Discriminant Analysis using Logistic Regression OLS1D XL4E: V0D XL4E - - PDF document

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Discriminant Analysis using Logistic Regression OLS1D XL4E: V0D XL4E - - PDF document

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Discriminant Analysis using Logistic Regression OLS1D XL4E: V0D XL4E : OLS1D V0D XL4E : OLS1D V0D 2016 Schield Logistic Regression using OLS1D in Excel2013 1 2016 Schield Logistic Regression using OLS1D in Excel2013 2 Discriminant Analysis

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Discriminant Analysis using Logistic Regression OLS1D XL4E: V0D 2016-Schield-Logistic-OLS1D-Excel2013-Slides.pdf 1

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 1

by Milo Schield Member: International Statistical Institute US Rep: International Statistical Literacy Project Director, W. M. Keck Statistical Literacy Project

Slides, output and data at: www.StatLit.org/ pdf/2016-Schield-Logistic-OLS1D-Excel2013-Slides.pdf pdf/2016-Schield-Logistic-OLS1D-Excel2013-Demo.pdf Excel/2016-Schield-Logistic-OLS1D-Excel2013-Data.xlsx

Discriminant Analysis using Logistic Regression

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 2

Discriminant Analysis:

Outcome must be Categorical Definition: A statistical technique used to classify

  • bjects into groups (to predict membership in groups).

Two-Group (Binary) Examples: Admission to grad, law or medical school Passing a test (CPA, CMA, etc.) Toxicity of a substance on insects (causes death in some) Making a loan; Bankruptcy Winning an election; Being unemployed Use of contraceptives; Driving drunk Pregnancy or divorce; Heart attack or Alzheimer's

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 3

Discriminant Analysis Uses Regression

Modelling a binary outcome (loan vs. no-loan) requires logistic regression. This presentation classifies college students by gender based on their height and weight. Three logistic models are referenced: * www.statlit.org/pdf/2015-Schield-Logistic-OLS1A-slides.pdf * www.statlit.org/pdf/2015-Schield-Logistic-OLS1B-slides.pdf * www.statlit.org/pdf/2015-Schield-Logistic-OLS1C-slides.pdf

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 4

1a: Model gender on Height

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

5

1b: Predict Sex given Height Diamond=Male; Circle=Female

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

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1c: Predict Sex given Height: Error Analysis Close-up

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Discriminant Analysis using Logistic Regression OLS1D XL4E: V0D 2016-Schield-Logistic-OLS1D-Excel2013-Slides.pdf 2

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

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  • 1d. Predict Sex given Height:

Error Analysis Summary

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

8

  • 2a. Model Gender on Weight
2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

9

  • 2b. Predict Sex given Weight

Diamond=Male; Circle=Female

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

10

  • 2c. Predict Sex given Weight

Error Analysis Close-Up

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

11

  • 2d. Predict Sex given Weight

Error Analysis Summary

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

12

  • 3a. Model Gender on

Height and Weight

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SLIDE 3

Discriminant Analysis using Logistic Regression OLS1D XL4E: V0D 2016-Schield-Logistic-OLS1D-Excel2013-Slides.pdf 3

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

P(male) = 50%: 66.37 = 0.759*Ht+0.11*Wt Weight(P50) = (66.37 – 0.759*Height) / 0.11

13

  • 3b. Model Gender on

Height and Weight

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

14

  • 3c. Model Gender on

Height and Weight

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

15

  • 3d. Model Gender on Ht & Wt:

Error Close-up

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

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  • 3e. Model Gender on Ht & Wt:

Error Summary

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 17

Summary

Using just height, 19.6% are mis-classified. Using just weight, 13.0% are misclassified. Using both height and weight, 13.0% are misclassified. What is the advantage of using weight instead of height? 34% reduction in error: (13-19.6)/19.6 Disadvantage of using both height & weight vs. weight? More complex. Can’t show in 2D. Advantage of using both height & weight vs. weight? Probably better at handling future subjects.

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 18

Appendix

  • Q. Why not just use the average? Mean height or weight?
  • A. Group average is influenced by the outcome mix.

