Your model-runs in each location, although "pseudo-replicated", constitute your local effects. Then your effects across each landscape are the "replicates". You can use GLM or PERMANOVA, with locations nested in landscapes. Don't worry about "pseudo-replication" too much since you have true "replicates" as well. "Pseudoreplication" is just another term for local effect!

At what scale is your bee abundance measured - if local I see no problem in using a multilevel model for counts - the replicated landscape variable is just a variable that is measured at the higher level - standard multilevel practice. See Chapter on higher level variables in this

Book Developing multilevel models for analysing contextuality, he...

The analysis of count data and explicitly spatial model is considered in volume 2

Book Developing multilevel models for analysing contextuality, he...

Simple solution: If you want to check non-independence, calculate ICC 1 for the outcome variables. If ICC values are less than 0.5 and also non-significant, non-independence is not the issue in your data. Then you can run the analysis on individual level.

Bliese, P. D. (2000). Within-group agreement, non-independence, and

reliability: Implications for data aggregation and analysis. In K. J. Klein

& S. W. J. Kozlowski (Eds.), Multilevel theory, research and methods in

organizations: Foundations, extensions, and new directions (pp. 349–

381). San Francisco, CA: Jossey-Bass

Kelvyn Jones the bee abundance was measured at a local scale. Thank you for providing references. I will have a look at these.

Andrew Paul McKenzie Pegman thank you for your response. I like the simplicity of this option :). Just to confirm that I have understood your recommendation correctly, is the following how you would set up the model?

bee abundance ~ (local var. 1 | landscape identity) + (local var. 2 | landscape identity) + landscape var. 1 + landscape var. 2 + landscape var. 3

Thank you!

Muhammad Usman thank you for your response! Just to clarify, what do you mean by running the analysis on an individual level? Would you be able to give an example of how the equation might look? (e.g. bee abundance at local scale ~ local var. + landscape var.)

Kelvyn Jones I had a look through the references you provided. The example given in Chapter 8 (volume 1) on modelling with higher-level variables looked relevant to my case; the examples in Volume 2 less so as I am not worried about geographical position of landscapes having a strong effect. However, I got a bit bogged down in the details of using MLwiN, as I am not familiar with this program (I usually use R).

Would you be able to explain, in a general way, how the equation in my case should be arranged? For example, are you saying that I can arrange the model like this, without worrying about pseudo-replication of the landscape variables?

bee abundance at local scale ~ local var. 1 + local var. 2 + landscape var. 1 + landscape var. 2

Thank you!

Yes but you will also need the unexplained random term at each level. I presume you will be using something like a Poisson or NBD if the data is a count or Bernoulli if presence/absence, if that is the case the variance at level 1 is not estimated as a separate parameter (as in the Normal theory model) but depends on the mean of the fixed part - see Volume 2.

Yes, that looks correct :)

Dear Margaret Sawatzky,

For instance if you want to see relationship between ethical leadership and learning and have collected data from employees working in 55 organization. First, I would check it for non-independence, before deciding the level of analysis. For non-independence, calculate the values of ICC1 just for the outcome variable, learning. If ICC value is < 0.05 and nonsignificant, you can do the analysis at the individual level. But in case ICC1 > 0.05 and significant, then check the data for aggregation and calcultate ICC1s and ICC2s for all the variable in the study. Signficant values of ICCs would mean aggregation of the data at the firm level and using HLM.