Multi Variate Part 2

8/13/2019 Multi Variate Part 2

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Multivariate Data Analysis Using

Statgraphics Centurion: Part 2

Dr. Neil W. Polhemus

Statpoint Technologies, Inc.

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Multivariate Statistical Methods

The simultaneous observation and analysis of more than one responsevariable.

*Primary Uses

1. Data reduction or structural simplification2. Sorting and grouping

3. Investigation of the dependence among variables

4. Prediction

5. Hypothesis construction and testing

*Johnson and Wichern, Applied Multivariate Statistical Analysis

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Data set: U.S. Demographics

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Variables

Education: percent completing college

Income per Capita: in 2011 dollars

Urban Percentage: percent living in urban areas

Population Density: people per square mile

Non-English Language: percent that dont speak English

Median Age: in years

Unemployment Rate: for 2012

Percent Female: of general population

Crime Rate: violent crimes per 100,000

Manufacturing: % of GDP

Infant Mortality: 2006

Poverty Rate: percentage below poverty level

Election 2012: results of 2012 presidential election (Obama or Romney)

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Urban Percentage

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Poverty Rate

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Star Glyphs

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Data Input

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Cluster Analysis

Method for assigning objects to groups so thatobjects in the same group are more similar toeach other than they are to objects in other

groups.

Some questions:

1. How many natural groups are there?

2. Which objects belong to each group?

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Data Input

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Dendrogram Nearest Neighbor

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Dendrogram Furthest Neighbor

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Agglomeration Distance Plot

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Dendrogram - 4 Clusters

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Save Cluster Numbers

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Map of Cluster Numbers

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Method of k-Means

1. Starts with a set of typical objects (seeds) foreach cluster.

2. Each object is assigned to group with nearest

seed.3. Centroids of groups are computed.

4. Objects are assigned to different groups ifnearer to a different centroid.

5. Steps 3 and 4 are repeated until no change.

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Method of k-Means

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Seeds

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Row 5 = California

Row 32 = New York

Row 34 = North Dakota

Row 43 = Texas

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Map for k-Means

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Classification

The classification problem deals with theassignmentof objects to knowngroups. Goalsinclude:

1. Understanding what differentiates the groups.

2. Predicting group membership for unclassifiedobjects.

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Methods

Discriminant Analysis (on the CenturionRelatemenu) based on Fishers lineardiscriminant functions.

Neural Network Classifier (on the CenturionRelatemenu) based on a Bayesian classifierwith priors and costs.

Uniwin(companion program to Statgraphics) includes methods for dealing with qualitative

factors.

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(Linear) Discriminant Analysis

Constructs linear functions of the standardizedclassification variables:

These functions are derived so as to maximize theseparation of the groups. If there are ggroups,there areg-1 discriminant functions.

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pjpjjj ZdZdZdD ...

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Example

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Data Input

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Analysis Options

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All Variables

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Discriminant Function Plot

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Backward selection

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Classification Functions

These functions create a score for each group:

Objects are assigned to whatever group has thelargest value of (Cj* priorj) wherepriorjis theprior probability of belonging to groupj.

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02211 ... jpjpjjj cXcXcXcC

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Classification Functions

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Classification Summary

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Classification Table

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Validation Set

May leave some of the objects out of the trainingset and use them to validate the results.

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Correctly classified 8 out of 10 omitted states.

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Neural Network Classifier

Implements a nonparametric method forclassifying objects based on the product of 3quantities:

1. The estimated density function in the neighborhood of the object(given a specified value of s).

2. The prior probabilities of belonging to each group.

3. The costs of misclassifying cases that belong to a given group.

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Bivariate Density (s= 0.5)

Bivariate Density

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115Urban Percentage

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Poverty rate0123

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(X 0.001)

density

Romney

Bivariate Density

3555

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115Urban Percentage

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20

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Poverty rate0123

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(X 0.001)

density

Romney

Bivariate Density

3555

7595

115Urban Percentage

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20

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Poverty rate0123

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(X 0.001)

density

Romney

Bivariate Density

3555

7595

115Urban Percentage

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12

16

20

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Poverty rate0123

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(X 0.001)

density

Romney

Bivariate Density

3555

7595

115Urban Percentage

8

12

16

20

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Poverty rate0123

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(X 0.001)

density

Romney

Bivariate Density

3555

7595

115Urban Percentage

8

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20

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Poverty rate0123

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(X 0.001)

density

Romney

Bivariate Density

3555

7595

115Urban Percentage

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20

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Poverty rate0123

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(X 0.001)

density

RomneyObama

Bivariate Density

3555

7595

115Urban Percentage

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20

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Poverty rate0

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4(X 0.001)

density

Obama

Bivariate Density

3555

7595

115Urban Percentage

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20

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Poverty rate0

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4(X 0.001)

density

Obama

Bivariate Density

3555

7595

115Urban Percentage

8

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20

24

Poverty rate0

1

2

3

4(X 0.001)

density

Obama

Bivariate Density

3555

7595

115Urban Percentage

8

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20

24

Poverty rate0

1

2

3

4(X 0.001)

density

Obama

Bivariate Density

3555

7595

115Urban Percentage

8

12

16

20

24

Poverty rate0

1

2

3

4(X 0.001)

density

Obama

Bivariate Density

3555

7595

115Urban Percentage

8

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16

20

24

Poverty rate0

1

2

3

4(X 0.001)

density

Obama

Bivariate Density

3555

7595

115Urban Percentage

8

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16

20

24

Poverty rate0

1

2

3

4(X 0.001)

density

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Schematic Diagram

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Data Input

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Analysis Options

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Classification Summary

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Reduced Set of Variables

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Some Improvement

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Classification Plot

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Classification Plot

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UNIWIN Plus from Sigma Plus

Software package written by our longtimecolleague Christian Charles at Sigma Plus inFrance.

Contains additional features for multivariateanalysis.

Reads Statgraphics data files.

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Uniwin Cluster and Classification

Handle qualitative variables.

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New Variables

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Uniwin Cluster Analysis

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Dendrogram

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Uniwin Clusters

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Uniwin Classification

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Classification Results

Wrongly classified only Nevada (only cattle state to vote for Obama).

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More Information

Statgraphics Centurion:www.statgraphics.com

Uniwin Plus:www.statgraphics.frorwww.sigmaplus.fr

Or send e-mail to [email protected]
http://www.statgraphics.com/http://www.statgraphics.fr/http://www.sigmaplus.fr/mailto:[email protected]:[email protected]://www.sigmaplus.fr/http://www.statgraphics.fr/http://www.statgraphics.com/


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Multi Variate Part 2

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Transcript of Multi Variate Part 2