UNIVERSITÀ DEGLI STUDI DI PADOVAFacoltà di Ingegneria

Dipartimento di Tecnica e Gestione dei Sistemi Industriali

TESI DI LAUREA MAGISTRALE IN INGEGNERIA GESTIONALE

PARAMETRIC AND NONPARAMETRIC METHODS APPLIED TO CONJOINT ANALYSIS

Relatore: Ch.mo Prof. Luigi SalmasoCorrelatore: Ch.mo Prof. Devin CaugheyCorrelatore: Ch.mo Prof. Teppei Yamamoto

Laureando: Paolo Balasso

Anno accademico 2015/2016

IndexINTRODUCTION OF CONJOINT ANALYSIS

data input and procedure

RATING CA

INTRODUCTION

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

PARAMETRIC CONJOINT ANALYSIS

Limits and shortcomings

Application to analyze a new patent

NONPARAMETRIC CONJOINT ANALYSISAverage Marginal Treatment Effect

FWER Simulation

Parametric Bootstrap

Application to Food and Beverage Sector

Market Share EstimationSales forecasting

Applications

Partial-worths Estimation

Type of Conjoint analysisCONJOINT ANALYSIS

RATING CA

INTRODUCTION

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

8 6 5

Data required

Parametric Statistic

procedures

METRIC CONJOINT ANALYSIS

CHOICE-BASED CONJOINT ANALYSIS

Ratings or rankings

Choices within profiles

K-way-Anova,Multiple regression

Multinomial logit analysis

Nonparametric Statistic

procedures

Average Marginal component Effect(AMCE)Permutation methods

Parametric methods

INTRODUCTION

RATING CA

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

Anti-theft patent for bicyclesRating marketing experiment applied to a company interested in evaluating his patent: an anti-theft product for bike with an innovative characteristic was developed.

Full integrated

Integration: it is a characteristic that keeps the GPS device safe from the burglar

3 attributes were taken into account:

External/camouflaged

External/visible

Difficult, technician needed

Maintenance/installation, this is a characteristic about charging the battery with three levels:

Difficult, no technician needed

Easy

Sound alarm, presence of sound alarm with two levels:

Yes – the alarm is present

No – the alarm is not present

The goal: to figure out if a full integration and the insertion of an alarm could be a competitive advantage that allowed to get a higher market share.

Types of integrations:

Parametric methodsMultiple regression

INTRODUCTION

RATING CA

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

Coefficients: Estimate Std. Error Pr(>|t|) (Intercept) 6,05156 0,06942 < 2e-16 ***Full-integrated 1,17682 0,08503 < 2e-16 ***External-Camouflaged 0,32760 0,09350 0,000495 ***Complex-technician -0,64635 0,08063 6,19e-15 ***Complex-no-technician -0,10417 0,10587 0,325571 Sound-alarm-yes 0,48672 0,07449 1,42e-10 ***---Signif. codes: 0 ‘***’ 0,001 ‘**’ 0,01 ‘*’ 0,05 ‘.’ 0,1 ‘ ’ 1

Market Share prediction

Partial utilities

Regression outcomes

Parametric methods-ExampleAssumptions and diagnostics

INTRODUCTION

RATING CA

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

“Most statistical tests rely upon certain assumptions about the variables used in the analysis. When these assumptions are not met the results may not be trustworthy, resulting in a Type I or Type II error, or over- or under-estimation of significance or effect size(s)”. Osborne, Jason & Elaine Waters , North Carolina State University and University of Oklahoma

This is confirmed by the following diagnostic procedure

Data indicate the assumptions of normality and homoschedasticity may be violated.

Nonparametric methodsA new permutation method

INTRODUCTION

RATING CA

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

Run regression by respondent and store the obtained estimates

This approach does not require normality or homoschedasticity but only a more relaxed assumption that is exchangeability. This method is proposed by Finos in "Permutation tests for between-unit fixedeffects in multivariate generalized linear mixed models”(2014)

(Intercept) Full-integ External-

Camouflaged Complex-technician

Complex-no-technician

Sound-alarm-yes

Sign Test 0.00e-16 0.00e-16 2,26E-10 7,05E-12 1,562E-03 4,74E-09

Wilcoxon 3,61E-06 3,78E-06 6,98E-06 4,16E-06 1,18E-02 6,66E-06

P values

Parametric methods-ExampleMarket share – Parametric bootstrap

INTRODUCTION

RATING CA

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

In order to add uncertainty into the model we have run a simulation in which, for each loop, the beta vector is computed by taking into account the estimates and the standard errors of the betas.

