Data Analysis Machine Learning and Applications Episode 2 Part 10 docx

Despite the claim that satisfaction ratings are linked to actual repurchase ior, the number of studies that actually relate satisfaction ratings to actual repurchase ior is limited Mitt

Conjoint Analysis for Complex Services Using Clusterwise HB Procedures 437

Table 3 Validity values for the total sample and for the clusters for HB estimation (“in

to-tal sample”: HB estimation at the individual toto-tal sample level; “in segment”: separate HBestimation at the individual cluster 1 resp 2 level)

(using draws, n=10,000) 0.727 0.780 0.778 0.677 0.671First-choice-hit-rate

(using mean draws) 65.22 % 75.95 % 74.68 % 54.88 % 57.32 %Mean Spearman

* one respondent had missing holdout data and could not be considered

considered Furthermore we were interested whether clusterwise estimation can timize the “results” of HB estimation A clear answer is not possible up to now Inour empirical investigation in some cases we had improvements with respect to thevalidity values (cluster 2) and in some cases not (cluster 1)

op-This means that our proposition in the paper can help to reduce the problems thatoccur when service preference measurement via conjoint analysis is the researchfocus HB estimation seems to improve validity even in case of complex serviceswith immaterial attributes and levels that cause perceptual uncertainty and preferenceheterogeneity However, going further with the more complicated way of performingclusterwise HB estimation doesn’t provide automatically better results

Nevertheless, further comparisons with larger sample sizes and other research jects are necessary Furthermore, the possibilities of other validity criteria for clearerstatements could be used

ob-References

ALLENBY, G.M and GINTER, J.L (1995): Using Extremes to Design Products and Segment

Markets Journal of Marketing Research, 32, November, 392–403.

ALLENBY, G.M., ARORA, N and GINTER, J.L (1995): Incorporating Prior Knowledge into

the Analysis of Conjoint Studies Journal of Marketing Research, 32, May, 152–162.

ANDREWS, R.L., ANSARI, A and CURRIM, I.S (2002): Hierarchical Bayes Versus nite Mixture Conjoint Analysis Models: A Comparison of Fit, Prediction, and Partworth

Fi-Recovery Journal of Marketing Research, 39, February, 87–98.

BAIER, D and GAUL, W (1999): Optimal Product Positioning Based on Paired Comparison

Data Journal of Econometrics, 89, Nos 1-2, 365–392.

BAIER, D and GAUL, W (2003): Market Simulation Using a Probabilistic Ideal Vector

Model for Conjoint Data In: A Gustafsson, A Herrmann, and F Huber (Eds.):

Con-joint Measurement - Methods and Applications Springer, Berlin, 97–120.

BAIER, D and POLASEK, W (2003): Market Simulation Using Bayesian Procedures in

Conjoint Analysis In: M Schwaiger and O Opitz (Eds.): Exploratory Data Analysis in

Empirical Research Springer, Berlin, 413–421.

BRUSCH, M., BAIER, D and TREPPA, A (2002): Conjoint Analysis and Stimulus tation - a Comparison of Alternative Methods In: K Jajuga, A Sokođowski and H.H

Presen-Bock (Eds.): Classification, Clustering, and Analysis Springer, Berlin, 203–210.

ERNST, O and SATTLER, H (2000): Multimediale versus traditionelle Conjoint-Analysen

Ein empirischer Vergleich alternativer Produktpräsentationsformen Marketing ZFP, 2,

161–172.

GREEN, P.E and SRINIVASAN, V (1978): Conjoint Analysis in Consumer Research: Issues

and Outlook Journal of Consumer Research, 5, September, 103–123.

GREEN, P.E., KRIEGER, A.M and WIND, Y (2001): Thirty Years of Conjoint Analysis:

Reflections and Prospects Interfaces 31, 3, part 2, S56–S73.

LENK, P.J., DESARBO, W.S., GREEN, P.E and YOUNG, M.R (1996): Hierarchical BayesConjoint Analysis: Recovery of Partworth Heterogeneity from Reduced Experimental

Designs Marketing Science, 15, 2, 173–191.

