Latent Class Models for Marketing: An Application to Pharmaceuticals

Transcription

1 Workng Paper Seres, N.4, February 2007 Latent Class Models for Marketng: An Applcaton to Pharmaceutcals Francesca Bass Department of Statstcal Scences Unversty of Padua Italy Abstract: In ths paper some extensons of the latent class (LC) approach are appled to analyze the Italan pharmaceutcal market. Ths sector s characterzed by a hgh level of compettveness, more lmted economc budgets than years ago and, at the same tme, expensve sales and promoton actvtes; n ths context, t s very mportant to know the reference market, so to desgn approprate marketng strateges. The paper has two ams: () dentfyng groups of doctors homogeneous for atttude towards pharmaceutcal representatves actvtes; () verfy whch aspects of the promotonal actvty may be sgnfcant n order to nfluence prescrpton quanttes. Keywords: multlevel latent class modes, latent regresson models, market segmentaton Fnal Verson ( )

2 Contents 1. Introducton 1 2. The data 2 3. Market segmentaton Multlevel latent class models Analyss of the Italan pharmaceutcal market 4 4. What nfluences prescrptons? 7 5. Conclusve remarks 8

3 1 Secton 1 Introducton Latent Class Models for Marketng: An Applcaton to Pharmaceutcals Francesca Bass Department of Statstcal Scences Unversty of Padua Italy Abstract: In ths paper some extensons of the latent class (LC) approach are appled to analyze the Italan pharmaceutcal market. Ths sector s characterzed by a hgh level of compettveness, more lmted economc budgets than years ago and, at the same tme, expensve sales and promoton actvtes; n ths context, t s very mportant to know the reference market, so to desgn approprate marketng strateges. The paper has two ams: () dentfyng groups of doctors homogeneous for atttude towards pharmaceutcal representatves actvtes; () verfy whch aspects of the promotonal actvty may be sgnfcant n order to nfluence prescrpton quanttes. Keywords: multlevel latent class modes, latent regresson models, market segmentaton 1. Introducton Snce the early 1980s marketng analysts and scholars have appled latent structure and other types of fnte mxture models wth ncreasng frequency. One varant of the fnte mxture models, the latent class (LC) model, has been perhaps the most popular. Fnte mxture models allow to account for respondents heterogenety (Dllon & Kumar, 1994), therefore they are a promsng nstrument especally for market segmentaton. It s not surprsng then the growng number of papers appearng n the marketng lterature that propose specal varants of fnte mxture models appled to market analyss (see, among many others, Dash, Schffman & Berenson, 1975; DeSarbo et al., 1992; Dllon & Mulan, 1989;Grover & Srnvasan, 1987; Kamakura & Russel, 1989; Jan et al., 1990). Recently, latent class models have ganed recognton of as a method of segmentaton wth several advantages over tradtonal methods (Magdson & Vermunt 2002). LC cluster analyss s a model-based clusterng procedure, as such, t s a probablstc and more flexble alternatve to K- means clusterng. In ths paper some extensons of the LC class approach are appled to analyse the Italan pharmaceutcal market, whch s the fourth largest n Europe, behnd Germany, France and UK. In 2004, there were 241 producers n Italy employng workers (Espscom, 2006); physcans enrolled n the Italan Physcan Roll were , among these, almost were general practtoners (Maran & Ventre, 2006). The pharmaceutcal sector n Italy s charactersed by a hgh level of compettveness, more lmted economc budgets than years ago and, at the same tme, expensve sales and promoton actvtes. In ths context, t s very mportant to understand whch factors nfluence doctors n prescrbng medcnes, so to desgn approprate marketng strateges. There s recent nternatonal lterature that tres to understand determnants of doctors, and also patents, demand for drugs; a study wth reference to the Italan market can be found, for example, n Coscell (2000). Pharmaceutcal ndustres, n general, am at understandng what doctors requre from ther products and ther representatves so to drect nvestments n order to acqure market share, possbly wthout wastng resources. Enterprse profts cannot be obtaned wthout consderng customer satsfacton, n the case of the pharmaceutcal sector, the prmary customer s the general practtoner prescrbng medcnes. The data at our dsposal was collected n a survey on Italan general practtoners. Each doctor was asked to express a judgment on varous aspects regardng the promotonal actvty

