Visualization of Competitive Market Structure by Means of Choice Data

Transcription

1 SFB 649 Discussion Pape 7-3 Visualization of Competitive Maket Stuctue by Means of Choice Data Wene Kunz* * Humboldt-Univesität zu Belin, Gemany SFB E C O N O M I C R I S K B E R L I N This eseach was suppoted by the Deutsche Foschungsgemeinschaft though the SFB 649 "Economic Risk". ISSN SFB 649, Humboldt-Univesität zu Belin Spandaue Staße 1, D-1178 Belin

2 Visualization of Competitive Maket Stuctue by Means of Choice Data Wene Kunz Institute of Maketing, Humboldt-Univesität zu Belin, Unte den Linden 6, D-199 Belin Summay This pape pesents a method fo visualizing competitive maket stuctues based on scanne panel data whee asymmeties ae taken into account. Fo this, I combined consume choice models based on mixed logit models with thee-mode pincipal component analysis. This appoach can be used to unfold a competitive maket stuctue map. The methodology pesented is able to quantify the clout and eceptivity of vaious bands. The esults can then be visualized ove time. Using this appoach, guidelines fo pomotional activities of new bands can be povided, and possible theats fom the competition detected. Keywods: Thee-mode PCA, elasticities, joint plots, maket stuctue analysis JEL: D49 This eseach was suppoted by the Deutsche Foschungsgemeinschaft though the SFB 649 Economic Risk

3 1 Motivation A clea pictue of the competitive maket stuctue is essential fo the development of solid maketing stategies. An undestanding of consume esponse to maketing activities and the impact of maketing instuments ae especially impotant (Coope 1988). Theefoe, stoe-tacking data in which this infomation is integated is a valuable esouce fo band manages. Howeve, some points must be noted fo the analysis of maket stuctue: Fist, the analysis of maketing mix vaiables is intinsically tied to poblems with non-symmetic effects of maketing activities acoss bands. Thus, the impact of a company s maketing activity can diffe acoss the bands; and if two companies ae in the same stategic goup a simila effect on them is moe assumable. Second, in eal competitive makets, dynamic effects acoss time often exist. Theefoe, it is possible that the balance of powe within the maket can change fom one time segment to anothe, and a static analysis of the maket is not vey appopiate to descibe such makets (Baid et al. 1988). Finally, eaction to band activities is usually not equal fo all consumes and hence consume heteogeneity should be consideed within a maket stuctue analysis because of its significance (Kamakua and Russell 1989; Wedel et al. 1999). The goal of a maket stuctue analysis is to detect the inteelationships between diffeent maket bands and to evaluate thei stengths and weaknesses (Elod et al. ). Elasticities seve as a measue of competition within a maket, and vaious analytical tools have been developed to analyze maket stuctue based on elasticity matices (Coope and Klappe 1996; Elod et al. ; Hildebandt and Klappe 1; Kamakua and Russell 1989; Klappe 1998). The elasticity matices ove time give insights into competitive stengths and weaknesses, eflect the asymmeties within the maket and descibe maket stuctue changes ove time. Theefoe, an analysis of elasticity is citical to undestanding competitive effects within a maket. Elasticity matices fo diffeent time peiods constitute a multi-dimensional data aay of the maket stuctue. To get a ealistic view of

