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Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 1
What’s New in Design‐Expert® software version 12.
Shari KraberStat‐Ease, Inc.
shari@statease.com
Oct 2019 Webinar
New DX12 Features
Logistic regression for experiments with binary response data.
Kowalski‐Cornell‐Vining (KCV) models to reduce the number of runs required for experiments combining mixture components and process factors.
Graph improvements that allow users to see more at a glance.
New options in Graph Columns: Histogram & 3D scatterplot.
Side‐by‐side view of half‐normal and Pareto plots of effects.
Model Graphs: Multi‐Graph ‘Notebook’.
Dockable legends.
New categoric codings to provide more meaningful comparisons.
What's New in DX12 2
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 2
Agenda
What's New in DX12 3
Logistic regression for experiments with binary response data.
Kowalski‐Cornell‐Vining (KCV) models to reduce the number of runs required for experiments combining mixture components and process factors.
Graph improvements that allow users to see more at a glance.
• New options in Graph Columns: Histogram & 3D scatterplot.
• Side‐by‐side view of half‐normal and Pareto plots of effects.
• Model Graphs: Multi‐Graph ‘Notebook’.
• Dockable legends.
New categoric codings to provide more meaningful comparisons.
Logistic RegressionBackground
When to use it?
The experiment is designed to study the effect of input factors on a binary response; e.g. success/fail data. Logistic regression is the appropriate regression analysis when the response is binary.
What is it?
In logistic regression Probability (p) or Odds of the response taking a particular value (0 or 1) is modeled as a function of the input factors.
Why use it?
If the distribution of the response is binomial, the normality and constant variance are violated in the ANOVA analysis. Logistic regression recognizes the boundaries of the proportion and is designed to handle binary responses.
What's New in DX12 4
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 3
Logistic RegressionBackground Math (page 1 of 2)
Logistic regression analysis estimates the odds (probability) of an event.
A logistic regression models the odds (or chance) of an outcome based on input factors. Because odds is a ratio, what will be actually modeled is the logarithm of the odds given by:
What's New in DX12 5
𝐿𝑜𝑔𝑖𝑡 𝑝 ln 𝑝 𝑦 1
1 𝑝 𝑦 1𝛽0 𝛽1𝑥1 𝛽2𝑥2 ⋯ 𝛽𝑘𝑥𝑘
�̂�𝑒 ⋯
1 𝑒 ⋯
11 𝑒 ⋯
Statisticaldetail
Logistic RegressionBackground Math (page 2 of 2)
We fit a model (𝑧) for 𝐿𝑜𝑔𝑖𝑡 𝑝 :
Then we apply the inverse transformation:
What's New in DX12 6
𝑧 𝛽0 𝛽1𝑥1 𝛽2𝑥2 ⋯ 𝛽𝑘𝑥𝑘
�̂�1
1 𝑒
Statisticaldetail
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Simple Logistic Regression ExampleMissile Test‐Firing (Brief Overview of Feature*)
Montgomery, et al1, present in problem 13.1 the test‐firing results for 25
SAMs aimed at targets of varying speeds in a range from 200 to 500
knots2. The results are either a hit (1) or a miss (0).
Imagine you are in an airplane flying over this SAM installation. How fast
do you need to fly to reduce your chances of being shot down to an
acceptable probability?
What's New in DX12 7
* Register for Martin Bezener’s November webinar on Logistic Regression to get the details of the tool as well as his tips on running experiments with binary data.
Simple Logistic Regression ExampleMissile Test‐Firing
What's New in DX12 8
Run Speedknots
Hit = 1Miss = 0
Run Speedknots
Hit = 1Miss = 0
1 400 0 13 420 0
2 220 1 14 330 1
3 490 0 15 280 1
4 210 1 16 210 1
5 500 0 17 300 1
6 270 0 18 470 1
7 200 1 19 230 0
8 470 0 20 430 0
9 480 0 21 460 0
10 310 1 22 220 1
11 240 1 23 250 1
12 490 0 24 200 1
25 390 0
Design‐Expert will DETECT the binary response and default to logistic regression.
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 5
Simple Logistic Regression ExampleAnalysis – Getting Started – auto‐detect binary response
What's New in DX12 9
Simple Logistic Regression ExampleAnalysis – ANOVA
What's New in DX12 10
P‐values
R‐squared
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Simple Logistic Regression ExampleAnalysis – Diagnostics
What's New in DX12 11
Simple Logistic Regression ExampleAnalysis – Model Graph
What's New in DX12 12
At slow speed, the probability of being Hit is high! At fast speed,
the probability of being Hit is low!
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 7
Agenda
What's New in DX12 13
Logistic regression for experiments with binary response data.