LIECHTY, J.C., FONG, D.K.H and DESARBO, W.S (2005): Dynamic models incorporating

individual heterogeneity Utility evolution in conjoint analysis Marketing Science, 24,

285–293.

ORME, B (2000): Hierarchical Bayes: Why All the Attention? Quirk’s Marketing Research

Review, March.

SAWTOOTH SOFTWARE (2002): ACA System Adaptive Conjoint Analysis Version 5.0

Technical Paper Series, Sawtooth Software.

SAWTOOTH SOFTWARE (2006): The ACA/Hierarchical Bayes v3.0 Technical Paper

Tech-nical Paper Series, Sawtooth Software.

SENTIS, K and LI, L (2002): One Size Fits All or Custom Tailored: Which HB Fits Better?

Proceedings of the Sawtooth Software Conference September 2001, 167–175.

ZEITHAML, V.A., PARASURAMAN, A and BERRY, L.L (1985): Problems and Strategies

in Services Marketing Journal of Marketing, 49, 33–46.

Heterogeneity in the Satisfaction-Retention

Relationship – A Finite-mixture Approach

Dorian Quint and Marcel PaulssenHumboldt-Universität zu Berlin, Institut für Industrielles Marketing-Management,

Spandauer Str 1, 10178 Berlin, Germany

dorian.quint@inbox.com,

paulssen@wiwi.hu-berlin.de

Abstract Despite the claim that satisfaction ratings are linked to actual repurchase

ior, the number of studies that actually relate satisfaction ratings to actual repurchase ior is limited (Mittal and Kamakura 2001) Furthermore, in those studies that investigate thesatisfaction-retention link customers have repeatedly been shown to defect even though theystate to be highly satisfied In a dramatic illustration of the problem Reichheld (1996) reportsthat while around 90% of industry customers report to be satisfied or even very satisfied, onlybetween 30% to 40% actually repurchase In this contribution, the relationship between satis-faction and retention was examined using a sample of 1493 business clients in the market oflight transporters of a major European market To examine heterogeneity in the satisfaction-relationship, a finite-mixture approach was chosen to model a mixed logistic regression Thesubgroups found by the algorithm do differ with respect to the relationship between satisfac-tion and loyalty, as well as with respect to the exogenous variables The resulting model allows

behav-us to shed more light on the role of the numerobehav-us moderating and interacting variables on thesatisfaction-loyalty link in a business-to-business context

an intention to repurchase (i.e the statement in a questionnaire) to an actual chase and continuous repurchasing might exist without satisfaction because of mereprice settings (see Söderlund and Vilgon 1999, Morwitz 1997) What is more, only

repur-1I.e Anderson et al (2004), Bolton (1998), Söderlund and Vilgon (1999)

a small number of studies has actually examined repurchase behavior instead of theeasier to get repurchase intentions (Bolton 1998, Mittal and Kamakura 2001, Rustand Zahorik 1993) The tenor of these studies is that the link between satisfactionand retention is clearly weaker than the link between satisfaction and loyalty.Many other factors were discovered to have an influence on retention Also moretechnical issues like common method variance, mere measurement effects or simplyunclear definitions added to raise doubt on the importance and the exact magnitude ofthe contribution of satisfaction (Reichheld 1996, Söderlund/Vilgon 1999, Giese/Cote2000) Another reason for the weak relationship between satisfaction and retention

is that it may not be a simple linear one, but one moderated by several differentvariables Several studies have already studied the effect of moderating variables onthe satisfaction-loyalty link (e.g Homburg and Giering 2001) However, the greatmajority of empirical studies in this field measured repurchase intentions instead

of objective repurchase behavior (Seiders et al 2005) Thus, the conclusion fromprior work is that considerable heterogeneity is present that might explain the oftensurprisingly weak overall relationship