4 3 the maket, all dimensions and the inteaction effects of the complex data aay should be analyzed simultaneously. Theefoe, specific data-eduction pocedues have been developed (Koonenbeg 1983; Smilde et al. 4). Hee, the Tucke3 model fom Tucke (1966) is one of the most geneal appoaches and has been applied vey often in chemometics (Smilde et al. 4), psychometics (Hofstee et al. 1997) and econometics (Coope and Klappe 1996; Hildebandt and Klappe 1). Coope (1988) was one of the fist eseaches to use multi-mode data eduction pocedues to visualize maket stuctue based on elasticity matices. By means of the CCHM-Model, he calculated the elasticity matices fo all time peiods based on aggegated etail data which wee visualized by the Tucke3 appoach fo evey week. Hildebandt and Klappe (1) have also used elasticity matices fo the visualization of maket stuctue and futhe integated pio knowledge of pomotion activities into the estimation of the competitive situation. Both appoaches used aggegated data fo the visualization of the maket stuctue. In the case of individual choice data, the data has to be aggegated, and consume heteogeneity cannot be taken into account. Futhemoe, no chaacteistic competitive maket situations fo specific time segments wee estimated whee a dynamic changeove of the maket powe fom one competitive situation to anothe can be visualized. Theefoe, in this pape, a method of visualizing competitive maket stuctues based on individual consume choice data is pesented. Fo this, I combine choice models based on mixed logit models with appoaches of thee-mode pincipal component analysis. The coe matix of the theedimensional data cube of elasticities ove time can be unfolded to a competitive maket stuctue map, and it is possible to quantify and visualize the clout and the eceptivity of the bands ove time. Futhemoe, chaacteistic competitive maket situations ae identified, which illustate the dynamic changeove of the maket powe. Elasticity Estimation as Key fo the Maket Inteelationships Fo the desciption of competitive maket stuctue, two concepts have acquied a significant ole (Coope 1988; Kamakua and Russell 1989): The clout (Clo i ) and the eceptivity (Rec i ) of a band.

5 4 Both concepts can be calculated based on the ow o column elements of the elasticity matix as follows Clo = η Rec = η i ji i ji j j whee η ij is the pice elasticity of band j on the sales of band i. Receptivity eflects the degee to which a band is influenced by maketing activities, wheeas clout indicates how a band exets influences on the sales of the competing bands. The meaning of eceptivity is close to the concept of band vulneability whee the diagonal element is excluded. Thus, eceptivity eflects also the influence of own maketing instuments on one s own sale. Futhe clout is often associated with band stength. But high clout can also be induced by a pice sensitivity of the consume; thus bands with high clouts ae not so independent in setting thei pice. Both eceptivity and clout ae cental fo the desciption of the competitive elationship and will theefoe be utilized in ou visualization appoach. Fo the analysis of disaggegated data choice models, multinomial logit models have especially gained a majo ole in consume choice analysis. In this study, I use a mixed logit appoach based on the finite mixtue logit model. The model estimates the choice pobability using a discete mixed distibution with a maximum likelihood appoach. The specification is documented by Kamakua and Russell (1989). They have also shown that the elasticities of the entie model can also be estimated based on the discete mixtue distibution, whee s indicates the specific pat of the mixtue distibution and π s is its shae on the entie distibution. β s is the estimated effect coefficient and P si is the choice pobability fo band i given s. S ii πspsi Psi s= 1 s s(1 P si)x i πspsi η = β, η ij = β P spx, sj j π s = 1 si S s= 1 s s= 1 S

6 5 Theoy of the Thee-Mode Analysis The decomposition of the Tucke3 model In the following, the fundamentals of the thee-mode pincipal component analysis ae biefly descibed, and an estimation appoach fo the Tucke3 model is pesented. Futhe infomation about multi-mode data appoaches can be obtained by Koonenbeg (1983) o Smilde, Bo & Geladi (4). The basis of thee-mode pincipal component analysis is a thee-dimensional (I J K)-data aay X, whee evey dimension is elated to one mode (i.e. mode A, B, and C). Ledyad R. Tucke (1966) was the fist to develop a model to analyze thee-mode data aays by integating the coss-mode inteaction effects. The Tucke3 model is a vey geneal specification fo data analysis and coves seveal othe models (e.g. PCA, SVD, WPCA, Tucke, PARAFAC). The majo idea of this model is to conduct PCA on the mode level simultaneously, while the elationships between the modes emain in a coe matix. The data is composed on evey mode level to specific components which ae descibed by facto-loading matices A, B, and C as well as a coe matix G of the component inteelationships (G is specified hee as a (P Q R)-data aay). Following the Tucke3 model, the thee-dimensional data aay X can be decomposed in the subsequent fom using the slide notation of X as (I J)-matix. By means of the unfolded fom of X as (I J K)-matix and the konecke poduct, it is possible to expess the elationships in a moe condensed fom. R X = A c G B' + E k = 1K K o X% = AG(C % B)' + E k k = 1 whee G and E ae the -th slide of the coe matix G and the esidual matix E. The solution of the Tucke3 model is in geneal not unique. If A, B, and C ae othonomal and tansfomed by othonomal matices O, P, and Q, then a counte-otation of the coe matix G exists to neutalize this. Aˆ = AO, Bˆ = BP, Cˆ = CQ Gˆ = O'G(Q % P), X% = AG(C ˆ ˆ ˆ B)' ˆ

