How to treat year variable in observational longitudinal data analysis?

Question

I have a huge multilevel longitudinal observational data of the concentration of certain chemical collected at various sites over 10 years (1990-2010). Sites are classified into different type of sites as A, B, and C. In the dataset year variable is coded as 1990,1991, 1993 etc. At one year, there can be many sample collects at 1 site. It is not like there is only 1 data point at 1 year period per site (like many experimental longitudinal data where there is repeated measurements per 1 subject and there is only 1 data point at each time point). Some sites have also but shut down over the years but I am grouping them together into groups because I am not interested in individual sites.

str(data)

data.frame': 60,000 obs. of 22 variables:

$ ID          : int...   3453, 3492, 4385
    $ SiteID      : Factor w/ 15000 levels "1234","1235”, “1236”, ecttg
$ Year        : int  1993 1993 1993 1993 1993 1993 1993 1993 1993 1993 ...
    $ NewCom.Group: Factor w/ 5 levels "A”,  “B”, “C",..: 1 1 1 1 2 
$ NewLoc.Group: Factor w/ 3 levels "","Type1",”Type2 “,..: 1 2 1
    $ NewJobGroup : Factor w/ 4 levels "Production",..: 4 2 4 2 2
$ NewIndJob   : Factor w/ 109 levels "TramOp",..: ..
    $ Log.conc : num  -0.5978 -0.0726 -0.7765 -1.1712 -1.273 ...
$ Log.Qconc   : num  3.5 3.14 3.76 2.89 3.09 ... 

I would like to see if the concentration has decreased over the years and by group.
My mixed model looks something like this:

Model.1 = lme(log.conc ~ Year + NewCom.Group, random=~1|siteID, data=data)

My question is how should I treat Year variable to answer the question of concentration over years.

1. Should I recode year as 1, 2, 3, 4 and leave it as continuous

2. Should I recode year as 1, 2, 3, 4 and make it categorical, Time <- factor(Time)

3. Leave the year as it is and treat it as continuous variable (Is this the same as in 1?)

4. Make it categorical, Year <- factor(Year)

I just want to make sure that the model does not compare the concentration of subsequent years the first year only.
What does each of those option imply in the interpretation of the output?

Answer 1

The only difference between the results for approaches (1) and (3) is that the intercept of your model will be different. Regression puts a line through the mean of the outcome and of every predictor; since the mean of 1990--2010 is different than the mean of 1--21, the intercept has to shift to make the regressions go through these points.

The only difference between the results for approaches (2) and (4) is the labels that will be attached to your output---1--21 or 1990--2010.

Typically, we follow approach 2/4. This strategy permits a different "effect" for each year (a "fixed effect"). In contrast, approach 1/3 assumes that the expected difference between 1991 and 1992 is the same as the expected difference between 2001 and 2002 (a "linear time trend").

We might prefer the linear time trend if we don't have very many observations (we only have to estimate one slope, rather than 20 fixed effects coefficients), but that doesn't sound like a problem for you.

We could go beyond the linear time trend model and allow each site to have its own linear time trend by using approach 1/3 with a random effect on the time variable. I think that fixed effects are easier to work with, though, and generally prefer them. (Note: there are some cases where fixed effects cannot be used alongside other variables in your model, in which case I would use random effects. This doesn't appear to be a problem for you.)