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Row-column experiment with two crossed blocking factors

frankderuyck

A situation that is frequently encountered in field experiments is where there are two crossed blocking factors e.g. "day" and "time in the day" e.g. 4 different time intervals in a day. This is a so called row-column experiment. Suppose one has to check 7 effects, how can this row-column DOE set up with the custom designer in JMP?

Accepted answers

Mark_Bailey

Use two blocking factors:

Screen Shot 2020-06-08 at 7.02.32 AM.png

Here is the JSL code to make this illustrative example:

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ), Add Factor( Blocking, 8, "Day" ),
	Add Factor( Blocking, 2, "Time of Day" ),
	Add Factor( Continuous, -1, 1, "X3", 0 ),
	Add Factor( Continuous, -1, 1, "X4", 0 ), Set Random Seed( 353 ),
	Add Term( {1, 0} ), Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {1, 1} ),
	Add Term( {2, 1} ), Add Alias Term( {3, 1}, {4, 1} ), Set Sample Size( 32 ),
	Simulate Responses( 0 ), Save X Matrix( 0 )}
);

All comments

Mark_Bailey

Use two blocking factors:

Screen Shot 2020-06-08 at 7.02.32 AM.png

Here is the JSL code to make this illustrative example:

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ), Add Factor( Blocking, 8, "Day" ),
	Add Factor( Blocking, 2, "Time of Day" ),
	Add Factor( Continuous, -1, 1, "X3", 0 ),
	Add Factor( Continuous, -1, 1, "X4", 0 ), Set Random Seed( 353 ),
	Add Term( {1, 0} ), Add Term( {3, 1} ), Add Term( {4, 1} ), Add Term( {1, 1} ),
	Add Term( {2, 1} ), Add Alias Term( {3, 1}, {4, 1} ), Set Sample Size( 32 ),
	Simulate Responses( 0 ), Save X Matrix( 0 )}
);

frankderuyck

So for 4 time intervals/day in Time of Day I need to turn the labels 5 6 7 8 and 9 10 11 12 and 13 14 15 16 to 1 2 3 4 ? And in the table the column Day must be ordenened 1 to 4 and then in each day block ordening Time in Day 1 to 4 I got the final DOE?

statman

You have an interesting situation. One could argue there is no way the time intervals within a day are crossed with day because the within day time intervals are nested within day. So the numbering is "in question". When you use the coding 1-4, 1-4 for the time intervals (for 2 days), the software recognizes the 1 for time interval for day 1 to be "identical" to the time interval 1 for day 2. While the time interval is similar, it can not be identical. I would call it systematic. I could argue (both ways) the systematic pattern within day is close enough to the same to investigate the interaction or I could argue that it is definitely not the same, hence it is nested. I think it extremely important that you have hypotheses to support the time intervals within day are similar enough to justify the crossed nature of the effects.

Mark_Bailey

The naming of the block levels will work either way. If you change the labels for time of day to mean first, second. and so on, then you must indicate that the level is nested in the day factor for the time of day effect in the model.

The ordering of the block levels is a convenience to you. It is not necessary for the analysis.

Mark_Bailey

Adding to @statman, the Day and Time of Day effects should probably be defined as random effects in the model.

frankderuyck

Thanks for reply. Indeed the levels of Time of day are nested in the day blocking factor; it is an experiment where several effects (quite a umber of runs are required) have to be tested during a number of days because only 4 runs/day are possible, however also during one day temperature and weather conditions can change so each day block needs to be split into 4 different time intervals (in each time interval conditions are assumed to be +/- stable) --> how do I indicate this nesting in custom design?

Mark_Bailey

You cannot indicate nesting or random effects in Custom Design. You modify the model in the Fit Model launch dialog. You can save the updated model to the data table for future use.

statman

The key to proper analysis is the model you create. The numbering in @Mark_Bailey's post would work for nesting (sequential, non-repeating).

The concept of a block is "theoretically" to hold the noise variables constant within the block thereby increasing the precision of detecting factor effects and allow (or manipulate) those noise variables so they change between blocks, thereby increasing the inference space while not negatively effecting the precision. You are in a situation, where some of the noise variables are changing within the block. This "theoretically" will increase the error within the block reducing the precision of detecting factor effects. Can you choose your blocks differently? Is the within day variation in ambient conditions greater than the between day? Some other options:

1. Measure ambient conditions and treat those measurements as a covariate (e.g., dew point)

2. Use a center point treatment (current conditions?) or perhaps an identical treatment combination to replicate over the course of the experiment. Analyze this and use the mean square of this replicated treatment as a basis for statistical tests (error estimate).