I need some help deciding whether my sample collection design qualifies as nested or crossed. The design is: I collect data once per site (at the same 47 sites), once per season (wet and dry; May-Nov and Dec-April), i.e. 2 times per year (~12-10 days a year). This is the ideal situation. Due to factors such as tides, bad weather, or just human error, some data gets lost or sampling efforts aren't repeated on exactly on the same days as the previous years.
When I build a model for my response variable, I know I need a random effect for my location (site) effect to capture within site variability and avoid pseudo-replication. My question is: if I want to use the full dataset, does my site variable also technically count as being "nested" within my year variable? I'm using "season" instead of "Month" to capture seasonality as well, since the month data is irregular spaced and contains large gaps.
One example of nested data I've heard: If one set the I.D. of hospital patients to be labeled 1-10 (equivalent to my site variable) and a hospital variable to be A-C (similar to my year variable), it's ambiguous as to which patient belonged to the right hospital. Patients are nested within hospitals, I believe. Does my data present with a similar problem? I realize in this example, the patients, labeled 1-10 in each hospital, are actually different people, but would anyone subscribe to the idea that "you never sample the same body of water twice"? I'm entertaining this idea because some sites are adjacent to freshwater canals while others are get influenced by ocean water on a slightly irregular basis. My thinking is that this could translate to different effects on my response variable within the same site, year-by-year.
Or, for all intents and purposes, they are the same sites each year (with some variability), but it's still a nest design because some sites are missing in certain years? Am I over complicating this? - probably. Just trying to be thorough.
Below is a table of the number of sites per year (note, not all years have the full 47 x 2 number of replicates):
> table(df$Month, df$CYR) 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 1 47 47 47 47 47 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 20 0 0 0 9 3 0 0 0 0 0 47 39 30 24 43 27 47 47 0 38 4 0 0 0 0 0 0 8 17 23 0 0 0 0 0 0 7 47 47 47 47 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 47 0 30 0 0 0 0 0 0 0 0 9 0 0 0 0 0 47 17 47 47 0 47 47 47 47 47 10 0 0 0 0 0 0 0 0 0 47 0 0 0 0 0 # Distribution by season...(note 2017 and 2021) > table(df$Season, df$CYR) 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 DRY 47 47 47 47 47 47 47 47 47 43 47 47 47 0 47 WET 47 47 47 47 47 47 47 47 47 47 47 47 47 47 47 
siteas random andyearas fixed. There may be a cyclic effect of the seasons throughout the year, but the effect of time is still fixed. So the answer is neither, you have only one random effect. $\endgroup$