Below is a hypothetical example of how my data looks like in excel. My actual data has 16 sites and each site has about 10 plots, so its a huge dataset). Plots are nested within Sites. I would like to know if there is a difference in tree density among the land use types. Can I use linear mixed model by setting 'Site' as random effect and 'Land use type' as fixed effect.
Site.........Plot number............. Land use type..........Tree density (trees/hectare)
1................1..............................Cropland......................12
1................2..............................Woodland.....................20
1................3..............................Grassland.....................5
2................1..............................Grassland.....................4
2................2..............................Cropland.......................1
2................3.............................. Woodland....................10
..................
n..................
Your approach looks basically ok. But the devil is in the details. Possible pitfalls are heteroscedasticity and that site effects are not additive (E.g. you assume that in site 1 there are 10 more trees per ha than in site 2. If site 1 has on average double the trees your assumptions are not right). Another issue that you have is heteroscedasticity (Land use types with a high density of trees will have higher variances than land-use types with a low tree density). Transformations or weighting of the data may be needed to address these issues.
Ditto what Berninger said, but add to Berninger's answer that count data is likely to be long tailed and therefore non-normal which is another reason transformation is most likely recommended. Select from among the Box Cox transformations:
Transformed Response = (Y^a - 1)/a, 0 < a < 1
a=0 (limit as a -> 0) is log(Y)
another common choice for count data is Y^0.5 which is of course a=0.5
If this is count data I'd use a linear mixed count model (Poisson, quasipoisson or negative binomial) - possibly with an offset. However if it is a density or rate then you'd need a transformation or a different form of GLM. Sixteen sites is at the low end for linear mixed modelling but probably OK.
Hi, Evans,
I fully agree with Thom.
May add that You use rate (trees/hectare) , so tray to use logarithm link function for GLMM.
Interpretation of coefs is (exp(beta)-1)*100 is percent change in DV (rate (trees/hectare).
Hi Evans, I agree with Prof. Frank. As you mentioned, you have a nested design and count data per plot. In case of count data, you can use generalized linear mixed-effects models (GLMM) with log-link function as suggested by Olga and Thom, instead of linear mixed-effects models. GLMM accounts for poisson/quasipoisson distribution of data (count data).
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