An important contribution has been put forth by Mittal and Kamakura (2001).They combined the concepts of response biases and different thresholds2into theirmodel to capture individual differences between respondents Based on their resultsthey created a customer group where repurchase behavior was completely unrelated

to levels of stated satisfaction However, their approach fails to identify real existinggroups that have a distinctive relationship between satisfaction and retention For ex-ample, if model results show that older people have a lower threshold and thus repur-chase with a higher probability given a certain level of satisfaction, this is not the fullstory Other factors, measured or unmeasured, might set off the age effect In order

to find groups with distinctive relationships between satisfaction and retention, wehave explicitly chosen a finite-mixture3approach, which results in a mixed-logistic

regression setup This model type basically consists of G logistic regressions – one for each latent group This way, each case i is assigned to a group with a unique

relation between the two constructs of interest However, in a Bernoulli case likethis (see McLachlan and Peel 2000, p.163ff), identifiability is not given The neces-

sary and sufficient condition for identifiability is G max ≤12(m + 1), where m is the

number of Bernoulli trials For m= 1 no ML-regression can be estimated But mann and Lambert (1991) prove theoretical identifiability of a special case of binaryML-regressions Only the thresholds O are allowed to vary over the groups, whileall remaining regression parameters are equal for all groups According to Theorem

Foll-2 of Follmann and Lambert (1991) theoretical identifiability then depends only on

the maximal number of different values of one covariate N maxgiven the values of allother covariates are held constant The maximal number of components is then given

by G max=√ N max + 2 − 1 Thus, the theorem restricts the choice of the variables,

2In our model thresholds are tolerance levels and can be conceived as the probability ofrepurchase given all other covariates are zero

3For an overview on finite-mixture models, see McLachlan and Peel (2002) and the ences therein

refer-Heterogeneity in the Satisfaction-Retention Relationship 473but ultimately helps building a suitable model for the relationship under investiga-tion In our final model we also included so-called concomitant covariate variables,which help to understand latent class membership and enhance interpretability ofeach group or class This is achieved by using a multinomial regression of the latent

class variable c on these variables x:

as a replacement for their old one – resulting in 1493 observations The retention link is now being operationalized in Mplus 4.0 using the response-bias-effect introduced by Mittal and Kamakura (2001), which enables us to use Theorem

satisfaction-2 of Follmann and Lambert (1991) Following Paulssen and Birk (satisfaction-2006) only graphic and by brand moderated demographic response-bias-effects are estimated inour model The resulting equation for the latent satisfaction in logit is then:

i = E1sat i+ E2sat i ∗ cons i+ E3sat i ∗ age i+ E4sat i ∗ brand i+

E5sat i ∗ cons i ∗ brand i+ E6sat i ∗ age i ∗ brand i+ Hi

The satisfaction-retention link for a latent class g can then be written as4:

4Here age stands for the standardized stated age, cons for consideration set and brand cates a specific brand

indi-P (Retention = y i |c gi = 1,sat,cons,age,brand) = P(sat ∗

i > O g)

= e −O g +sat

∗

1+ e −O g +sat ∗

The latent class variable c is being regressed on the concomitant variables using a

multinomial regression As concomitant variables we used: Length of ownership ofthe replaced van (standardized), Ownership (self-employed 0, company 1), Brand ofreplaced van (other brands 0, specific "brand 1" 1), Consideration Set of other brandsthan the owned one (empty 0, at least one other brand 1) and Dealer (not involved intalks 0, involved 1) The model was estimated for several numbers of latent classes,with the theoretical maximum of classes being five The fit indices for this modelseries can be found in table 1 All four ML-models possess a better fit than a simplelogistic regression, but show a mixed picture The AIC allows for a model with fourclasses and BIC allows for only one To decide on the number of classes, the adjustedBIC was used, which allows for three classes5 This model was estimated using 500random starting values and 500 iterations as recommended by Muthen and Muthen(2006, p.327) The Log-Likelihood of the chosen model is not reproduced in onlynine out of 100 sequences, which, according to Muthen and Muthen (2006, p.325),points clearly toward a global maximum

