Intro Multivariate Stats(Lecture10)

8/13/2019 Intro Multivariate Stats(Lecture10)

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For example, a client may be interested inunderstanding the effect of price and promotionalactivity on a products market share among bothloyal and not loyal customers Technical result is a linear model of the form

Y = a0 + a1X1 + a2X2 + +anXn

Best visualizations of the results control all but one(or two) of the independent variables and examinehow the value of dependent variable changes withrespect to the free independent variables


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Market share for loyal customers

Promotion Index

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Market share for not-loyal customers


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Properties Single interval scale dependent variable Multiple independent variables, preferably on interval scale Familiar and useful techniqueIssues Assumes linear relationship between dependent and

independent variables Overused and often assumptions not fully checked Often misapplied to classification problems


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Logistic Regression is a dependence techniquesused to model the relationship between a singlecategorical dependent variable and a set of metric

independent variables Typically dependent variable takes one of two values

success/failure, buy/do not buy Multinomial formulations

A logistic model gives the probability that thedependent variable takes a target value given thevalues of the independent variable


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For example, which credit and demographicfactors best predict whether a customer will

keep a loan current Dependent variable taken as 60 days past due or

worse Independent variables are credit and employment

history, and demographic descriptors


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Properties Powerful technique for predicting group membership and

identifying important independent variables Becoming more widely used Procedures and results similar to linear regressionIssues

Adequate data Model validation Communicating probabilistic concepts


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Decision trees are a dependence technique used todevelop a model to classify the value of a singledependent variable based on a set of independentvariables Dependent and independent variables can be any data

typeThe typical product of CART is a straightforward,easily interpretable set of segmentation rules For example, classify existing customers as high or low

likelihood buyers of a new product based ondemographics and historical purchasing behavior.

Classification could be used to focus advertising campaign


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Decision trees can be also used to examineprofiles of different market segments with

respect to underlying demographic andpsychographic variables

For example, what are the most significant

demographic variables determining whether theInternet is a persons most important informationsource?


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Properties Single dependent variable of any scale Multiple independent variables of any scale Free of model assumptions typical in other dependencetechniques Powerful statistical learning algorithm able to identify

complex variable interactionsIssues Not as familiar Standard inferential statistics not applicable Often leads to asymmetric relationships


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Factor analysis is an interdependence techniqueused to identify a set of underlying latent traits(factors) that explain the correlations between alarge number of variables Data summarizing

Derive a set of underlying concepts that summarize a larger setof variables

Data reduction Develop a set of factor variables that serves as a more

parsimonious description of the data


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Interested in defining underlying dimensionsinfluencing the perception of online destinations Survey respondents are asked to rate a set of destinations

(including clients) with respect to a number of traits Factor analysis can be applied to develop a succinct set of

perception dimensions This manageable set of dimensions can be used to

characterize a clients site and to develop a focused plan toreposition it


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Properties Very useful in identifying structure and relationships in

data Provides tractable set of concepts for both managerial

and analytical uses Provides opportunities for visualizationsIssues Questionnaire design Variable selection Factor interpretation and validity


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Cluster analysis is an interdependence techniqueused to segment cases into homogeneousgroups based on a specified set of variables Data reduction

Develop a more parsimonious description of cases which canthen be used in analytical classification methods

Identify similarities between cases with respect to

clustering variables Characterize clusters with respect to other sets ofvariables


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Want to identify and then characterize similargroups of TV pilot shows based on survey responsesrating shows on various traits For one or two traits it may be possible to do this

subjectively. Cluster analysis provides anobjective method for multiple traits

Clusters can be characterized with respect to variables notused in the analysis, such as show success, and clustermembership can be used as a dependent variable inclassification method


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Cluster 1: Low likelihood of success

Cluster 2: Moderate likelihood of success

Cluster 3: High likelihood of success

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Properties Many cluster techniques are available for data of all scales Can identify structure in large data sets that may be

difficult to discover in any other way Provides objective segmentation methodIssues Selecting appropriate clustering method

Determining appropriate number of clusters Validating clusters

Intro Multivariate Stats(Lecture10)

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