Small sample size and the number of covariates
Joanna Wu
I'm currently in the phase of study design and want to understand whether there is a general rule of thumb for how many covariates you can analyze given n sample size. We will likely have a small number of sites, <20, that will be visited 3 times in one year. Any thoughts on how many covariates, if any, we might be able to look at? How can this change if we were to boost the number of sites?
Thanks,
Joanna
Kery Marc
Dear Joanna,
Generally, I would use similar rules of thumb as for regression modeling (e.g., 5-20 data points per parameter), but:
- Remember that there are two n's in hierarchical models as say a site-occ model: one for sites and one for observations. Hence, you have much more information to estimate covariates that act on p than covariates that act on psi
- You should perhaps have more sites per parameter for site-specific covariates in psi than according to any regression rules (e.g., 5-20 or whatever you choose), because you are estimating a regression on these covariates of an on- or only partially observed thing: the true presence/absence
One of the best ways of answering the "how many" questions such as yours is always to use simulation: simulate data sets of different size, analyse them with different numbers of covariates and save the estimates. Repeat for 1000 times and see how things vary as a function of sample size etc.
Kind regards --- Marc
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Joanna Wu
Thanks very much for your response. That is a great suggestion to do some simulation to figure out sample sizes. However, I am a beginner to Unmarked. Can you point me to any links or examples of how to do this in R that is relevant to site covariates?
Best,
Joanna
Kery Marc
Dear Joanna,
attached is a modified book draft chapter that shows how you can simulate occupancy data. Hopefully you can go from there.
Regards --- Marc
______________________________________________________________
Marc Kéry
Tel. ++41 41 462 97 93
marc...@vogelwarte.ch
www.vogelwarte.ch
Swiss Ornithological Institute | Seerose 1 | CH-6204 Sempach | Switzerland
______________________________________________________________
*** Hierarchical modeling books ***
(1) Kéry (2010): Introduction to WinBUGS for Ecologists, Academic Press; see www.mbr-pwrc.usgs.gov/pubanalysis/kerybook
(2) Kéry & Schaub (2012): Bayesian Population Analysis using WinBUGS, Academic Press; see www.vogelwarte.ch/bpa
(3) Kéry & Royle (2015): Applied hierarchical models in ecology, Academic Press.
*** Hierarchical modeling workshops: www.phidot.org/forum/viewforum.php?f=8
*** Hierarchical modeling Google Group mailing lists ***
(1) unmarked: for questions specific to the R package unmarked
(2) hmecology: for material covered in Royle & Dorazio (2008), Kéry & Schaub (2012), Kéry & Royle (2015); see groups.google.com/forum/?hl=en#!forum/hmecology
Joanna Wu
-Joanna