[R] Help with plit plot design in logit model

[Dilan Paranagama]

Hi,

I'm trying to fit a logit model to a set of data that was collected under a split plot scheme. The structure of the data is

Whole plot factors: Watering Frequency (2 levels: Hi/Lo) and Fertilizer type (3 factors A/B/C)
Subplot factor: slope type (2 factors up/down)

Response: Proportion of infected leaves(Infected leaves/Total leaves) of the plant (2 plants recorded from each plot)

Dataset (Partial)

Water  Fert   Slope   Plant   Total   Infect
Hi     A      up      1       24      2
Hi     A      up      2       31      1
Hi     A      down    1       21      0
Hi     A      down    2       34      0
Hi    ...
Hi    ...
Lo
Lo

All of the factors (Whole plot and subplot) are fixed

In addition there are a lot of plants that are not affected at all, so there are lot zeros

I'm trying to use the vglm function in VGAM package with zibinomial distribution. I'm a little confused about how to input the covariates to indicate a split plot design. My first try was 

bmod<-vglm(cbind(Infect, Total)~Water*Fert+Slope/(Water*Fert), zibinomial, data=FertPlots)

I would like to know if the syntax I have used in the predictors is right for the split plot model. If not, how do I give the split plot model in R.

summary(bmod) does not give any p-values for individual tests or a degrees of freedom to test them. How do I test these factors using the vglm function?

Thank you
Dilan Paranagama