4 Francesca Bass 2 organsed by the pharmaceutcal ndustres he was n contact wth and to declare the percentage of drugs, produced by each frm, he usually prescrbes. We apply LC models for multlevel data (Vermunt, 2003) n order to dentfy segments n the market. Tradtonal latent class models assume that observatons are ndependent, n our case ths assumpton s volated snce doctors judge more than one pharmaceutcal ndustry; multlevel LC models make t possble to modfy ths assumpton. A second am of the paper s to verfy whch aspects of the frms promotonal actvty may be determnant n nfluencng doctors prescrptons. LC regresson models estmate a lnear relaton between a dependent varable and a set of explanatory varables accountng for the fact that observatons may arse from a number of unknown heterogeneous groups n whch regresson coeffcents dffer (Wedel & DeSarbo, 1994). LC regresson models can be vewed as randomcoeffcents models that, smlarly to multlevel or herarchcal models, can take nto account dependences between observatons. Ths extends the applcaton of LC regresson models to stuatons wth repeated measurements (Magdson & Vermunt 2004). The paper s organsed as follows. Secton 2 descrbes the dataset. In secton 3 the Italan pharmaceutcal market s segmented applyng multlevel LC models. In secton 4 the LC regresson model s used to dentfy factors nfluencng medcnes prescrptons. Secton 5 contans some bref concludng remarks. 2. The data The data used n ths paper was collected from 489 Italan general practtoners. On a sevenpont scale, doctors expressed how mportant the followng tems were n nducng them to prescrbe a drug proposed by a pharmaceutcal ndustry: (1) attenton of the ndustry for doctors updatng (ATT), (2) frequency and regularty of vsts by pharmaceutcal representatves (FRE), (3) assstance on dagnostc and therapeutc problems (ASS), (4) consderaton for doctors experence and suggestons (EXP), (5) qualty of tranng of pharmaceutcal representatves (QUA), (6) nformaton on ndustry actvtes (INF), and (7) global qualty of nformaton and promoton actvtes (PRO). Few demographc characterstcs of doctors were also collected: number of years from unversty degree - as a proxy of age - area of the country n whch workng (North, Centre or South of Italy), dmenson of the cty n whch operatng (less or more than nhabtants), number of patents. Doctors were asked to judge each pharmaceutcal ndustry they were n contact wth. Moreover, they were requred to supply the percentage of prescrptons, over ther total prescrptons of drugs, accorded usually to each brand judged. Overall, 68 ndustres have been rated recevng from 1 up to 255 judgments from doctors ( a total of 2537 judgments). Ths result descrbes qute well the Italan pharmaceutcal market n whch a group of less than 20 bg and well known ndustres operates together wth a larger group of smaller and local frms. Doctors dffer n the number of responses gven, from 1 to 8, as well as n the pharmaceutcal ndustres judged. Our analyss has two man goals. 1) Identfyng groups of doctors homogeneous for atttude towards pharmaceutcal representatves actvtes. Specfcally we want to verfy f mportance assgned to the varous servces offered by pharmaceutcal ndustres vares across practtoners n order to possbly devse approprate marketng strateges for the dfferent segments. We also expect groups to dffer for doctors demographc characterstcs. 2) Verfy whch aspects of the promotonal actvty may be sgnfcant n order to nfluence prescrpton quanttes takng nto account that the market may be composed by segments of doctors showng dfferent atttudes towards medcnes brands.