Kowalski‐Cornell‐Vining (KCV) models to reduce the number of runs required for experiments combining mixture components and process factors.
Graph improvements that allow users to see more at a glance.
• New options in Graph Columns: Histogram & 3D scatterplot.
• Side‐by‐side view of half‐normal and Pareto plots of effects.
• Model Graphs: Multi‐Graph ‘Notebook’.
• Dockable legends.
New categoric codings to provide more meaning comparisons.
Process versus MixtureCuboidal versus Simplex
What's New in DX12 14
Process
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Mixture Quadratic by Factorial ProcessThree Mixture Components and Two Process Factors
What's New in DX12 15
1 1 2 2 3 3 12 1 2 13 1 3 23 2 3
0 1 1 2 2 12 1 2
Y x x x x x x x x x x
Y z z z z z
x,z Y x Y z 24 terms
Z1
Z 2
Mixture (6)
Process (4)
Crossed (24)
Crossed ModelCombining Mixture and Process
The big reason to combine mixture components and process factors in a single DOE is to model the dependence of one on the other. The crossed model is the ultimate realization of this.
Mixture quadratic:
Process quadratic:
Crossed quadratic by quadratic model:
What's New in DX12 16
q q
i i ij i ji 1 i j
x x x x
q q q q qn n n
i i ij i j ik i k ijk i j k ikl i k li 1 i j i 1 k 1 i j k 1 i k l
q q qn n n2 2
ijkl i j k l ikk i k ijkk i j ki j k l i 1 k 1 i j k 1
x,z x x x x z x x z x z z
x x z z x z x x z
n n n
20 k k kl k l kk k
k 1 k l k 1
z z z z z
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 9
Option: Additive ModelCombining Mixture and Process
The advantage of an additive model is fewer coefficients, therefore fewer runs are required. However, the ability to model the dependence of mixture components and process factors on one another is lost.
Mixture quadratic:
Process quadratic:
Additive quadratic and quadratic model:
What's New in DX12 17
q q n n n
2i i ij i j k k kl k l kk k
i 1 i j k 1 k l k 1
x,z x x x z z z z
q q
i i ij i ji 1 i j
x x x x
n n n
20 k k kl k l kk k
k 1 k l k 1
z z z z z
Crossed vs AdditiveCombining Mixture and Process
The crossed model:
Completely links the mixture components and process factors. I.e. all model terms are crossed.
This requires lots of coefficients (therefore lots of runs).
The additive model:
Has a smaller model (requires fewer runs).
Does not link the mixture and process factors. I.e. does not contain any cross product terms.
Might as well do separate designs on the mixture components and process factors.
What's New in DX12 18
Is there a compromise?
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KCV ModelCompromise Model
A compromise model was proposed by Kowalski, Cornell and Vining1. In their approach the linear models are crossed and higher order terms are additive.
Red terms from crossed linear models, Blue terms are additive.
What's New in DX12 19
q q n
i i ik i ki
q n
i i 0 i ii 1 k 1
q n n2
ij i j kl k l k
1 i
k ki
1 k 1
q
i
j k l k 1
ii 1
Cross linear models:
Add second order terms:
KVC combined mode
x x z z
Mix: x x Process:
x,
z z z
x, xz
z
l:
z x x
qq n n
2ij i j kl k l
n
ik i kk ki
ki 1j k l 11 kk
x x z zx z z
KCV ModelCompromise Model (3‐Mix + 2‐Process)
E.g.: If we had three mixture components and two process factors, the quadratic by quadratic KCV model is:
What's New in DX12 20
12 1 2 13 1 3 23 2 3
2 2
1 1 2 2 3 3
0 4 4 5 5
1 1 2
45 4 5 44 4 55 5
12 1 2 13 1 3 23 2 3
2 245 4 5 4
2 3 3
14 1 4 24 2 4 34 3 4
15 1 5 2
4 4 55 5
5 2 5 35 3 5
,
x x x
z z
x x x
x x x x x x
z z z z
x x x x x x
z z z
x
z
x z x z x z
x
x
z x z x
z
z
z
Red crossed linear models
Blue terms are additive
15 terms in KCV model, vs 36 in Combined model
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3 Mixture + 2 Process VariablesKCV Model ‐ Build
Change the model, “Edit model…”, to “KCV Model” by “KCV Model”:
What's New in DX12 21
Kowalski, Cornell and ViningKCV Combined Models
What's New in DX12 22
MixtureComponents
ProcessFactors
CrossedQ by Q
KCVQ by Q
2 2 18 10
3 2 36 15
4 2 60 21
3 3 60 21
4 3 100 28
5 3 150 36
4 4 150 36
5 4 225 45
6 4 315 55
This reduction in runs makes combined designs much more feasible!
