# Inclusion of correlated dependent variables in a logistic regression (seed dispersal from shrubs)

I am trying to model seed dispersal from shrubs, and I am wanting to explore if number of seeds on an individual shrub, plus the seeds in the surrounding neighborhood, affect percentage of seeds dispersed. However, I can't quite think through how to include the neighborhood seed number without including the seeds on the individual shrub being monitored. I have included the seeds on the individual in the neighborhood seed count, but this results in a strong correlation between individual seed number and neighborhood seed number. But I don't want to simply remove the seeds from the individual from the neighborhood seed number.

Here is some example data.

    Ind_seeds = c(29, 12, 157, 50, 119, 26, 65, 104, 45, 73, 22, 50, 125, 149,
37, 66, 18, 39, 150, 124, 117, 24, 75, 13, 61, 65, 49, 35, 61,
77, 26, 37, 50, 44)

NH_seeds = c(29, 12, 157, 50, 119, 26, 121, 104, 60, 73, 22, 60, 125, 149,
37, 75, 169, 39, 169, 124, 117, 202, 210, 13, 98, 210, 49, 98,
202, 77, 202, 98, 50, 44)

success = c(0, 0, 8, 4, 9, 0, 42, 29, 1, 71, 21, 7, 0, 31, 32, 9, 8, 37,
15, 53, 102, 14, 10, 3, 9, 51, 46, 13, 28, 23, 11, 23, 28, 23
)

fail = c(29, 12, 149, 0, 0, 20, 10, 22, 7, 2, 1, 4, 57, 2, 5, 4, 6,
2, 12, 0, 15, 10, 16, 10, 29, 14, 3, 22, 10, 24, 6, 14, 8, 12
)

dat = data.frame(success,fail,Ind_seeds,NH_seeds)
dat$$Ind_seeds_scale = scale(dat$$Ind_seeds)
dat$$NH_seeds_scale = scale(dat$$NH_seeds)


The correlation between individual seeds and neighborhood seeds is 0.41 cor(dat$Ind_seeds,dat$NH_seeds) and the plot looks like this

How can I account for the individual seed number in the neighborhood seed number? It just seems like a model like this model = glm(cbind(success,fail) ~ Ind_seeds_scale * NH_seeds_scale,family = "binomial",data = dat) is not quite accurate.

• 0.41 is not a strong correlation. – Robert Long Jun 4 at 18:30
• The plot of the points is enough to give me pause. There is clearly a relationship between the number of individual shrub seeds and the number of neighborhood seeds. – user44796 Jun 4 at 18:41
• Well, the plot also shows that in many cases, there is almost no neighboorhood seeds. Maybe use the difference? Anyhow, it would be strange to use a predictor that includes the outcome! – kjetil b halvorsen Jun 5 at 16:18
• I think you are right. I subtracted out the individual seeds and that leaves the neighborhood seeds. I "think" that it tests what I am looking for. Does the addition of neighborhood seeds affect the parameter estimates for individual seeds. The answer, based on the inclusion of an interaction term, suggests that it does. If you write you comment as an answer, I will accept it. – user44796 Jun 7 at 12:07