Which error option to use if individual is a random effect?

[HendrikSchultz]

Hi Brian,

I am using the MixSiar package to estimate diet proportions in a seabird. I have 68 consumer individuals some of which have been sampled once, twice and three times adding up to approx. 100 samples. I have 6 resources 3 of which I have grouped a priori resulting in 4 sources. I use a two tracer system (d13C, d15N).

I would like to test for sex differences and have therefore included 'sex' as a fixed effect. Since I have multiple samples from some individuals I have included 'individual' as a random effect.

My question is: would it be appropriate to use the multiplicative (process and residual error option) since some individuals have multiple data points or would it have to be the process error only option?

I have tried both options and both my models converge, but dietary proportion estimates vary slightly.

Thank you very much in advance for your advice!

Kind regards,

Hendrik

[brianstock]

An isospace plot would help - somewhat dangerous to recommend model structure without looking at the data.

Sex as fixed effect + Individual as random effect seem like good choices. Re: error models, the question is about the variability within individuals. Either way you get diet proportion estimates for individual birds. The "process error only" model assumes the variability within individual is determined by the proportions and source + TDF variances (for each tracer). The process*residual error model allows for more/less variance within individual. It sounds like you have ~30 "repeat" samples, and that these are enough to estimate the epsilon terms (the model converges). If that model converges I would tend to go with it for the reasons outlined in https://esajournals.onlinelibrary.wiley.com/doi/full/10.1002/ecy.1517.

Are the error terms (epsilon) estimated near 1 or < 1? That'd be my expectation with Individual already included. If they're not, would be looking closer at the data... lots of unexplained variability would indicate that Sex + Individual does a poor job of explaining diet proportions.

[HendrikSchultz]

Hi Brian,

Thank you very much for the prompt and very helpful response.

The epsilon values are 0.4 and 0.2 respectively, which if I understand right suggests that sex and individual do a good job at explaining variability in the data. On closer inspection of the diagnostics I did notice that one of three chains did not pass the geweke diagnostic (appx. 10% out rather the expeced 5% alhthough Gelman looks fine. I will rerun the model under a longer setting and see if this fixes it. If it doesn't I will use the process only option.

With respect to the isospace plot I hope you don't mind if I send it to you via email along with some more detail about my data.

Again thank you very much for your swift response, very much appreciated!

All the best Brian and have a good day!

Hendrik