실험 설계의 강화 - 단순함에서 정교함으로 (Empowering Experimental Designs: From Simplicity to Sophistication) Ryan Lekivetz (JMP), Elizabeth Claassen (JMP) Discovery Summit Korea 2023

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Empowering Experimental Designs
(실험 설계의 강화)
: From Simplicity to Sophistication
(단순함에서 정교함으로)
Elizabeth A. Claassen, PhD
Senior Research Statistician Developer

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Why Mixed Models?
• Limitations can exist to our ability to perform experiments
– We may be restricted in the number of experimental units available
– Some factors may be easier or harder to change between runs
• After designing the experiment with these limitations, the analysis
should also account for the restrictions
• JMP makes this more complex (and sometimes daunting) analysis
easier
• While today’s focus is on designed experiments, mixed models are
often used in survey analysis and some observational studies

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Generalized Linear Mixed Models
Modeling non-Normal data with random effects
• Mixed Modeling has been the standard for analyzing data with more
than one source of random variation (blocking, split-plots, etc.).
• The Linear Mixed Model (LMM) assumes the response is continuous
with no bounds.
• What if your response is a discrete count? Or a binary response? Or a
proportion in terms of y/n?
• Enter the Generalized Linear Mixed Model (GLMM)

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▪Examples of GLMs
• Logistic regression
• Poisson regression
• Normal regression
• Analysis of variance models
Generalized Linear Model (GLM)

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Two Things a Model Must Do
5
▪ Plausibly describe the process that gives rise
to the observed data
– how explanatory variables affect response
– probability distributions involved
▪ Allow / facilitate addressing the objective that
motivated collecting the data
− test a hypothesis
− make a decision
− estimate a parameter

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Working Example
6
▪ Split plot experiment:
− 10 Blocks that are whole plots
− 2 x 3 Factorial
− Factor 1 is hard to change with Low/High levels
− Factor 2 is easier to change with Low/Medium/High
− Response: proportion, y/n
− Y is number of parts that passed QC
− N is the number of parts per “batch”, N=20 for all in
this case

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Linear Model for Split Plot Proportion Data
• ANOVA – linear model for split plot with categorical factors
• Model: proportion = intercept + whole plot factor + whole plot error +
split plot factor + interaction + residual error
–
• Implement in JMP with Standard Least Squares or JMP Pro with Mixed
Model
( )
ijk i j k ijk
ik
proportion w e
=  +  + + +  +

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8
Experiment Treatment Combined
Source d.f. Source d.f. Source d.f.
X1 1 X1 1
whole plot 9 Whole plot|X1 9-1=8
X2 2 X2 2
X1*X2 2 X1*X2 2
unit(wp)
10*(3-1)
=20
“parallels” 24
unit(wp) | X1 & X2
a.k.a. “residual”
a.k.a “wp x X2”
20-4=16
Total 29 Total 29 Total 29
Repurposed ANOVA Table

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JMP Demo

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Further Resources
JMP for Mixed Models (2021), Hummel, Claassen and Wolfinger
SAS for Mixed Models: Introduction and Basic Applications (2018), Stroup,
Milliken, Claassen and Wolfinger
Generalized Linear Mixed Models: Modern Concepts, Methods and
Applications (2012), Stroup
Statistically Speaking Webinar: The “What, Why, and How” of Generalized
Linear Mixed Models, Stroup and Claassen