5 3 Secton 1 Introducton 3. Market segmentaton Segmentaton methods can be classfed n a-pror, when the type and number of segments are determned n advanced by the researcher, and post-hoc, when the type and number of segments are determned on the bass of results of data analyses. A pror methods nclude loglnear models, regresson, logt and dscrmnant analyss. Among post-hoc methods we can fnd clusterng, AID, mxture models. Clusterng methods are the most popular tool for descrptve segmentaton; for a revew, see, among many others, Arabe and Hubert (1994) and Punj and Stewart (1983). Latent class (LC) analyss attempts to explan the observed assocaton between the factors that make up a multway contngency table (Goodman, 1974) by ntroducng unobservable underlyng classes (clusters). Green et al. (1976) frst suggested the applcaton of latent class analyss to market segmentaton; other nterestng applcatons may be found n Kamakura and Mazzon (1991); Lehman et al. (1982); Paas et al. (2004). The LC approach to clusterng s model-based: the fundamental assumpton s that of local ndependence, whch states that objects n the same latent class share a common jont probablty dstrbuton among the observed varables (Vermunt, 1997) Multlevel LC models In standard LC models t s assumed that the model parameters are the same for all persons (level-1 unts). The basc dea of multlevel LC models s that some of the model parameters are allowed to dffer across groups, clusters or level-2 unts. Such dfferences can be modelled by ncludng group dummes n the model, as t s done n multple-group LC analyss (Clogg & Goodman, 1984), whch amounts to usng a fxed-effects approach. Alternatvely, n a randomeffects approach, the group specfc coeffcents are assumed to come from a partcular dstrbuton, whose parameters should be estmated. Dependng on whether the form of the mxng dstrbuton s specfed or not, ether a parametrc or non parametrc random-effects approach s obtaned. Vermunt (2003) proposes a multlevel LC model as an extenson of a random-coeffcents logstc regresson model (Agrest et al., 2000) n whch the dependent varable s not drectly observed but rather s a latent varable wth several observed ndcators. Let: Y, =1,,I, j=1, J, k=1, K, denote the response of ndvdual or level-1 unt wthn group or k level-2 unt j on ndcator or tem k; s, s = 1,... S, a partcular level of tem k; k k k X, a latent varable wth T classes; t, a partcular latent class, t=1,,t; Y, the full vector of responses of case n group j; s, a possble response pattern. The probablty structure defnng a smple LC model can be expressed as follows: T P( X = t) P( Y = s X = t) = P( X = t) P( Y = s) = P( Y = s X = t) (1) t= 1 t= 1 k= 1 T As t s specfed n equaton (1), the probablty of observng a partcular response pattern s a weghted average of class-specfc probablty P( Y = s X t) wth weght the probablty K k k k = that unt n group j belongs to latent class t. As the local ndependence assumpton mples, ndcators Y k are assumed ndependent condtonal on latent class membershp. k

6 Francesca Bass 4 A multlevel latent class model (Vermunt, 2003) conssts of a mxture model equaton for level-1 unts and level-2 unts, where a group-level dscrete latent varable s ntroduced so that parameters are allowed to dffer across latent classes of groups: M n j T K P( Y = s) = P( W j = m) P( X = t W j = m) P( Yk = sk X = t) (2) m= 1 = 1 t= 1 k= 1 where W denotes the latent varable at the group level, assumng value m, wth m=1,,m; j n j s the sze of group j. Equaton (2) s obtaned wth the addtonal assumpton that the n j members responses are ndependent of one another condtonal on group class membershp. A natural extenson of the multlevel LC model nvolves ncludng level-1 and level-2 covarates to predct membershp, as an extenson of the LC model wth concomtant varables (Dayton & McReady, 1988) Analyss of the Italan pharmaceutcal market Multlevel LC models were estmated n order to dentfy market segments 1. Our level-1 unts, or stuatons, are judgments expressed by doctors on the seven aspects of the promotonal actvty performed by pharmaceutcal ndustres, our level-2 unts, or cases, are doctors. We are nterested n defnng clusters of doctors, called, from now on classes, on the bass of responses gven wth regard to the varous brands. In ths respect we may say that we are dealng wth a three-way data set snce doctors provde multple ratngs for multple objects (Vermunt, 2006). Table 1. Model ft (BIC ndex) for alternatve numbers of classes and clusters M T BIC The software Latent Gold 4.0 was used (Vermunt & Magdson, 2005).

