Correctly specifying temporal pseudo-replication in a mixed effects model in R/nlme

Question

I would like to correctly specify that my data is temporally pseudo replicated in a mixed effects model in R using lme() of the nlme package. I have done this following the example in Crawley's R text book, but I need some confirmation that the fixed and random effects are specified correctly. I have checked previous postings on similar questions and I see conflicting information. Hence, I decided to ask specifically on this forum. Also, included in the model is a covariate controlling for spatial structure, and I would like to confirm that it should be a fixed effect.

The structure of my data: The response variable is turnover in species composition (Tsc) between two censuses in 26 transects in a tropical forest. Transects are grouped based on their logging status into four levels (unlogged, lightly logged, moderately logged, and heavily logged). There are three time intervals for which turnover was computed (0, 7, 14). Transects of the same logging status occur in the same location, so Latitude is included as a covariate to control for logging status. My interest is in the effect of logging status and time on turnover.

The model I constructed following Crawley's R text is as follows:

m1<-lme(Tsc~Logging.status*Time.interval+Latitude, 
        random=~Time.interval|Transect, data=mydata)

My questions:

• Is it right for Time.interval to be in both the fixed and random effects? How do I correctly specify that each transect has repeated measures for three time intervals?
• Should Latitude be a random effect since I am not really interested in it per say, but only need it to control for spatial structure?

Answer 1

This is just a general comment on pseudoreplication discussions.

Many of the discussions and queries regarding pseudoreplication in the current literature and on the internetrefer only my initial 1984 paper and seem unaware of many later clarifying papers by myself and my colleagues that focus partly or completely on the topic. These are listed below. Pdfs of most of these can be accessed at my university website, at http://www.bio.sdsu.edu/pub/stuart/stuart.html

Reading of these may be helpful to researchers. It is regrettable that confusing or simply fallacious re-definitions of the “sin” are so prevalent in articles, books, and on the internet. Be careful who you accept as your “statistical gurus” and of all that you see on the glossy pages of “reputable” journals!

Hurlbert, S.H. 1990. Pastor binocularis: Now we have no excuse [review of Design of Experiments by R. Mead]. Ecology 71: 1222-1228.

Hurlbert, S.H. and M.D. White, 1993. Experiments with invertebrate zooplanktivores: Quality of statistical analyses. Bulletin of Marine Science 53:128-153. PDF

Hurlbert, S.H. 1993. Dragging statistical malpractice into the sunshine [Citation Classic: Pseudoreplication and the design of ecological field experiments]. Current Contents 1993:18.

Lombardi, C.M. and S.H. Hurlbert, 1996. Sunfish cognition and pseudoreplication. Animal Behaviour 52:419-422 PDF

Hurlbert, S.H. and W.G. Meikle. 2003. Pseudoreplication, fungi, and locusts. Journal of Economic Entomology 96:533-535.

Hurlbert, S.H. 2003. On misinterpretations of pseudoreplication and related matters: a reply to Oksanen. Oikos 104:591-597. PDF

Hurlbert S.H. and C.M. Lombardi. 2004. Research methodology: experimental design, sampling design, statistical analysis. In M.M. Bekoff, (ed.), Encylopedia of Animal Behavior, 2:755-762. Greenwood Press, London. PDF

Kozlov, M. and S.H. Hurlbert. 2006. Pseudoreplication, chatter, and the international nature of science. Journal of Fundamental Biology 67(22):128-135. [In Russian; English translation available as pdf]. PDF

Hurlbert, S.H. 2009. The ancient black art and transdisciplinary extent of pseudoreplication. Journal of Comparative Psychology 123:434-443 PDF

Hurlbert, S.H. 2010. Pseudoreplication capstone: Correction of 12 errors in Koehnle & Schank (2009). Department of Biology, San Diego State University, San Diego, California. 5 pp. PDF

Hurlbert, S.H. 2013. Pseudofactorialism, response structures and collective responsibility. Austral Ecology 38: 646-663. PDF + suppl. inform. PDF

Hurlbert, S.H. 2013. Affirmation of the classical terminology for experimental design via a critique of Casella's Statistical Design. Agronomy Journal 105: 412-418 + suppl. inform. PDF

Hurlbert, S.H. 2013. [Review of Biometry, 4th edn, by R.R. Sokal & F.J. Rohlf]. Limnology and Oceanography Bulletin 22(2): 62-65. PDF