My question relates to my previous question about GAMMs (if some of the same people should read this).
I am working in R with the package mgcv and the function gam.
My data:
A lot of bacterial samples (isolates) taken over time from different patients. For each sample/isolate I have some continuous, binomial, factorial data describing different traits of the isolates.
I have tried:
Initially I was only interested in the correlation with time and had a continuous trait as the predictor and time as explanatory with patient as a random smooth with time.
My question is:
For now I want to input this information into a single GAMM for each of the traits to see correlations with time AND all the other traits (I am inputting patients as random smooth together with time).
Do I need to treat my data as time series data or can I simply input time as an explanatory variable together with everything else?
Before I began doubting my method I used the following code:
(trait1 to trait4 are continuous and trait5 and trait 6 are binary -I have more variables than this)
gammTrait1
Good morning Lea,
This is a pretty well known phenomenon in econometrics time-series analysis [ Charles Nelson and Charles Plosser (1982); Granger's and Engle (1987) ]; not sure if anyone really reported this as a serious problem in toxicology. Basically the time series data is endogenous and will have high correlations because the errors are correlated over time. So OLS/GLM assumptions aren't quite met. I don't remember that much about GAMM from the top of my head, but I think it can parse out subject/group variability and maybe you can use a mixture of distributions, but i'm not sure if it has options to deal with serial correlation in the data. So what you are seeing can quite well be a great example of spurious correlation. Something is happening to all the biological samples over time (i.e. they might be growing) and a lot of output are changing in with the growth. However, this "growth", or whatever temporal effect it might be, obscures the true relationship between the individual predictors. Typically you'd try to co-integrate the data to assess the exact relationship between the various parameters after "removing" the effects of time.
If this is helpful, i can try to write more later.
Thank you Fjodor, it is helpfull, and I would be very happy if you could elaborate.
As far as I am aware GAMMs can (in the same way as GLM, i think) handle serial correlation... But I am very new to this method and I might be wrong.
The thing is, I would very much like to handle time as any other variable, to see if e.g. growth correlates with time, but also all the other variables, without looking at time per se (I guess this is where the co-integration comes in). As I can see at the moment I have inputted Patient as a random smooth with time, so that in essence I have Patients as random intercepts and slopes of time. I thought this might help reduce the time influence on all the other variables?
Do you know if there is a way to plot this or in anyway see if there is serial correlation?
I will try to read up on the co-integration of the data and see if this changes my results. However, I am not so sure how much this effects my analysis in the sense that there is biological reasoning for the correlations that I do find, and I also find correlations between variables without them correlating with time.
Thank you,
Lea
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