Analysis for multiple animals and partial pooling

[bniebuhr]

Hello,

I have been using moveHMM to perform some movement analysis. When I have several animals from a population to analyze, and I prepare data for all of them, as I understand, the analysis is performed for all of them simultaneously, i.e., they are completely pooled in a single dataset for the analysis, although the classification of behavioral states may be inferred for each one (but based on a single set of distributions of step length and turning angle for all). Am I correct?

Based on that, I have two questions:

• If I believe they may have different responses to environmental features or something like that, is there a way of running the analysis considering individuals separately (i.e., no pooling) without making a loop or something like that?

• The second: beyond that, is there a way to perform a partial pooling analysis, using individuals as "random effects", with distributions of step lengths and turning angles whose parameters are samples from population hyperparameters?

(please tell me if something is not clear in my questions)

[TheoMichelot]

[Edit 05/07/2019: The formulas suggested here are incorrect. Please see my response at the end of this thread.]

Dear Bernardo,

Indeed, if you provide a data set with several tracks (possibly from different individuals) to fitHMM, a single set of parameters will be estimated for all of them.

If you want different parameters to be estimated for the different individuals, then you could fit a separate model to each (e.g. with a loop, as you suggest). If you are mostly interested in individual heterogeneity in the behavioural dynamics, you could also include the ID as a "fixed effect", i.e. as a covariate in the transition probabilities. For example, using the argument formula of fitHMM, you could estimate different transition probabilities for each animal, using

formula = ~ animalID

Here, animalID is a column of your data, which identifies the individual animals. You could do something similar to estimate different covariate effects for the different animals, with something like

formula = ~ animalID * temp

With this interaction term, the effect of the covariate temp on the transition probabilities is estimated separately for the different individual animals.

Unfortunately, random effects are not available in moveHMM. A few papers have used random effects in HMMs for animal movement (McKellar et al., 2014; Towner et al., 2016; DeRuiter et al., 2017), but you would need to use custom code to implement them.

I hope this helps; please let me know if anything is unclear.

Théo

References:

• McKellar et al. (2014). Using mixed hidden Markov models to examine behavioral states in a cooperatively breeding bird. Behavioral Ecology, 26(1), 148-157.
• Towner et al. (2016). Sex‐specific and individual preferences for hunting strategies in white sharks. Functional Ecology, 30(8), 1397-1407.
• DeRuiter et al. (2017). A multivariate mixed hidden Markov model for blue whale behaviour and responses to sound exposure. The Annals of Applied Statistics, 11(1), 362-392.

[bniebuhr]

Hi, @TheoMichelot ,

thanks a lot for your answer. Yes, considering the animal ID as a fixed effect is a good idea for the "no pooling" I mentioned, and considering the differential effect of covariates in different individuals using the argument formula is a great idea. Thanks for that!

Thanks for the additional literature, also.

I'll make some tests here and I tell you if I find any problem.

[TheoMichelot]

Following from @windstorm13's related question (#15), I realised that the code that I suggested was incorrect.

The animal ID is a categorical covariate and, in moveHMM, it should be included using dummy variables. That is, for K individuals, K - 1 binary variables need to be included in the data set. Each takes value 1 if the row comes from the corresponding animal, and 0 otherwise. Then, the K - 1 dummy variables should be included as covariates in the model.

Sorry about the confusion.

Théo

[bniebuhr]

Hi @TheoMichelot

Thanks for adding that to the answer. However, I didn't get why one would need so many dummy variables instead of a single categorical factor representing individual ID (which, as I understand, would define the same number of parameters). Maybe in general lmand glm, this trick of transforming categorical into dummy variables is already implemented, but it need to be addressed explicitly in moveHMM?

Anyway, in this case, the formula would be something like formula ~ K1 + K2 + ... + Kn-1?

Thanks Bernardo

[TheoMichelot]

Maybe in general lm and glm, this trick of transforming categorical into dummy variables is already implemented, but it need to be addressed explicitly in moveHMM?

Yes, that's exactly right. The problem is that moveHMM doesn't deal with categorical covariates automatically.

The formula would look something like what you suggest, if you wanted to estimate different transition probabilities for the different individuals.

Best wishes, Théo