7 5 Secton 1 Introducton The model requred for our scope s an adaptaton of the standard multlevel LC model. The basc assumpton s that cases may be n a dfferent latent class dependng on the stuaton or, more specfcally, cases are clustered wth respect to the probablty of beng n a partcular latent class at a certan stuaton. The basc dea s to treat the three ways as herarchcally nested levels and assume that there s a mxture dstrbuton at each of the two hgher levels;.e., one at the case and one at the case-n-stuaton level. The LC multlevel model whch revealed the best ft to the data 2 estmates 4 latent classes of doctors and 4 classes of level-1 unts (clusters), ts BIC value s lower than the that of models wth alternatve values of the number classes (M) and the number of clusters (T), as t appears form Table 1. Table 2. Multlevel LC model estmaton results, standard errors n parentheses Sze Cluster 1 Cluster 2 Cluster 3 Cluster 4 Sze (0.0174) (0.0180) (0.0142) (0.0111) Class (0.0562) (0.0294) (0.0325) (0.0592) (0.1077) Class (0.0442) (0.0346) (0.0373) (0.0414) (0.0456) Class (0.0450) (0.0179) (0.0180) (0.0434) (0.1171) Class (0.0376) (0.0132) (0.0402) (0.0137) (0.0246) Mean values ATT (0.0370) (0.0536) (0.0352) (0.0945) FRE (0.0318) (0.0479) (0.0306) (0.1034) ASS (0.0421) (0.0531) (0.0458) (0.0965) EXP (0.0514) (0.0610) (0.0524) (0.1028) QUA (0.0322) (0.0429) (0.0273) (0.0969) INF (0.0623) (0.0717) (0.0638) (0.0980) PRO (0.0334) (0.0496) (0.0294) (0.0861) Estmaton results wth the best fttng model are reported n Table 2. Four clusters of judgments of pharmaceutcal representatves actvty and four classes of doctors have been dentfed. In the lower part of the table average judgments on each aspects of the promotonal actvty n the four clusters are reported. These same results are used n Fgure 1 to descrbe clusters profles n order to ad nterpretaton. Cluster 3 contans the hghest judgments (hgher than 6.3), all aspects related to promotonal actvty are consdered very mportant dfferences among aspects judged are neglgble. Cluster 1 contans hgh levels of responses though aspects are dfferentated: frequency and regularty of vsts, global qualty of promotonal actvty and qualty of tranng representatves are rated as very mportant, whereas nformaton on ndustry s actvty s consdered non relevant at all. Cluster 4 contans the lowest judgments (lower than 4.5), ths means that promotonal actvty s not consdered mportant n any of ts features. Cluster 2, fnally, contans judgments whch are n between the other groups: some aspects such as frequency and regularty of vsts and qualty of tranng of pharmaceutcal representatves are rated as mportant (average score hgher than 5.5), the other aspects are consdered almost neglgble. The upper part of table 2 ndcates that the four doctor-level classes have qute dfferent dstrbutons of judgments among clusters. Class 1 s assocated wth cluster 2, class 3 wth cluster 1, class 4 wth cluster 3; n class 2 we can fnd an smlar percentage of judgments assgned to cluster 1 and cluster 2. Lookng at these results we may try do descrbe doctors segments whch s the fnal scope of ths analyss. 2 We carred out the estmaton procedure usng a few dfferent sets of startng values n order to avod local maxma. Responses on tems have been treated as measured on an ordnal scale.