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 12
Agenda
What's New in DX12 23
Logistic regression for experiments with binary response data.
Kowalski‐Cornell‐Vining (KCV) models to reduce the number of runs required for experiments combining mixture components and process factors.
Graph improvements that allow users to see more at a glance.
• New options in Graph Columns: Histogram & 3D scatterplot.
• Side‐by‐side view of half‐normal and Pareto plots of effects.
• Model Graphs: Multi‐Graph ‘Notebook’.
• Dockable legends.
New categoric codings to provide more meaningful comparisons.
New options in Graph ColumnsHistoric Data Set
What's New in DX12 24
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 13
New options in Graph ColumnsHistogram
What's New in DX12 25
New options in Graph Columns3D Scatter Plot
What's New in DX12 26
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 14
Agenda
What's New in DX12 27
Logistic regression for experiments with binary response data.
Kowalski‐Cornell‐Vining (KCV) models to reduce the number of runs required for experiments combining mixture components and process factors.
Graph improvements that allow users to see more at a glance.
• New options in Graph Columns: Histogram & 3D scatterplot.
• Side‐by‐side view of half‐normal and Pareto plots of effects.
• Model Graphs: Multi‐Graph ‘Notebook’.
• Dockable legends.
New categoric codings to provide more meaningful comparisons.
Side‐by‐Side ViewHalf‐Normal and Pareto Plots of Effects
Reflow Soldering Study a 25 Factorial in 2 Blocks (lot of solder paste):
What's New in DX12 28
Name Units Type Low High
A [Numeric] Conveyor cm/min Numeric 80 90
B [Numeric] Preheat deg C Numeric 150 170
C [Numeric] Soak deg C Numeric 170 180
D [Numeric] Reflow deg C Numeric 220 270
E [Numeric] Cooling deg C Numeric 70 80
For 2‐level designs, graphical methods to select effects beat out numerical methods!
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Side‐by‐Side ViewHalf‐Normal and Pareto Plots of Effects
What's New in DX12 29See both views simultaneously
Agenda
What's New in DX12 30
Logistic regression for experiments with binary response data.
Kowalski‐Cornell‐Vining (KCV) models to reduce the number of runs required for experiments combining mixture components and process factors.
Graph improvements that allow users to see more at a glance.
• New options in Graph Columns: Histogram & 3D scatterplot.
• Side‐by‐side view of half‐normal and Pareto plots of effects.
• Model Graphs: Multi‐Graph ‘Notebook’.
• Dockable legends.
New categoric codings to provide more meaningful comparisons.
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 16
Model GraphsMulti‐Graph ‘Notebook’
What's New in DX12 31Click “+” to add graphs
Agenda
What's New in DX12 32
Logistic regression for experiments with binary response data.
Kowalski‐Cornell‐Vining (KCV) models to reduce the number of runs required for experiments combining mixture components and process factors.
Graph improvements that allow users to see more at a glance.
• New options in Graph Columns: Histogram & 3D scatterplot.
• Side‐by‐side view of half‐normal and Pareto plots of effects.
• Model Graphs: Multi‐Graph ‘Notebook’.
• Dockable legends.
New categoric codings to provide more meaningful comparisons.
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 17
Dockable LegendsChange Dock Location and Edit Info
Right click in the Legend area to choose the docking location:
What's New in DX12 33
Dockable LegendsDrag and Drop
Hover over the Legend area and click
Now drag and drop the legend where you want it:
What's New in DX12 34
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 18
Agenda
What's New in DX12 35
Logistic regression for experiments with binary response data.
Kowalski‐Cornell‐Vining (KCV) models to reduce the number of runs required for experiments combining mixture components and process factors.
Graph improvements that allow users to see more at a glance.
• New options in Graph Columns: Histogram & 3D scatterplot.
• Side‐by‐side view of half‐normal and Pareto plots of effects.
• Model Graphs: Multi‐Graph ‘Notebook’.
• Dockable legends.
New categoric codings to provide more meaningful comparisons.
Categoric ContrastsExample 3.1 Data*
One four‐level categoric factor with five replicates.
Contrasts: Sum
Treatment (compare to control)
Helmert (New)
Ordinal
Custom (New)
* Douglas C. Montgomery (2013), Design and Analysis of Experiments, 8th edition, John Wiley and Sons, Inc.
What's New in DX12 36
Right‐click: Edit Info
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Categoric ContrastsSum Coding
The Intercept is the overall mean. The first coefficient is the difference of level 1 from the overall average, the second coefficient is the difference of level 2 from the overall average and so on. The negative sum of all the coefficients is the difference of the last level from the overall average.