7 6 Theefoe, otation pocedues fo facto stuctue simplification (e.g. Vaimax o Oblimin) can also be applied and used fo a bette intepetation of the solution. Estimation of the Tucke3 model To detemine the solution of the Tucke3 model, the esidual matix E has to be minimized. One of the most pominent appoaches is the Altenating Least Squae Appoach (TuckALS3) of Koonenbeg and de Leeuw (198). The optimization poblem can be specified as follows: min A, B, C, G ~ ~ X AG( C B)' If the mode matices A, B, and C ae esticted to be othonomal, the coe matix G can be calculated based on A, B, C and X (i.e. G = A X(C B)) and only a solution fo A, B, and C must be found. Futhe, it can be shown that A is an eigenvecto matix of the following specific SVD: X= AG(C B)' [ A,D,V] = svd(x(cc BB')) The TuckALS3-algoithm stats with thee abitay othonomal initial matices of A, B, and C and estimates altenating updates of each mode matix based on the othe and the data aay X until an exit citeia is eached (e.g. squae sum of esiduals). Koonenbeg showed that the algoithm conveged if A, B, and C ae othonomal (Koonenbeg 1983). Andesson and Bo (1998) showed that fo the estimation of the eigenvecto matices within the TuckALS3-algoithm, the Nonlinea Iteative Patial Least Squaes (NIPALS)-algoithm is one of the most efficient appoaches. Restictions on the matices can be implemented if the esticted paametes ae ecoveed to thei initial values afte each updating iteation (Hildebandt and Klappe 1). Visualization of the Tucke3 model The intepetation of the coe matix can become quite complicated. One possibility fo the intepetation is to visualize the coe matix by means of joint plots (Koonenbeg 1983). Fo this, the poduct of the coe matix slides G and the two mode matices A and B (defined as the inne

8 7 poduct matix IP of the -th component of C) can be decomposed into two equally sized matices by means of SVD of the coe matix slides G, in the following fom G = U Λ V ' 1 1 ( 4 I )( 4 J J AU Λ I BVΛ ) ( = 1Κ R) ' IP = AG B' = AU Λ V B' = whee Λ is a diagonal matix of the singula values; U and V ae the othonomal eigenvecto matices of the SVD. The two pats of this decomposition epesent the elements of the modes A and B in a joint space, and the dimension of this space depends on the numbe of extacted singula values. The joint plot is otational invaiant. If an element is fa away fom the oigin, it indicates a stong impact of this element on all othe elements. Two elements of the same mode ae simila if the distance between them is low. Two elements of diffeent modes coespond to each othe if the angle between them is low and both elements ae elatively fa away fom the oigin. The inne poduct matices can be used to estimate idealized slides of X and it is late used to estimate idealized elasticities fo specific competitive situations. To estimate the idealized slides, the inne poduct matices wee weighted by the facto loadings of pedefined chaacteistic weeks. R A B = c IP s S K s s = 1 3 Visualization of the Maket Stuctue In the following, I demonstate the stengths of visualizing the competitive stuctue of a specific maket. The necessay analyzing pocedues have been implemented in the Matlab softwae package. The application is based on scanne panel data povided by the GFK, Nuembeg. I used consume choice data of pesonal-cae poducts which cove the puchase behavio of 1,95 households ove a peiod of 5 weeks. The maket is dominated by eight bands which compise 7% of the total maket. In the following, these bands ae efeed to as Band 1 to Band 8 fo confidentiality easons.

