Hello R users,

I am working with the GAM to inspect the effect of some factors (year, area) and continuous variables (length, depth, latitude and longitude) on the intensity and prevalence of the common parasite Anisakis. I would like introduce interaction in my models, both "continuous variables-continuous variables" and "continuous variables-factor". I have read some questions-answers regard to this subject but I still have doubts. 
The solution that I have seen to introduce an interaction "continuous covariate-factor" is using "by" (explained in ?gam.models). Below, I show an example of my model with the interactions using "by" both to prevalence (distribution=binomial) and to intensity (distribution=negative binomial):
 
gam(prevalence~s(length)+factor(year)+factor(area)+s(length,by=area)+s(length,by=year), family=binomial,data=X)

gam(intensity~s(length)+factor(year)+factor(area)+s(length,by=area)+s(length,by=year), family=negbin(c(1,10)),data=X)
 

The solution that I have seen to introduce an interaction "continuous covariate- continuous covariate" is using the function "te". Below, I show an example of my model with the interactions using "te" both to prevalence (distribution=binomial) and to intensity (distribution=negative binomial):

gam(prevalence~s(length)+s(depth)+s(latitude)+s(longitude)+te(depth,length)+ te(latitude,length)+ te(longitude,length),family=binomial,data=X)
gam(intensity~s(length)+s(depth)+s(latitude)+s(longitude)+te(depth,length)+ te(latitude,length)+ te(longitude,length),family= negbin(c(1,10)),data=X)



My main doubts are: 
1.	Is the use of "by" and "te" right with the negative binomial distribution and with the binomial distribution?
2.	Do these interactions have the same meaning that the interaction "factor*continuous covariate" and "continuous covariate* continuous covariate" used in the GLM?
3.	Is right to introduce in the model the continuous covariates and the factor moreover their interactions?


Thanks in advance.

Best regards,

Lucía Cañás

Lucía Cañás Ferreiro
Instituto Español de Oceanografía
Centro Oceanográfico de A Coruña
Paseo Marítimo Alcalde Francisco Vázquez, nº 10
15001 - A Coruña, SPAIN
e-mail: lucia.canas@co.ieo.es
Tel: +34981205362; Fax: +34981229077
http://www.ieo.es



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