Table 1 Model Fit criterion Simple LR G= 1 G= 2 G= 3 G= 4

Table 2 Miss-classification matrix

Heterogeneity in the Satisfaction-Retention Relationship 475The results of this model are shown in table 3 The thresholds of latent classes

2 and 3 were fixed after the first models we used showed extreme values for them,resulting in a probability of repurchase of 0% respectively 100% This means thatfor both groups repurchase probability is independent of the values of the covariates

In this way the algorithm eventually works as a filter and puts those respondentswho repurchase or do not repurchase independent of their satisfaction into separategroups Thus, the only unfixed threshold is 3.174 for latent class 1 This class has

a weight of 49.4%, while class 2 has 27.7% and class 3 represents 29.9% of therespondents The estimated value for E1 is 0.944 and is, like all other coefficients,significant on the 5% level The value for E1represents the main effect of satisfactionwith the previous van in case all other covariates are zero In this case the odds

ratio for repurchasing the same brand is increased by e 0.944 = 2.57, which means

satisfaction has a positive effect on the odds of staying with the same brand versusbuying another brand The estimates E2and E3correspond to response-bias-effects

in case, the brand is not the specific brand 1 Both estimates are significant, meaningthat response bias is present The interpretation of the beta-coefficients is similar asbefore in that all other covariates are assumed to be zero When considering only

respondents who had previously a van of brand 1, that is brand= 1, things change

The effect for age, given the consideration set is empty, becomes 0.147 − 0.131 = 0.016 almost completely wiping out the influence of response bias For the covariate

consideration set results are analogous: Given a sample-average age the

response bias-effect for respondents who replaced a van by brand 1 collapses to −0.244 + 0.254 = 0.01 As to the multinomial logistic regression of the latent class variable

c on the concomitant variables, class 3 has been chosen to be the reference class.

The constants Dgcan be used to compute the probabilities of class membership foreach respondent, who has an average length of ownership, who are self-employed,had not replaced a van of brand 1, did not consider another brand and who were

not involved in talks with the dealer For this group class membership for class g is

increasing length of ownership For low lengths of about one year, probability ofmembership is highest for class 3 However, probability of membership in class 2

is hardly influenced by the length of ownership Self-employed respondents have aprobability of belonging to class 1 of more than 80% despite the non-significance ofthe owner variable The influences on class membership for the other concomitantvariables can be explained analogously

This model with three latent classes fits the data better than a simple linear gression of retention on satisfaction The latter results in a marginal Nagelkerke-R2

re-of a bad 0.063 Now, if we look again at table 2, we might make a hard allocation

of respondents to class 1, despite the fact that separation of the classes is not perfect

6The probability of belonging to class 1 is 67.94%, for class 2 17.94% and for class 314.12% If the values of all concomitant variables are 1, the corresponding probabilitiesbecome 65.83%, 27% and 7.17% If all other values of the concomitant variables are 0, achange from 0 to 1 in the brand variable, means that the odds to belong to class 1 compared

to class 3 are just e 1.455 = 4.28.

Table 3 ML-regression results

Response Bias for all classes

Consideration∗Satisfaction -0.244 0.113 -2.157∗

Brand 1∗Satisfaction -0.367 0.100 -3.673∗

Age∗Brand 1∗Satisfaction -0.131 0.056 -2.349∗

Consideration∗Brand 1∗Satisfaction 0.254 0.123 2.075∗

∗significant on the 5% level

For class 1 we then arrive at a very good Nagelkerke-R2value of 0.509 This meansthat the estimated model basically works as a filter leaving one group of respondentswith a very strong relation between satisfaction and retention and two smaller groupswith no relation at all At this point the classes of the final model shall be interpreted.While average satisfaction ratings are essentially the same (6.77, 6.82 and 6.60 forclasses 1 to 3), the relation between satisfaction and retention is very different Asindicated above, class 1 describes a filtered link between satisfaction with the re-placed van and retention This class contains predominantly respondents who areself-employed, who were involved in talks with the dealer, who had a long length

of ownership of their previous van and who drove a van of brand 1 In this classincreasing satisfaction corresponds to a higher retention rate This means in turn thatmarketing measures to increase retention via satisfaction campaigns are feasible forthis group Respondents of class 2 considered brands other than the brand of theirreplaced van prior to their purchase decision, which increased the number of choicesthey had for making the purchase decision However, this class can also be consid-

