Analysis for behavior change over sample treatments

[caddyhair]

Hello all!

My research examined if social behaviors in animals changed with the distribution of food treatment (clumped vs. dispersed food). My data is non-parametric. I have matrices of interaction rates between individuals.

I ran Mantel tests between the interaction matrices of the clumped treatment and the dispersed treatment. This told me if behaviors were correlated between the food treatments. But, I need to know if the behaviors changed with the food treatment.

Does anyone have a suggestion on a statistical test to run between matrices to see if behaviors changed with the distribution of food? My committee said there may be a test that would subtract the numbers from each cell in the matrix to determine if their was a change. Any help would be greatly appreciated!

BTW, sorry if this is in the wrong section!

 

[staassis]

Please describe your data more carefully...

 

[caddyhair]

Hello thanks for the reply,

I collected data during 2 treatments of food distribution. One treatment where food was clumped in 1 location and one treatment where food was dispersed over multiple locations. I then collected data on the frequency of behavior between individuals. So lets say animal A and animal B interacted 30 times during the clumped food treatment and animal A and animal B interacted 100 times during the dispersed food treatment. I then corrected the frequencies by the number of times each individual was seen interacting overall during that food treatment to get an interaction rate. So, lets say during the clumped treatment animals A and B had an interaction rate of 0.3 and during the dispersed treatment they had an interaction rate of 1.

I then have matrices containing all the interaction rates between all possible pairs of animals. There were 29 animals in the study so my matrices are 29x29 and each cell contains a number for the interaction rate between that pair of individuals.

I need to compare the interaction rate matrix from the clumped food treatment to the interaction matrix of the dispersed food treatment to determine if there was a significant change between interaction rates due to the dispersion of food. Essentially, I need to determine if the treatment of food significantly changed the behaviors. So is the difference between an interaction rate of 0.3 and 1 significantly different?

I ran Mantel tests between the matrices but this only tells me if the interaction matrices are still correlated it does not tell me if there was a change in the behaviors.

Hopefully this is more clear, let me know if you need any other details. Any help is appreciated!

 

[staassis]

Ok, as I understand, each intensity is actually the probability that the two entities interact whenever they get a chance... This is yet another case for a likelihood ratio test. In this test you compare two models, the full one and the reduced one. In the full model you assume that the interaction probabilities are different between the treatments. In the reduced model you assume that they are the same between the treatments. In each of the two models, you would need to model the interaction in pairs (A,B) and (A,C) in a correlated manner. You can use some simple rule for that.

The likelihood ratio test is a by-product of maximum likelihood estimation of the two models, which can be implemented in R or Matlab relatively easily.