8 Francesca Bass 6 In class 4 (11%), doctors can be defned as loyal and demandng at the same tme; all tems are mportant for them n order to choose among drugs. In class 3 (18%) we fnd loyal practtoners who are very concerned about the frequency and regularty of vsts, the qualty of tranng of representatves, and the global qualty of nformaton and promoton actvtes; nformaton on ndustry s actvty s valued rrelevant. Class 1 (46%) contans practtoners who consder mportant only frequency and regularty of vsts and qualty of tranng for representatves, all other aspects are non consdered. Lastly, class 2 s a mxture of doctors totally unconcerned wth promoton and nformaton by ndustres, wth a prevalence of ths group, and others practtoners only modestly nterested n some aspects. Fgure 1. Clusters profles ATT FRE ASS ESP QUA INF PRO Cluster 1 Cluster 2 Cluster 3 Cluster 4 Indcatons emergng form analyses are mportant for pharmaceutcal ndustres n order to desgn approprate promotonal actvtes for each segment. Industres can concentrate efforts on features of ther representatves actvty consdered sgnfcant n each group, not wastng resources on other aspects that do not have an mpact on customers. The most nterested segment, although the smallest one, deserves certanly great attenton by representatves; on the other hand, ndustres should medtate f t worth to contnue vstng doctors classfed n class 2. A parsmonous strategy towards the remanng doctors could be to keep frequency and regularty of vsts, emphasze qualty of tranng and do not waste resources on other aspects of promotonal actvty. Demographc characterstcs of doctors have been nserted n the model as covarates. Unfortunately, they resulted non sgnfcant n descrbng classes, whch means that the groups are not sgnfcantly dfferent for what concerns doctors age, area of the country, dmensons of the cty where doctors work, average number of patents. Relaton wth demographc varables usually facltates segments dentfcaton; ths s not the case n our market, segments are defned only n terms of atttude towards promotonal and nformaton actvty. On the other hand, our segments fulfl a number of the usual crtera requred for effectveness of market segmentaton (Wedel & Kamakura, 2000). Segments are large n sze (substantalty); snce we do not expect that doctors change frequently ther opnons on promoton actvty by pharmaceutcal ndustres, segments should not change dramatcally over tme (stablty). Segments can be easly reached by ndustres (accessblty) and ther characterstcs mmedately suggest marketng strateges (actonablty), revealng whch aspects of the promotonal actvty are consdered most mportant by doctors. For what concerns responsveness, n the next secton, a method s proposed to evaluate whch specfc aspects of promotonal actvty

9 7 Secton 1 Introducton may drectly nfluence the quantty of prescrbed medcnes. 4. What nfluences prescrptons? In order to verfy f the varous aspects of promotonal actvty consdered n our survey may sgnfcantly nfluence prescrptons, latent class regresson models have been estmated. The dependent varable s the percentage of drugs produced by a certan pharmaceutcal ndustry prescrbed by the practtoners, predctors are the judgments expressed by the doctors on the seven aspects of the actvty of pharmaceutcal representatves descrbed n secton 2. In a LC regresson model, the latent varable s a predctor that nteracts wth observed predctors. The LC regresson model provdes several useful functons. Frst, t can be used to weaken standard regresson assumptons about the nature of the effects and the error term. It makes t possble to dentfy and corrects for sources of unobserved heterogenety. It can be used to detect outlers. An mportant applcaton area for LC regresson modellng s clusterng or segmentaton (Popper et al., 2004; Wedel & Kamakura, 2000). The most general probablty structure for a LC regresson takes on the followng form: K T cov P( X z ) x= 1 t= 1 cov pred pred f ( y z, z ) = f ( y X, z ) (3) where y t s the value of the dependent varable observed on unt at occason t; T s a the number of replcatons for unt ; cov z s a vector of covarates; pred z s a vector of predctors; X s sngle nomnal latent varable wth K categores, or classes. Table 3. LC regresson model estmaton results. Class 1 Class 2 Overall Sze 0,5532 0,4468 R 2 0,0082 0,0114 0,1528 z-values z-values Intercept 0,1965 8,9577 0,2870 4,9765 t t Predctors ATT 0,0006 0,1740 0,0093 1,0600 FRE 0,0076 2,2224 0,0016 0,1719 ASS -0,0059-1,7539-0,0098-1,1719 ESP 0,0032 1,1385-0,0014-0,1711 QUA -0,0019-0,5132-0,0077-0,7410 INF 0,0037 1,5619 0,0081 1,3485 PRO -0,0014-0,3401 0,0128 1,2182 A two-class soluton provded the best ft to the data, wth an unsatsfactory R 2 of 0,1528 tough. Table 3 contans estmated parameters and the correspondng value of the z-statstc. As t can be seen n the estmated regresson model for class 1, whch contans 55% of doctors, only the ntercept and mportance assgned to the frequency and regularty of vsts are sgnfcant n explanng percentage of prescrpton. In the regresson model estmated for class 2 (45% of