Heterogeneity in the Satisfaction-Retention Relationship 477ered as being influenced by other factors than were observed in our study Thesefactors might further explain why the retention rate is zero, although some memberswere in fact satisfied with their replaced van It is easy to imagine that a large number

of reasons, including pure coincidence, can lead to such a behavior The third class,where respondents repurchase independent of their satisfaction, has at least one dis-tinctive feature This class is dominated by very short lengths of ownership, whichmight be explained by the presence of leasing contracts

3 Discussion

Previous studies have examined customer characteristics as moderating effects of thesatisfaction-retention link In order to further investigate this, we built on a modeldeveloped by Mittal and Kamakura (2001) that we expanded by including manu-facturer and company characteristics as additional moderating variables Previousresearch did not fully investigate the moderating role of manufacturer/brand andcompany characteristics on the satisfaction retention link Furthermore, by apply-ing a concomitant logit mixture approach we applied a new research method to thisproblem Our results imply that similar to findings of Mittal and Kamakura (2001)customer groups exist where repurchase behavior is completely invariant to ratedsatisfaction In the largest customer group a strong relationship between satisfactionand repurchase was present Respondents in this group were self-employed, partici-pated in dealer talks and kept their commercial vehicles longer than members of theother classes It is notable that for respondents who stated they were self-employedand participated in dealer talks the satisfaction-retention relationship is strong, indi-cating that those respondents had substantial leverage on decision making That is,these respondents immediately punished bad performance of the incumbent brandand switched to other brands For respondents that worked for companies other fac-tors (purchasing policies of the company, satisfaction from other members of thebuying center) than their stated satisfaction may play a role It also seems to be nec-essary that the respondent had a significant involvement in the buying process as in-dicated by his participation in dealer talks This result also points to limitation of theoften applied key informant approach – key informants have to be carefully screened

It does not suffice to ask whether they participate in certain business decisions

References

ANDERSON, E W., FORNELL, C., MAZVANCHERYL, S K (2004): Customer

Satisfac-tion and Shareholder Value Journal of Marketing, 68, 172–185.

BOLTON, R N (1998): A Dynamic Model of the Duration of the Customer’s Relationship

with a Continuous Service Provider: The Role of Satisfaction Marketing Science, 17,

45–65.

FOLLMANN, D A., LAMBERT, D (1991): Identifiability of finite mixtures of logistic

re-gression models Journal of Statistical Planning and Inference, 27, 375–381.

GIESE, J L., COTE, J A (2000): Defining Consumer Satisfaction Academy of Marketing

Science Review, 2000, 1–24.

GREMLER, D D., BROWN, S W (1996): Service Loyalty: Its Nature, Importance, and

Implications Advancing Service Quality: A Global Perspective International Service

Quality Association, 171–180.

HOMBURG, C., GIERING, A (2001): Personal Characteristics as Moderators of the

Rela-tionship Between Customer Satisfaction and Loyalty: An Empirical Analysis

Psychol-ogy & Marketing, 18, 43- ˝ U66.

MCLACHLAN, G., PEEL, D (2000): Finite Mixture Models Wiley, New York.

MITTAL, V., KAMAKURA, W A (2001): Satisfaction, Repurchase Intent, and Repurchase

Behavior: Investigating the moderating Effect of Customer Characteristics Journal of

Marketing Research, 38, 131–142.

MORWITZ, V G (1997): Why Consumers Don’t Always Accurately Predict Their Own

Fu-ture Behavior Marketing Letters, 8, 57–70.

MUTHEN, L K., MUTHEN, B O (2006): Mplus User’s Guide Fourth issue, Los Angeles.