Logistic regression models the chance of the outcome. Chance is not influenced by the outcome mix. ======================================== Interpreting the coefficients in Logistic Regression: This important topic is beyond this introductory presentation. Read The Chicago Guide to “Writing about Multivariate Analysis” by Jane Miller. See p. 220-243 and 418-431.

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SLIDE 4

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 1

by Milo Schield Member: International Statistical Institute US Rep: International Statistical Literacy Project Director, W. M. Keck Statistical Literacy Project

Slides, output and data at: www.StatLit.org/ pdf/2016-Schield-Logistic-OLS1D-Excel2013-Slides.pdf pdf/2016-Schield-Logistic-OLS1D-Excel2013-Demo.pdf Excel/2016-Schield-Logistic-OLS1D-Excel2013-Data.xlsx

Discriminant Analysis using Logistic Regression

slide-5
SLIDE 5

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 2

Discriminant Analysis:

Outcome must be Categorical Definition: A statistical technique used to classify

  • bjects into groups (to predict membership in groups).

Two-Group (Binary) Examples: Admission to grad, law or medical school Passing a test (CPA, CMA, etc.) Toxicity of a substance on insects (causes death in some) Making a loan; Bankruptcy Winning an election; Being unemployed Use of contraceptives; Driving drunk Pregnancy or divorce; Heart attack or Alzheimer's

slide-6
SLIDE 6

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 3

Discriminant Analysis Uses Regression

Modelling a binary outcome (loan vs. no-loan) requires logistic regression. This presentation classifies college students by gender based on their height and weight. Three logistic models are referenced: * www.statlit.org/pdf/2015-Schield-Logistic-OLS1A-slides.pdf * www.statlit.org/pdf/2015-Schield-Logistic-OLS1B-slides.pdf * www.statlit.org/pdf/2015-Schield-Logistic-OLS1C-slides.pdf

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SLIDE 7

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 4

1a: Model gender on Height

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SLIDE 8

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

5

1b: Predict Sex given Height Diamond=Male; Circle=Female

slide-9
SLIDE 9

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

6

1c: Predict Sex given Height: Error Analysis Close-up

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SLIDE 10

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

7

  • 1d. Predict Sex given Height:

Error Analysis Summary

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SLIDE 11

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

8

  • 2a. Model Gender on Weight
slide-12
SLIDE 12

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

9

  • 2b. Predict Sex given Weight

Diamond=Male; Circle=Female

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SLIDE 13

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

10

  • 2c. Predict Sex given Weight

Error Analysis Close-Up

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SLIDE 14

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

11

  • 2d. Predict Sex given Weight

Error Analysis Summary

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SLIDE 15

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

12

  • 3a. Model Gender on

Height and Weight

slide-16
SLIDE 16

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

P(male) = 50%: 66.37 = 0.759*Ht+0.11*Wt Weight(P50) = (66.37 – 0.759*Height) / 0.11

13

  • 3b. Model Gender on

Height and Weight

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SLIDE 17

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

14

  • 3c. Model Gender on

Height and Weight

slide-18
SLIDE 18

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

15

  • 3d. Model Gender on Ht & Wt:

Error Close-up

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SLIDE 19

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D

.

16

  • 3e. Model Gender on Ht & Wt:

Error Summary

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SLIDE 20

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 17

Summary

Using just height, 19.6% are mis-classified. Using just weight, 13.0% are misclassified. Using both height and weight, 13.0% are misclassified. What is the advantage of using weight instead of height? 34% reduction in error: (13-19.6)/19.6 Disadvantage of using both height & weight vs. weight? More complex. Can’t show in 2D. Advantage of using both height & weight vs. weight? Probably better at handling future subjects.

slide-21
SLIDE 21

2016 Schield Logistic Regression using OLS1D in Excel2013

XL4E: OLS1D V0D 18

Appendix

  • Q. Why not just use the average? Mean height or weight?
  • A. Group average is influenced by the outcome mix.

Logistic regression models the chance of the outcome. Chance is not influenced by the outcome mix. ======================================== Interpreting the coefficients in Logistic Regression: This important topic is beyond this introductory presentation. Read The Chicago Guide to “Writing about Multivariate Analysis” by Jane Miller. See p. 220-243 and 418-431.