# What's the best approach for analyzing non-normal multivariate time-series data?

I'm comfortable with simple linear models and GLMs but I've never used either for multivariate analysis. My data is counts of three developmental stages of an insect, over time, in randomized complete blocks, with 3 treatments + no treatment control.

My count data is non-normal (zeroes omitted for easier visualization)...

... and over-dispersed:

                    egg                 l.nymph                 s.nymph
"M (SD) = 9.08 (26.11)"  "M (SD) = 0.56 (2.28)"  "M (SD) = 1.04 (3.78)"


and treatment B seems to have a pretty good effect in reducing counts! ...

I figured I'd model the data using a negative binomial GLM... but I'm just not really sure how one would set that up or interpret the results. Given the variables (response = count; explanatory = treatment, developmental stage, sample date, block), would my model be additive? Multiplicative? And is the coefficient and significance output in the nbGLM summary sufficient for my analyis?

• looking at the graph i see a decreasing count. have you considered fitting a poison model? probably truncated since you do not have the zeros? Jul 28, 2020 at 20:59
• something like glmmTMB(response ~ treat*stage*date + (treat*stage|block), family=nbinom2, data= ...) might be good as a start. It will be a little tricky to model and interpret the full three-way (treatstagedate) interaction. Can you start by simplifying, e.g. just model the peak or the endpoint or the mean of each treat*stage combo? This could be done with GAMs but would get more complicated ... rpubs.com/bbolker/ratgrowthcurves Jul 29, 2020 at 2:15
• Are the three stages examined separately, or is this in some way following a progression from stage to stage? From the plots it seems like the latter (nymphs go up as eggs go down), which would require different analysis from the former. If sequential, is there a progression from small nymphs to large nymphs or are there 2 different fates of the eggs?
– EdM
Jul 29, 2020 at 20:49
• I think it might be easiest and make more sense to analyse the egg and nymph data separately. I'm not a huge fan of log transforming my counts in an attempt to reach normality, and I'm unsure of how to evaluate longitudinal data using a GLM. Jul 29, 2020 at 22:34

• @DieterKahl you need to account for any internal correlations in the data, so if you have repeated measurements on the same plants then plants need to be specified as random effects. For the 4x4 Latin square design, you could consider using row and column as random effects or just treat all 4x4=16 blocks in the square as a random effect. Either way, make sure that the data are coded in a way that the grouping of plants within blocks is understood; if you give each plant a separate ID, the software should figure that out.