Rating of product j and respondent i in simulation s

Dummy variable:0 or 1

Coefficients that will be extracted from generated normal distributions for each simulation

Error terms that will be extracted from a generated normal distribution for each simulation

Calculate for each simulation the MKS of the products

Average Marginal Component Effect (AMCE)Advantages

INTRODUCTION

RATING CA

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

Weaker assumptions than other usual methods

Randomizing the profiles across respondents

AMCE does not require normality and homoschedasticity

The randomized design substitutes the fractional and orthogonal designs typical of other approaches which confounds the interaction effects

AMCE allows to decide the distribution of the treatment components actually used in the experiment

It allows to create a design that simulates the real world distribution of the treatment

Shortcomings

Its statistic properties need to be tested further

Average Marginal Component Effect (AMCE)

INTRODUCTION

RATING CA

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS If the FWER is equal to alpha(in this case set to 0,05) the test can be considered exact. Note that the value are higher especially when interactions are considered

Correction for multiplicity are useful to reduce the FWER, thus other simulations were conducted by implementing Bonferroni, Holm, Hochberg, Benjamini-Hochberg and

Benjamini Yekutieli adjustments

Family Wise Error Rate (FWER) is the probability of making one or more I type errors on the whole of the considered hypotheses (Marcus et al., 1976).

Average Marginal Component Effect (AMCE)

INTRODUCTION

RATING CA

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

Adjustment procedures of

FWER main effects

Adjustment procedures of

FWER interaction

effects

Bonferroni-Holm Benjamini-Hoch Benjamini-Yekut

Average Marginal Component Effect (AMCE)

INTRODUCTION

RATING CA

CHOICE-BASED CA

MARKET SEGMENTATION

CONCLUSIONS

CONJOINT ANALYSIS APPLIED TO FOOD AND BEVERAGE SECTOR

Attribute Level Estimate Std. Err z value Pr(>|z|) Significance Holm adjust.consistency Plain 0.0392 0.005 69.273 4,29E-08 *** 8,58E-06consistency Crunchy 0.0899 0.006 141.066 3,46E-41 *** 1,38E-38organic No -0.1567 0.005 -277.191 4,11E-165 *** 3,29E-162price $5.99 -0.0896 0.006 -147.767 2,07E-45 *** 1,04E-42price $8.99 -0.1605 0.006 -257.044 1,04E-141 *** 6,27E-139Taste chocolate 0.1678 0.006 268.345 1,28E-154 *** 8,96E-152taste Coconut 0.0769 0.006 121.243 7,85E-30 *** 2,36E-27taste strawberries 0.0563 0.008 65.856 4,53E-07 *** 4,53E-05

Choice-based marketing experiment where an American industry of granola is interested to figure out what kind of product may get the highest market share and how the levels of each attribute affect the choice of purchasing the product.

Price $3.99, $5.99, $8.99

Organic yes,no

Consistency chewy, plain, crunchy

Taste cereal, chocolate, coconut, strawberries

Attribute Level

From the simulation Holm adjustment seems to be a good control for the Family Wise Error Rate

MARKET SEGMENTATIONMarket Segmentation

INTRODUCTION

CHOICE-BASED CA

CONCLUSIONS

The general goal of market segmentation is to find groups of customers that differ in important ways associated with product interest, market participation, or response to marketing efforts. One way is to use priori segmentations as proposed in the paper “Market Segmentation with Choice-BasedConjoint Analysis “, Wayne S.

Steps:

Collect priori segmentation information for each respondent

Choose a statistical approach to perform to CA data(in our case AMCE)

Run the method for each priori cluster and deal with multiplicity adjustment(Holm)Interpret the results

Level Holm adj.-Healthy Holm adj.-Unhealthyplain 9,89E-04 1,98E-09

crunchy 1,16E-10 1,76E-34no 0,00E+00 1,55E-51$5.99 2,42E-10 6,94E-41$8.99 2,92E-31 1,96E-117chocolate 3,74E-29 3,85E-134coconut 2,26E-08 1,33E-19strawberries 5,54E-173 4,75E-07

MARKET SEGMENTATION

RATING CA

GUIDELINES FOR CA APPLICATIONSFinally we try to provide a best practice guideline for a Conjoint Analysis experiment

Holm adjustment for Multiplicity

Collect data from respondents using profiles with a

rondomized design

Choice-based CAwith AMCE or Mnlogit model

Market Share

Tools or service Procedures

Cost for each response: 99c

Opensource Software

Opensource Software

Sales forecasting

B2B

B2C

www.revolutionanalytics.com/companies-using-r

CONCLUSIONS: NEW CONTRIBUTION TO CA

AMCE method

Nonparametric method used to validate estimators of parametric approaches

Nonparametric Approaches

Bootstrap method used to consider the uncertainty in market share estimations

It requires weaker assumptions and allows to get more reliable outcomes