What's New in DX12 37
TreatmentEstimated Mean
Standard Error
1‐A1 551.20 8.17
2‐A2 587.40 8.17
3‐A3 625.40 8.17
4‐A4 707.00 8.17
TermCoefficient Estimate
Intercept 617.75
A[1] ‐66.55
A[2] ‐30.35
A[3] 7.65
66 55 30 35 7 65 89 25 . . . .
Statisticaldetail
Categoric ContrastsTreatment Coding – compare to a control
The Intercept is the controlmean. The first coefficient is the difference of level 1 from the control average, the second coefficient is the difference of level 2 from the control average and so on.
What's New in DX12 38
TreatmentEstimated Mean
Standard Error
1‐A1 551.20 8.17
2‐A2 587.40 8.17
3‐A3 625.40 8.17
4‐A4 707.00 8.17
TermCoefficient Estimate
Intercept 551.20
A[1] 36.20
A[2] 74.20
A[3] 155.80
Statisticaldetail
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Categoric ContrastsHelmert Coding* ‐ compare tomean of previous levels
The Intercept is the overall mean. The first coefficient is the mean of the first two levels minus the first level, and the second coefficient is the mean of first three levels minus the mean of the first two levels and so on.
What's New in DX12 39
TreatmentEstimated Mean
Standard Error
1‐A1 551.20 8.17
2‐A2 587.40 8.17
3‐A3 625.40 8.17
4‐A4 707.00 8.17
TermCoefficient Estimate
Intercept 617.75
A[1] 18.10
A[2] 18.70
A[3] 29.75
* Our version of Helmert coding is sometimes referred to as Reverse Helmert Coding. The mean of the dependent variable for a level is compared to the mean of the dependent variable over all previous levels.
Statisticaldetail
Categoric ContrastsOrdinal Coding
For sequential evenly spaced levels the coefficients represent linear, quadratic, cubic, …, contributions.
What's New in DX12 40
TreatmentEstimated Mean
Standard Error
1‐A1 551.20 8.17
2‐A2 587.40 8.17
3‐A3 625.40 8.17
4‐A4 707.00 8.17
TermCoefficient Estimate
Intercept 617.75
A[1] 25.27
A[2] 11.35
A[3] 2.09
Statisticaldetail
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 21
Categoric ContrastsCustom Coding
I entered the contrasts for backward difference coding. In backward difference coding, the mean of the response for a level is compared with the mean of the response for the prior level.
What's New in DX12 41
TreatmentEstimated Mean
Standard Error
1‐A1 551.20 8.17
2‐A2 587.40 8.17
3‐A3 625.40 8.17
4‐A4 707.00 8.17
TermCoefficient Estimate
Intercept 617.75
A[1] 36.20
A[2] 38.00
A[3] 81.60
Statisticaldetail
Agenda
What's New in DX12 42
Logistic regression for experiments with binary response data.
Kowalski‐Cornell‐Vining (KCV) models to reduce the number of runs required for experiments combining mixture components and process factors.
Graph improvements that allow users to see more at a glance.
• New options in Graph Columns: Histogram & 3D scatterplot.
• Side‐by‐side view of half‐normal and Pareto plots of effects.
• Model Graphs: Multi‐Graph ‘Notebook’.
• Dockable legends.
New categoric codings to provide more meaningful comparisons.
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 22
What’s Next?
November webinar on logistic regression
Watch previously recorded webinars from our website(see next slide for some favorite topics)
Attend a public workshop, or bring us on‐site!
What's New in DX12 43
Recorded WebinarsExisting DX features
Sizing for precision.Webinars: Sizing Mixture (RSM) Designs for Adequate Precision via Fraction of Design Space (FDS) and Unleashing Evaluation: Giving Perspective to Power, Precision, and Problems.
Multilinear constraints (MLCs) and non‐linear constraints.Webinar: Advanced Tools for Building Designs for Irregularly Shaped DOE Spaces.
Propagation of error (POE).Webinar: Overview of Robust Design, Propagation of Error, and Tolerance Analysis.
Optimization using Cpk and Ppk.Webinar: Practical DOE – “Tricks of the Trade”.
Using intervals to frame your operating space.Webinar: Quality by Design (QbD) Space for Pharmaceuticals and Beyond.
What's New in DX12 44
Copyright © 2019 Stat‐Ease, Inc. Do not copy or redistribute in any form. 23
Thank You for Attending!
What’s New in Design‐Expert® software version 12.
Shari KraberStat‐Ease, Inc.
shari@statease.com
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