9 8 The maketing activities consideed ae pice, display and featue of evey competito pe week. The paid pice, the use of displays and featues wee explicitly epoted in the aw data fo the specific chosen band. The maketing instuments of the competition ae calculated based on the weekly mean values. To avoid multi-colineaity poblems, a new vaiable pomotion is intoduced which indicates the joint use of display and featue fo a band. Accodingly, display and featue indicate only the exclusive use of a display o a featue. Table 1 shows the maket shaes, the mean pice, the numbe of pomotion, display, and featue weeks of the eight bands ove the complete peiod of time. Because featues ae seldom used exclusively, I only conside pice, pomotion and display in the futhe analysis. Band 1 Band Band 3 Band 4 Band 5 Band 6 Band 7 Band 8 MS Pice Pomotion Display Featue Table 1: Desciption of the data set Estimation of elasticity ove time Fo the estimation of the pice-elasticities, a mixed logit appoach based on the finite mixtue logit model is used (Tain 3). The undelying choice model is based on a andom utility model, whee the choice utility (U) of the band i fo custome n is specified as follows π Usni =α i +β1s P icei +βs P omi +β3s Displayi +εi εi EV(, ) 6 whee s indicates the index of the mixtue distibution and ε i is the exteme value distibuted esidual tem of the utility. Futhemoe, a band-specific constant α i is estimated fo evey band. Based on this, the maximum likelihood estimato of the finite mixtue logit appoach is specified and the estimation is done fo evey week sepaately. Thus, time intedependencies of the puchases

10 9 wee kept in the esult of these estimations and wee analyzed late by the tucke model. The pice elasticities pe week wee estimated by the appoach of Kamakua and Russell (1989). Pice-elasticity effects in a eal maket vay extemely ove time if they ae calculated on shot peiods. This can be caused by shot-tem context effects that ae not integated into the model (e.g. pomotion that is not epoted, income effects at the end of the month). Because I am inteested in the majo development of the maket stuctue, such shot-tem effects can be intepeted as noise. To avoid an ove-fitting of the elasticities on such shot-tem effects, I integate the adjacent weeks in the paamete estimation pe week. This pocedue will smooth the estimation in the sense of moving aveage (Hamilton 1999). If the focus of the analysis would be the desciption of a pedefined specific maket scenaio, such an appoach is not ecommendable. Fo this, Hildebandt and Klappe (1) have shown an appoach whee a pedefined maket situation can be integated into the estimation of a constained Tucke3 model. Because the sample size of the dataset pe week is elatively small (13 puchases pe week on aveage), the heteogeneity of the dataset is consideed by a two segment finite mixtue distibution and no stoe dummy vaiables wee integated into the model. A moe sophisticated model may fit the data bette, but the stability of the estimation fo evey week cannot be ensued. Futhe, I expected the puchase decisions of one household pe week to be independent, because puchase incidents of the undelining poduct usually do not happen moe than once pe week. As a esult of the choice model, I got a thee-mode data aay consisting of pice-elasticities of all bands fo evey week. Estimation of the Tucke3 model Fo the calculation of the Tucke3 model I applied the TuckALS3-algoithm poposed by Koonenbeg and de Leew (198). Fo the initial solution of the algoithm, andom matices fo A, B and C ae used and the NIPALS-Algoithm applied fo the SVD within each iteation,. The estimation of the Tucke3 model mainly elies on the N-way toolbox developed by Andesson and Bo () fo the Matlab softwae envionment.

