I have a 30 year dataset of fish sampling. I know from previous analyses that there is a huge amount of variation between years in catch rates. What I would like to do is create a plot that shows the average catch rate for each month that was sampled for a single species after removing this inter-year variation.
I started by just taking the average for each month and using that, but the amount of inter-year variation creates huge error bars, so it's not clear that anything is happening. I thought about scaling everything so that all within year catch data was presented as a proportion of the maximum monthly catch rate, so trends would appear as percentage changes rather than the absolute value, but in a given year samples weren't collected for every single month; so I don't think this would work.
Is there a statistical test which would allow me to do this? I thought about a GLMM with year as a random effect, but I don't anticipate there being a linear increase in catch rates over time. Would an ANOVA with year as a random effect and month as a categorical variable work?
I think Linear Mixed Models would still be your best bet.
For one because you can also model changes that do not follow a linear increase (what are your hypotheses, concerning change?).
Additionally, you already stated, that you have missing data in the form of monthly catch rates. LMMs can reliably deal with missing data casewise, whereas ANCOVa (if I remember correctly) will discard data listwise.
In general, it might be a good idea to rescale your catch rates on the basis of the yearly catch rates as you suggested. Have you thought about imputation for solving your plot issue?
Why would you want to remove the variation? It is probably a true effect. The large error bars sort of capture this by telling you that the year you go fishing may be just as important, or more important, than the month you go fishing. This is just a guess on my part, I don't know what the underlying hypothesis is.
Thanks for the feedback! To clarify this is less about hypothesis testing and more about providing descriptive plots that show how the abundance of a given species is changing seasonally. For example I'm interested in showing how species exhibit seasonal changes in their preference for sites with artificial reefs (see attached plots for rough examples). I'd like to remove the noise resulting from inter-year variation so that I can shrink those error bars and make the seasonal trend more obvious. I've already highlighted the fact that year has a large impact on abundance, so I don't see any benefit to including it here.
LMMs still want to fit a trend line through the data though, right? I don't need that for my purposes. Some species may show linear patterns, quadratic, sinusoidal or something else entirely. It's more about showing the patterns of seasonal change.
Hi Dugan, I am always happy to try to help a fellow Canadian. I was not referring to hypothesis testing in the statistical sense but rather in the sense of what point are you trying to make. As I said before, the error bars are telling you that the seasonal effect is perhaps less significant than the annual trend. If you have reason to believe the trend is important, even though it is hidden by the data, you could follow up on Sven's idea and try to scale your data to make it relative within a year and that might shrink the error. In other words, instead of comparing May 2019 to May 2020 compare May 2019/January 2019 to May 2020/January 2020 (obviously the months are just an example).
Unfortunately I do not know much about LMMs so I can't help you there. It does seem that you don't need to fit a curve if you are just looking for a descriptive graph.
Greg
I totally agree with Greg, however my idea of scaling was to use year's mean catch rate and calculate the difference for each month from the yearly mean. You could also incorporate the sd to get z-values and thus obtain a value that can be reliably compared between years and species.
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