NYLUND, K L., ASPAROUHOV, T., MUTHEN, B (2006): Deciding on the number ofclasses in latent class analysis and growth mixture modeling A Monte Carlo simulation

study Accepted by Structural Equation Modeling.

PAULSSEN, M., BIRK, M (2006): It’s not demographics alone! How demographic,

com-pany characteristics and manufacturer moderate the satisfaction retention link

Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät Working Paper.

REICHHELD, F F (1996): Learning from Customer Defections Harvard Business Review,

74, 56–69.

RUST, R T., ZAHORIK, A J (1993): Customer Satisfaction, Customer Retention, and

Mar-ket Share Journal of Retailing, 69, 193–215.

SEIDERS, K., VOSS, G B., GREWAL, D., GODFREY A L (2005): Do Satisfied Customers

Buy More? Examining Moderating Influences in a Retailing Context Journal of

On the Properties of the Rank Based Multivariate Exponentially Weighted Moving Average Control

Charts

Amor Messaoud and Claus WeihsFachbereich Statistik, Universität Dortmund, Germany

messaoud@statistik.uni-dortmund.de

Abstract The rank based multivariate exponentially weighted moving average (rMEWMA)

control chart was proposed by Messaoud et al (2005) It is a generalization, using the datadepth notion, of the nonparametric EWMA control chart for individual observations proposed

by Hackl and Ledolter (1992) The authors approximated its asymptotic in-control mance using an integral equation and assuming that a sufficiently large reference sample

perfor-is available The actual paper studies the effect of the use of reference samples of limitedamount of observations on the in-control and out-of-control performances of the proposedcontrol chart Furthermore, general recommendations for the required reference sample sizes

are given so that the in-control and out-of-control performances of the rMEWMA control

chart approach their asymptotic counterparts

1 Introduction

In practice, rMEWMA control charts are used with reference samples of limited

amount of observations In this case, the estimation effect may affect its in-controland out-of-control performances This issue is discussed in this paper based on theresults of Messaoud (2006) In section 2, we review the data depth notion The

rMEWMA control chart is introduced in section 3 The effect of the use of

refer-ence samples of limited amount of observations on its in-control and out-of-controlperformances is studied in section 4

2 Data depth

Data depth measures how deep (or central) a given point X ∈ R dis with respect to

(w.r.t.) a probability distribution F or w.r.t a given data cloud S= {Y1, , Y m}.There are several measures for the depth of the observations, such as Mahalanobisdepth, simplicial depth, half-space depth, and majority depth of Singh, see Liu et al.(1999) In this work, only the Mahalanobis depth is considered, see section 4.1

The Mahalanobis depth

The Mahalanobis depth of a given point X ∈ R d w.r.t F is defined by

1+ (X − z F)6−1 F (X − z F),

where z Fand 6F are the mean vector and covariance matrix of F, respectively The sample version of MD is obtained by replacing z F and 6F with their sample esti-mates

3 The proposed rMEWMA control chart

Let Xt = (x 1,t , , x d,t) denote the d × 1 vector of quality characteristic ments taken from a process at the t th time point where x j,t , j = 1, , d, is the

measure-observation on variate j at time t Assume that the successive X t are independent

and identically distributed random vectors Assume that m > 1 independent random

observations {X1, , X m} from an in-control process are available That is, the

Let RS = {X t−m+1 , , X t } denote a reference sample comprised of the m most recent observations taken from the process at time t ≥ m It is used to decide whether

or not the process is still in control at time t The main idea of the proposed rMEWMA

control chart is to represent each multivariate observation of the reference sample by

its corresponding data depth Thus, the depths D (RS,X i ), i = t − m + 1, , t, are calculated w.r.t RS.

Now, the same principles proposed by Hackl and Ledolter (1992) are used to

con-struct the rMEWMA control chart Let Q ∗ t denote the sequential rank of D (RS,X t)

3m2 , see Hackl and Ledolter (1992)

The control statistic T tis the EWMA of standardized sequential ranks It is puted as follows

com-T t= min;B,(1 − O)T t−1 + OQ m

t

<