11 1 To detect the ight mode configuation, diffeent configuations fom (1 1 1) until (5 5 9) wee estimated and compaed by the maginal incease of explained vaiance. The last high incease of vaiance is contibuted by the (5 5 3)-configuation and the explained vaiance fo this is total 9%. The stability of the solution was tested by a split half-method. The coelation between the diffeent paamete estimation was.98. Futhemoe, the esidual plot of the thee-mode data aay was obseved and shows in total a good fit of the solution with the oiginal data. No chaacteistic patten could be detected. A1 A A3 A4 A5 B1 B B3 B4 B5 Band Band , Band Band Band Band Band Band Exp. Vaiance Table 4: Facto loadings of A and B

12 11.3 C1 C C3..1 facto loading week Figue 1: Facto loadings of mode C C1 (exp Va. =.1) C (exp Va. =.11) B1 B B3 B4 B5 B1 B B3 B4 B5 A A A A A C3 (exp Va. =.79) B1 B B3 B4 B5 A A A A A Table 5: Coe matix of the Tucke3 solution

13 1 To ensue a bette intepetation of the esults, I applied VARIMAX-Rotation and futhe othonomal tansfomation to the mode matices A, B, and C. The mode A indicates the eceptivity and mode B the clout of the diffeent bands. Mode C epesents a time mode consisting of 5 weeks. The esulting facto loading matices fo A and B ae shown in Table 4. The loadings of the thee components of C ae illustated in Figue 1. The time mode C is decomposed into thee components. It can be clealy seen that the components split the 5 weeks in thee majo pats (weeks 6- C1; weeks -33 C; 33-5 C3). The most pat of the vaiance is explained by the last component C3. The elations between the diffeent modes ae epesented by the coe matix which is shown in Table 5 (unfolded fom). C1 C C5 R1 C8 C4 R5 R6 R3 C6 C3 C1 R4 R C8 R1 R4 R6 R3 C6 C4 C5 C1 R8 R5 C C3 C4 Mode A (Receptivity) Mode B (Clout) 6 4 C5 R1/R8 R3 R6 C1 C8 C3 R5 the 3 d Dimension is additionally indicated by a vetical line. C, C7, R and R7 ae all close to zeo and wee eliminated to claify the pictue. - C R Figue : Joint plots of the thee coe slides

14 Gaphical illustation of the coe matix 13 Fo the intepetation of the maket stuctue, joint plots of each time component wee calculated based on the Tucke3 solution. Because in all time components the contibution of the thid dimension is citical fo the visualization, I decide to unfold thee dimensional joint plots (C1: D:67,7% 3D: 86,4%; C: D:63,9% 3D: 88,8%; C3: D:61,7% 3D: 86,7%). The plots of the thee time components ae shown in Figue. Based on the inne poducts, an idealized elasticity matix can be calculated (idealized citeia: factoloadings.1). The eceptivity and clout of the bands elative to the mean value in evey scenaio ae futhe measuements to illustate the powe balance within evey time component. The esults ae plotted in a two-dimensional space. Fo the thee time components, the plots ae shown in Figue 3. The plots indicate the dominance of Band 5 in the fist time component and the ise of Band 3 and late of Band 4 in the following time components, while the patial ise of Band 8 and Band 1 in the second time component can also be obseved. The elative eceptivity-clout-plot shows the powe elationships within a maket stuctue fo the diffeent time components, but detailed infomation about the inteaction effects within specific competitive goups ae not visualized by this plot.

15 5 4.5 B C1 C C el. eceptivity B5 3.5 B B1 B3 1.5 B4 B5 1 B8 1 B8 1.5 B1 B4 B3 B B4 B B6 B1 B8 4 6 el. clout el. clout el. clout Figue 3: Relative eceptivity and clout fo the diffeent time components 4 Summay This pape pesents a method fo visualizing competitive maket stuctues based on consume choice behavio affected by diffeent maketing activities. Fo this, a combination of consume choice models with appoaches of n-way data analysis is used. The appoach significantly educes the complexity of competitive elations in the data and obtains inteaction effects between the diffeent dimensions simultaneously. Futhemoe, elasticity changes between specific time components can be visualized ove time and asymmeties between the bands ae consideed. Ou methodology used scanne panel data which is becoming moe and moe available fo companies. Even small and medium-sized entepise can today paticipate fom this infomation at lowe ates. Even though today stoe-tacking data ae easy to achieve, manages who ae esponsible fo planning ae mostly ovestained by vast amounts of data. With this appoach I have shown an easy way to educe this amount of infomation into a compact fom fom which deep manageial implications can be deived.

