New Treatments as Random Effect

To make sure everyone fully understands the concepts discussed so far and their applications, let's restate a key piece of what we had said earlier.

- Fixed effects are factors where all the possible levels are included in the study (experiment), whereas random effects are factors where only a subset of all possible levels of the factors are included in the study.

If we think deeper, about Jennifer's data, it can be debated whether we want to treat the new entries (the plant varieties) as fixed or random. Previously we considered that the new Entries were fixed based on the underlying assumption that all the new entries that we wanted to test have been included in the experiment.

However, if we were to say that the new entries which we have included in our experiment are only a portion of all possible new entries (all possible, meaning all new plant varieties that the scientists have developed) - in that case we must treat the new entries as Random Effects.   Keeping that in mind, let's add two additional columns i.e.  'entryc' and  'new'  to Jennifer's dataset that we are working with. The reason to add these two columns is to be able to accomplish the following:

1. Group all the new entries in a single pool, yet treat all checks as separate (Column 'entryc' ). This allows us to treat this factor (control plant varieties) as fixed.  We can use this column to see if there is any difference among the checks and the collective means for the new entries. 
2. Divide the data set into two groups with one group being new entries and one group being checks (Column 'new' ). 

We will follow this video to see how this is done

Click here to download the source of the R script used in the talk

Click here to download an example data file that may be used along with the Script

Recall that our domain scientist, Jennifer, is wanting to determine relationships between TSW, Entry, and Block; and after adding the new columns the relationship with entryc and new.

Now we will define our Mixed Linear Model as:

TSW ~ entryc +(1|Block) +(1|Entry:new)

Again we have defined our new model into a notation that R understands as a linear mixed model.  Specifically, we are telling R that we have both a fixed effect and a random effect: TSW depends upon entryc being treated as fixed and that Block and the interaction between Entry and new are being treated as random effects.

Again random effects are signified in the formula with the factor surrounded by a parenthesis and prepended (prefixed)  by "1|" (i.e. one and a vertical bar).