and information about the interaction between YO and FS.

In general, if YO requires n parameters and FS requires m parameters then
YO*FS will require n*m parameters

John

 

[jm_kinuthia]

How do you derive the parameterised form for YO*FS*TC ?

 

[John Lee]

How do you derive the parameterised form for YO*FS*TC ?

Depends on whether the covariates are factors or variables....

But think of it as multiplying and you won't go far wrong.

So if they are all variables then you would have something like:

\( (\alpha_1 + \beta_1 x)(\alpha_2 + \beta_2 y)(\alpha_3 + \beta_3 z) \)

which you can multiply out and simply the constants to something like:

const + const x + const y + const z + const xy + const xz + const yz + const xyz

If they are all factors then you would have something like:

\( \alpha_i * \beta_j * \gamma_k \)

The easiest way of simplifying this would be to something like:

\( \delta_{ijk} \)