16 15 It allows the detection of elative powe of diffeent bands fo specific time components. Futhemoe, inteaction effects between the bands can be visualized and specific goups of competition can be identified. The methodology pesented is also able to quantify and visualize the clout and eceptivity o vulneability between bands. By means of this, potential theats and own weaknesses can be noticed at an ealy stage. The application has been focused on pice pomotion, but also othe maketing instuments can be taken as a basis fo the visualization. Hence, the method can give manageial guidance fo holistic pomotional planning. Thus, the elevant competitos can be detected, whee the pice competition is impotant, while othe competitive goups can be identified if consideing a display campaign. Refeences Andesson, Claus A. and Rasmus Bo (1998), "Impoving the speed of multi-way algoithms: Pat I. Tucke3," Chemometics & Intelligent Laboatoy Systems, 4 (1), (), "The N-way Toolbox fo Matlab," Chemometics & Intelligent Laboatoy Systems, 5 (), 1-4. Baid, Inga S., D. Sudhashan, and Howad Thomas (1988), "Addessing Tempoal Change in Stategic Goup Analysis: A Thee-Mode Facto Analysis Appoach," Jounal of Management, 14 (3), Coope, Lee G. (1988), "Competitive Maps: The Stuctue Undelying Asymmetic Coss Elasticities," Management Science, 34 (6), Coope, Lee G. and Daniel Klappe (1996), "Competitive-component analysis: A new appoach to calibating asymmetic maket-shae models," Jounal of Maketing Reseach, 33 (), 4. Elod, Tey, Gay J. Russell, Allan D. Shocke, Rick L. Andews, Lynd Bacon, Bay L. Bayus, J. Douglas Caoll, Richad M. Johnson, Wagne A. Kamakua, Pete Lenk, Josef A. Mazanec, Vithala R. Rao, and Venkatesh Shanka (), "Infeing Maket Stuctue fom Custome Response to Competing and Complementay Poducts," Maketing Lettes, 13 (3), 1-3.

17 16 Hamilton, James (1999), Time Seies Analysis. Pincton: Pincton Univesity Pess. Hildebandt, Lutz and Daniel Klappe (1), "The analysis of pice competition between copoate bands," Intenational Jounal of Reseach in Maketing, 18 (1/), Hofstee, Willem K. B., Henk A. L. Kies, Boele De Raad, Lewis R. Goldbeg, and Fitz Ostendof (1997), "A Compaison of Big-Five stuctues of pesonality taits in Dutch, English, and Geman," Euopean Jounal of Pesonality, 11 (1), Kamakua, Wagne A. and Gay J. Russell (1989), "A Pobabilistic Choice Model fo Maket Segmentation and Elasticity Stuctue," Jounal of Maketing Reseach, 6 (4), Klappe, Daniel (1998), Die Analyse von Wettbewebsbeziehungen mit Scannedaten. Belin: Spinge. Koonenbeg, Piete M. (1983), Thee-mode Pincipal Component Analysis. Theoy and Applications. Leiden: DSWO Pess. Koonenbeg, Piete M. and J. de Leew (198), "Pincipal Component Analysis of Thee-Mode Data by Means of Altenating Least Squaes Algoithms," Psychometika, 45 (1), Smilde, Age, Rasmus Bo, and Paul Geladi (4), Multi-way Analysis - Applications in the Chemical Sciences. Chicheste: Wiley. Tain (3), Discete Choice Methods with Simulation. Boston: Cambidge Univesity Pess. Tucke (1966), "Some mathematical notes on thee-mode facto analysis," Psychometika, 31 (3), Wedel, Michel, Wagne Kamakua, Neeaj Aoa, Albet Bemmao, Chiang Jeongwen, Tey Elod, Rich Johnson, Pete Lenk, Scott Neslin, and Casten Stig Poulsen (1999), "Discete and Continuous Repesentations of Unobseved Heteogeneity in Choice Modeling," Maketing Lettes, 1 (3), 19-3.

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