Model structure for RCBD, split-plot repeated measures mixed effect in lme4 and glmmTMB

Question

As the title says, the experimental design for one of my projects is giving me some real data analysis headaches. I’ve got a blocked experiment (n=13) with 8 plots/block. The blocks are treated with the full factorial combination of three treatments, each treatment having two levels (control and treated). Additionally, the blocks are split with a fourth treatment applied to a randomized half of every plot.

Our goal is to identify the treatment combinations which most influence a suite of response variables. We monitored a number of response variables which each have their own complexity. This includes:

1. a set of soil measurements which we recorded pre-treatment and three years post-treatment. My PIs suggested using a metric of (Pre-post)/Pre for a % change which is scaled by the pre-treatment value.

2. A soil measurement with 6-months and 3 years post-treatment time points. We will eventually have a mid-time point but are still processing samples. Miraculously, this variable is normally distributed and I’ve analyzed this with a repeated measures lmer model.

3. A repeated measure of a continuous variable which is highly zero inflated. I’m exploring the use of a zi beta distribution in a glmmTMB model.

4. Repeated measures of plant count data which is also highly zero inflated. This includes total number of plants, and a measure of the non-native plants which may be (total-invasive)/Total but I’m not sold on this method. I’m looking into zi Poisson or negative bionmial for this analysis.

I started with 1 to build my understanding of this analysis method. My PIs don’t work in R, so I’ve scoured the internet for guidance and met the stats consulting lab at my institution. Unfortunately, the stats consultant is also not an experienced R user so I’m worried that the model I’ve been running may not be structured properly.

Here’s a generalized example of my data for any given variable

Block	Plot	T1	T2	T3	Split	Treatment	Time	Response
1	1	Applied	Control	Control	Applied	Applied_Control_Control	Apr-18	12
1	1	Applied	Control	Control	Control	Applied_Control_Control	Apr-18	3
1	2	Control	Applied	Control	Control	Control_Applied_Control	Apr-18	7
1	3	Control	Applied	Applied	Applied	Control_Applied_Applied	Apr-18	12

1. lmer.1 <- lmer(Change ~ Block + T1*T2*T3*Split + (1|Treatment:Block), data=data1) where change= (Pre-Post)/Post ; Block=Block ; T1-3 are the three whole-plot treatments which each have two levels (control, treated) ; Split is the treatment applied at the split plot level ; and Treatment is the specific combination of T1-3 applied to a plot, so it has 8 levels.

2. lmer.2 <- lmer(Response ~ Block + T1*T2*T3*Split*Time + (1|Treatment:Block) + (1|Time) , data=data2) Time is the month/year of the sample and is in date format

3. gme.3<- glmmTMB(Measurement~Block + T1*T2*T3*Split+ (1|Treatment:Block), data=data3, ziformula=~1, family=beta_family(link='logit')) Here I’m trying to do that zero inflated beta distribution. I was unable to get model convergence when including Time in this model in any way so I’ve so far opted to look at each of the four time points separately.

I tried running it this way: gme.3<- glmmTMB(Measurement~Block + T1*T2*T3*Split*Time + (1|Treatment:Block) + (1|Time) , data=data3, ziformula=~1, family=beta_family(link='logit')) And got the warning: Warning in (function (start, objective, gradient = NULL, hessian = NULL, : NA/NaN function evaluation With the output having NAs for everything other than the estimate.

Here’s a histogram of the raw data broken up by time point to show the kind of shape we’re working with:

4. Haven’t attempted this yet, but it would likely go the way of 3) but with a different family specified.

My questions/concerns about what I’ve done so far include

1. Does this model structure adequately capture my experimental design, especially in regards to the split plot. The two sides of the split plot aren’t independent in space and that doesn’t seem to be reflected in the code but I can’t find any examples of how better to handle this. I also suspect my nesting structure is backwards and should be (1|Block:Treatment)

2. For the repeated measures, I put time as an interactive effect with the treatments and included its as a random effect (1|Time) at the instruction of the statistician I consulted. My reading suggests that it should be included only as a random effect?

3. I can accept if my sample size just isn’t large enough to support the repeated measures aspect of the glmmTMB model, but is there otherwise an obvious problem in this model construction?

Long time reader; first time asker. Please let me know if any more information or details would aid in answering my questions.