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Copyright © JMP Statistical Discovery LLC. All rights reserved.
Empowering Experimental Designs
(실험 설계의 강화)
: From Simplicity to Sophistication
(단순함에서 정교함으로)
Elizabeth A. Claassen, PhD
Senior Research Statistician Developer
Copyright © JMP Statistical Discovery LLC. All rights reserved.
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
Copyright © JMP Statistical Discovery LLC. All rights reserved.
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)
Copyright © JMP Statistical Discovery LLC. All rights reserved.
▪Examples of GLMs
• Logistic regression
• Poisson regression
• Normal regression
• Analysis of variance models
Generalized Linear Model (GLM)
Copyright © JMP Statistical Discovery LLC. All rights reserved.
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
Copyright © JMP Statistical Discovery LLC. All rights reserved.
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
Copyright © JMP Statistical Discovery LLC. All rights reserved.
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
=  +  + + +  +
Copyright © JMP Statistical Discovery LLC. All rights reserved.
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
Copyright © JMP Statistical Discovery LLC. All rights reserved.
JMP Demo
Copyright © JMP Statistical Discovery LLC. All rights reserved.
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

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기조강연2: 조직의 업무를 보다 스마트하게 만들기 위한 엔지니어링 효율성 개선 (JMP Dan Valente)기조강연2: 조직의 업무를 보다 스마트하게 만들기 위한 엔지니어링 효율성 개선 (JMP Dan Valente)
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1-1: 바이오 의약품 공정개발 및 특성분석을 위한 DOE 연구사례 (종근당 권상오 수석)
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2-2: 다양한 무고장 조건에서 필드차량 클레임 분석 자동화 (현대차 이동복 책임)2-2: 다양한 무고장 조건에서 필드차량 클레임 분석 자동화 (현대차 이동복 책임)
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4-3: 네거티브 디자인 개념을 활용한 군함 초기설계에 적용되는 디자인영역 탐색 (Team AP 김재준 책임)4-3: 네거티브 디자인 개념을 활용한 군함 초기설계에 적용되는 디자인영역 탐색 (Team AP 김재준 책임)
4-3: 네거티브 디자인 개념을 활용한 군함 초기설계에 적용되는 디자인영역 탐색 (Team AP 김재준 책임)
 
4-2: 제조 계측장비 비정형 데이터파일 기반으로 데이터변환 및 관리도분석 서비스 (한화오션 박진원 박사)
4-2: 제조 계측장비 비정형 데이터파일 기반으로 데이터변환 및 관리도분석 서비스 (한화오션 박진원 박사)4-2: 제조 계측장비 비정형 데이터파일 기반으로 데이터변환 및 관리도분석 서비스 (한화오션 박진원 박사)
4-2: 제조 계측장비 비정형 데이터파일 기반으로 데이터변환 및 관리도분석 서비스 (한화오션 박진원 박사)
 

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기조강연3: 실험설계의 강화 - 단순함에서 정교함으로 (JMP Ryan Lekivetz & Elizabeth Claassen)

  • 1. Copyright © JMP Statistical Discovery LLC. All rights reserved. Empowering Experimental Designs (실험 설계의 강화) : From Simplicity to Sophistication (단순함에서 정교함으로) Elizabeth A. Claassen, PhD Senior Research Statistician Developer
  • 2. Copyright © JMP Statistical Discovery LLC. All rights reserved. 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
  • 3. Copyright © JMP Statistical Discovery LLC. All rights reserved. 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)
  • 4. Copyright © JMP Statistical Discovery LLC. All rights reserved. ▪Examples of GLMs • Logistic regression • Poisson regression • Normal regression • Analysis of variance models Generalized Linear Model (GLM)
  • 5. Copyright © JMP Statistical Discovery LLC. All rights reserved. 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
  • 6. Copyright © JMP Statistical Discovery LLC. All rights reserved. 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
  • 7. Copyright © JMP Statistical Discovery LLC. All rights reserved. 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 =  +  + + +  +
  • 8. Copyright © JMP Statistical Discovery LLC. All rights reserved. 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
  • 9. Copyright © JMP Statistical Discovery LLC. All rights reserved. JMP Demo
  • 10. Copyright © JMP Statistical Discovery LLC. All rights reserved. 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