nav[aria-label="Primary Navigation"] { padding: 0; & ul { list-style: none; width: 100%; display: flex; flex-direction: row; justify-content: start; align-items: start; gap: 30px; padding: 0; & li { margin: 0; } & ul li { list-style: none; } } }

Specifying Random Block factor in classic DOE designs

hxnduke

Hi all,

When generating a classic DOE design in JMP, any block factor is automatically defaulted as fixed block factor. I know I can change it to random block effect to utilize the REML method by adding to it the "random effect" attribute in the Fit Model platform. However, I notice that I could also change its design role to "Random block", it is not automatically assigned the "random effect" attribute in Fit Model. So is there any difference between "Blocking" and "Random block" as design role options? The only thing I've noticed is that the block factor is shown in the Prediction Profiler when it's assigned "Random block" but not when it's "Blocking". Also, Fit Definitive Screening platform only works with "Blocking" but not "Random block" design role.

Thank you.

Accepted answers

All comments

cwillden

Fixed blocks and random blocks are treated differently in the design optimization, and you should use the type of block that corresponds to how you will fit your model. They consume degrees of freedom differently, so there will be an impact in how points are allocated in your design space depending on the type of blocks you selected. Notice the difference in minimum and recommended design sizes between the 2 approaches. Fixed blocks generally require more runs.

There are some reasons you might treat a block as fixed, but I find that random blocks make more sense in most contexts that I've seen, particularly if your objective is to account for the variation caused for the blocks and not needing make any inference about effects. For example, if I include multiple lots of raw material in my design, I don't care that Lot A increases the average response by 1.5 and Lot B by -0.6 because once Lots A and B are consumed, they are gone forever and we'll never have another Lot A or Lot B. I only want the lots I use in the design to by representative of the typical variation in raw material lots I will encounter in the future.

hxnduke

Thanks for clarifying the difference between the two blocking effects. I agree that random block effect makes the most sense in most scenarios, at least those relevant to my studies.

What I'm curious about is how to assign the block factor as "random block" when generating a classic DOE design or DSD design. In the custom DOE platform, you can specify this pretty easily. However, in classic DOE/DSD, the block factor is defaulted as fixed effect and you can only change its attribute after the design table is generated (at least as far as I'm aware of).

Does it make sense to used random block effect and REML method for classic DOE design or is this something specific to custom design?

cwillden

It's not really something specific to optimal DOEs, so you can totally analyze a blocked classical design with random blocks even if it defaults to fixed. There's not really any downside there. That being said, if you are doing a DSD, I highly recommend using Fit Definitive Screening for the analysis, where I don't think you'll be able to coerce it into treating Block as random.

hxnduke

Since you mentioned that fixed block consumes more DOF than random block, would it mean that changing the block factor attribute to "random effect" in existing data table generated via classical DOE would increase power of parameter estimates if there are multiple levels of the block factor?

Mark_Bailey

There are many cases for which the DSD is not appropriate. One of these cases is when you have random effects do to blocking or split-plot randomization.

See Bradley Jones blog post about this issue.

statman

I will offer a different perspective regarding blocks, block effects and block-by-factor interactions. The concept of blocking (replication) goes back to Sir Ronald Fisher. The idea of a block is to minimize noise within the block (hold constant) and maximize the noise between the blocks (select blocks purposefully to make sure the noise that was held constant within the block, changes between the blocks). Doing this increases the precision of detecting factor effects (e.g., reduces the MSE) while simultaneously increasing inference space (the study is replicated over changing noise). When treating blocks as a fixed effect, you are able to assign the effect of the noise and more importantly determine if the effects of the experimental factors repeat over changing noise. The later being estimated by block-by-factor interactions. In industrial experimentation and product design, robust means the absence of noise-by-factor interactions (The effect of the factors/interactions are the same over changing noise). If not, you will run into problems over time. Using the example of lot-to-lot incoming materials; If there is an effect (factor or interaction) that depends on lot of incoming material, you want to identify this early in design so you can design your product robust to incoming material. If you confound the raw material with the block and treat the block as a fixed effect, you can estimate the effect of the variables in the block and block-by-factor interactions. Unfortunately, most software programs confound the block-by-factor interactions with the error term. You will need to specify those effects manually (write your own model). I'll quote Dr. Box "Block what you can, randomize what you cannot". My interpretation of this quote is if you can identify the noise you are better off "blocking it". Of course, if you can't identify the noise, you randomize. I have had several discussion with Brad Jones over this topic...

hxnduke

In Bradley Jones blog post, he mentioned that DSD is not appropriate for split plot design but I don't really see him mentioning that random effects in general cannot be done.
In this paper from Jones and Nachtsheim, they did provide methods for DSD blocking with random effects by adding two centerpoint runs in the same block to estimate residual variance and another one in other block to estimate random block variance.

Just to clarify, in our planned studies, we have to divide up the runs into 2 blocks due to limited number of machines. We're planning to run the 2 blocks on the same set of machines but on separate days so the blocking factor here would be day-to-day variability. I'm assuming that this should be random effect but wondering whether it's worth blocking at all.