Random effect in the model

Modeling
1

Please share your Stan program and accompanying data if possible.

Hi, all,
I’m doing an analysis of the influence of different factors (neighborhood crowding and soil) on tree growth across the disturbance gradient. Now I have the data of ten 1-ha forest plots, which have different disturbance intensity. In each plot, individuals have been censused twice.

  1. Tree growth was calculated by the difference of DBH (diameter at breast height) between two censuses.
  2. Neighborhood crowding was calculated by the sum of the basal area of neighbors (within 10m) around each individual
  3. Soil effect was based on the soil nitrogen that collected from the 20m quadrat in each plot.
  4. Disturbance intensity was calculated for each plot

Following is the structure of two types of models. One has two random effects of individual and plot, which is the tag number for each individual and the name of each plot, respectively. The other one didn’t include any random effect.

1. Random model 
  Growth = b0+b1 * size + b2 *  Neighborhood+ b3 * Soil+ b4 * disturbance+
           b5 * Neighborhood * disturbance+ b6 * soil * disturbance+ 
           ind+plot  

2. Nonrandom model 
  Growth = b0+b1 * dbh+b2 *  Neighborhood+ b3 * Soil+ b4 * disturbance+ 
           b5 * Neighborhood * disturbance+ b6 * soil * disturbance

I read some paper in forest ecology,

  1. the author will include the individual as a random effect when there is repeated growth data for the same individuals(e.g. there are more than twice censuses). However, I only have twice census data, that is, each individual only has one growth data.
  2. Here, I assign a specific disturbance intensity to each plot. So whether it is correct to include a random based on the plot names?

Now I’ a little confused. Should I include the random effect of the individual and plot in the model, or should I just use the nonrandom model?

Thank you so much!

2

I think there’s quite a few people on the forums here who are very well versed in hierarchical/random effects/mixed effects/whatever your field calls it modeling, but I’ll offer my 2 cents as well. One of the benefits of Bayesian modeling is there really isn’t a limit to how many levels of hierarchy you can add to the model, provided you can properly constrain the model with data or weakly informative priors. I think that if you suspect a need to include a hierarchical structure on any coefficient because of repeated measurements on an individual, spatial or temporal data clustering etc go ahead and do it. Then look at the posterior estimates of the standard deviation of the varying coefficients; if they are small then the hierarchical structure probably isn’t necessary.

3

Nice to see another tree person around here!

From what you are saying, it doesn’t sound like you really have repeated measurements here, since your response is actually growth increment, not DBH. If you had a lot of repeated measures of DBH you could set it up as a time series and model an individual DBH increment effect hierarchically as a function of time increment, but that doesn’t sound like your data.

On the other hand, it would make sense to me to build a hierarchical model (what you are calling random effects), with some effects entering at the plot-level.

So I am assuming that for each 1-ha plot there is a single soil nitrogen measurement and disturbance intensity measurement that are associated with all stems in that plot? If that is the case, I think I would add at least soil nitrogen as an intercept-level predictor in the model. Disturbance intensity is a little trickier, since depending on how it was measured you might choose to include it as a categorical or continuous variable. That could impact how you incorporate it into the hierarchical model.