Cui Yang writes:

I have a question about the use of BRT (Boosting regression tree). I am planning to write an article about the effects of soil fauna and understory fine roots on forest soil organic carbon. The experiment was conducted in a subtropical forest area in China. There were 16 blocks each with 5 coarse-mesh nylon bag wrapped and 5 fine-mesh nylon bag wrapped soil cores throughout four forests (forests A/B/C/D). Each forest had four different blocks. The coarse mesh (4 mm) bags allowed the access of both the entire soil fauna and understory plant fine roots. The meshes of fine bags were on the whole 0.038 mm, except that a row of 4 mm holes were distributed evenly at the lateral side and a circle of 4 mm holes at the circumferential bottom. Ideally, we supposed that this kind of fine bags could allow the access of most of soil fauna through 4 mm holes, while getting rid of the roots by the overall 0.038 mm meshes.

Originally, the dataset generated from this experiment should be 160 pieces of record constituted of soil total carbon, dissolved organic carbon, microbial biomass carbon plus soil fauna abundances and fine roots biomass. The soil fauna data was of coarse taxonomic resolution and mainly included six abundant fauna taxa, i.e., Acari, Collembola, Hymenoptera, Nematode, Enchytraeid. For fine roots data, parts of records in forests B (18 records) and C (17 records) were missing because of faulty operation. As a result, fine roots biomass had records at only 78% soil cores.

Because BRT can handle missing data in predictor variables by using surrogates, I decided to use BRT to determine the relative influence of predictor variables on the individual response for soil carbon, especially for the abundant fauna taxa and fine roots. So, can BRT be applicable to the abovementioned dataset, which only has 160 records and one of its main explanatory variable covers less than 80% records?

I have sent a similar mail to Professor *** who advised me to read your book “Data Analysis Using Regression and Multilevel/Hierarchical Models” for the resolution. Since my data are structured (samples within blocks within forests), a generalized linear mixed model will be suited. But I am worrying about that, while removing the records with missing data about fine roots, the experimental design would be an unbalanced one and at the expense of less useful data of other variables such as soil carbon and soil fauna taxa. Upon the unbalanced design, I will use Redundancy Analysis as a tool for multivariate ANOVA. Through RDA, I might select the several most influential fauna taxa probably with fine root. After this action, I would use Variation Partitioning to quantifying the variation explained by these factor. However, I am puzzled that, should the model used by RDA involve the effects of mesh size of nylon bag (fine mesh versus coarse mesh) and blocks factors or as well as forests? I am mainly using software R for statistical analyses. If the alternative of BRT is RDA, how can the model of RDA involve the data structure which seems to be a split-plot design? I feel that it is difficult to use functions such as adonis {vegan} in R to define the data structure of split-plot designs, especially under the condition of unbalanced design. What’s worse, my focus is the effects of soil fauna and fine root instead of mesh size/blocks factors/forests.

My reply:

You write, “BRT can handle missing data in predictor variables by using surrogates.” But any method for prediction can handle missing data by using surrogates, no? Or maybe I’m missing something here. In any case, here are some general comments:

– If your missingness is only in the outcome variable, then just fit a multilevel model, no problem.

– If some of your predictors have some missingness, I recommend imputing the missing values first using some multivariate imputation method. We have an R package “mi” to do this, but other options are available too.

– Unbalanced data don’t present any difficulty; indeed, multilevel models are well suited to unbalanced data. Unbalanced data is one of the main motivations for fitting multilevel models.

– Similarly, you’re fine with any mix of nested and non-nested factors. Split-plot is fine too, the multilevel model will handle it automatically, as discussed in my 2005 paper.

– Once it’s time for you to fit your multilevel model, I recommend you use Stan. In my book with Jennifer we use lmer, but now I use Stan. We just haven’t updated the book yet.