Is linear regression the best method for these data?

Question

Background: I’m looking at harbor seal weights by year to understand trends over time. Each year represents a distinct pupping season (May-July) so I treated year as a categorical variable to avoid seeing declines in seal populations in other months. Each individual is only measured once (not measuring same individuals year after year). I'm interested in describing the data rather than predicting. I fitted linear models as such:

model<-lm(weight~(as.factor(year)),data=seal)

This gives me an output of parameter estimates for each year, which is helpful in understanding trends over time. However parameter estimates are in reference to the intercept, 2005, which has no biological significance aside from being the first year of data collection.

My question is, did I perform the "best" test to help me understand trends over time? Or is there another test that allows me to regress continuous data on a categorical variable without using any level as a reference? (Or if such a thing is illogical, and references are always required...)

Also, I’ve performed numerous t-tests to compare years, but I was curious if there was a method that compared >2 levels at once in absence of a reference.

Answer 1

You have effectively run an ANOVA. If you want to see whether there are differences across years without the intercept, then you should just be able to wrap your fitted model in the anova() function like this: anova(model).

There's not going to be a right answer to this because what statistic you use ultimately is informed by what question you want answered. If you don't want to do prediction, then maybe framing things as a regression is not needed. If you don't care about differences between years but want to know trends, then ANOVA is probably not "correct". That ultimately is up to you and your research question, though.

I would just point out that I'm not sure that you can ignore any dependency from year to year. In other words, I think it's a hard sell to say that weights in 2006 are independent from weights in 2005. I get that you aren't measuring any of the same seals from year to year, but the seals still live in the same environment and are going to be impacted by that. The current method, to me at least, seems like a tough argument that years are totally independent from one another. If you are doing this at multiple sites, then you'd also probably want to be considering clustering and transition to a multilevel model. Similarly, there may be reason to think that there is a non-linear relationship between time and weight. For example, I would imagine that weights have some general (albeit soft) upper and lower limits for seals, and I can see how maybe an exponential function in time could help capture the dynamic nature of the ecosystem and weight. All this said, I'm 100% unfamiliar with modeling these kinds of things, so I wholly recognize that I could be barking up the wrong tree here. Just wanted to through out some of these thoughts because I think that modelling makes more sense when you're thinking about the data generation process (i.e., what potentially measurable things combined to give the data you have observed)