10 Francesca Bass 8 practtoners) only the ntercept s statstcally sgnfcant, no aspects of the promotonal actvty affect doctors prescrbng behavour. Doctors characterstcs were nserted n the model as actve covarates but they resulted non sgnfcant. Ths results s for sure nterestng, tough not very postve, for pharmaceutcal ndustres. It confrms the dffcultes n dentfyng factors nfluencng doctors prescrbng behavour. Ths result ndcates that other factors than those surveyed may be mportant n affectng prescrpton of drugs; ether other aspects of the promotonal actvty, or, hopefully, ntrnsc characterstcs of the products lke qualty or performance n curng dsorders. 5. Conclusve remarks The results presented above deserve some summarsng comments nto two drectons: regardng the evdences about the Italan pharmaceutcal market that emerged and regardng the models estmated. From our analyss t emerges that the Italan pharmaceutcal market, at least lookng at general practtoners, s a segmented market. Four dstnct segments of doctors emerge wth dfferent atttudes towards promotonal actvty; t s reasonable for ndustres to contact these four groups wth dversfed and approprate strateges. One group appears very nterested n all aspects consdered, another group s composed by doctors not nterested at all, possbly dsturbed by promotonal actvty, other two groups are n between wth doctors moderately nterested and concerned only wth specfc aspects of pharmaceutcal representatves work. For what concerns prescrpton behavour, two segments n the market are dentfed. For one group of doctors only the mportance assgned to frequency and regularty of the vsts of the pharmaceutcal representatves s sgnfcant, and wth a postve effects, n determnng the percentage of prescrptons of the varous brands; for the other group none of the aspects consdered affects prescrpton behavour. Ths topc deserves for sure further attenton and research. From our analyss t emerges also that LC models and ther recent extensons deserve attenton form researchers nvolved n market analyss. At s has already been ponted out, the LC approach may help n answerng to many questons n marketng analyss, wth reference to segmentaton but not only. References Agrest, A., Booth, J. G., Hobert, J. P., & Caffo, B. (2000). Random-effects modelng of categorcal response data. Socologcal Methodology, vol. 30, pp Arabe, P., & Hubert, L. J. (1994). Cluster analyss n marketng research. In R. P. Bagozz (ed.) Advanced Methods n Marketng Research. Cambrdge MA: Blackwell Publsher. Clogg, C. C., & Goodman, L. A. (1984). Latent structure analyss of a set of multdmensonal contngency tables. Journal of the Amercan Statstcal Assocaton, vol. 79, pp Coscell, A. (2000). The mportance of doctors and patent preferences n the prescrpton decson. The Journal of Industral Economcs, vol. 3, pp Dash, J F., Schffman, L. G., & Berenson, C. (1975). Informaton search and store choce. Journal of Advertsng Research, vol. 16, pp Dayton, M. C., & McReady, G. B. (1988). Concomtant-varable latent class models. Journal of the Amercan Statstcal Assocaton, vol. 83, pp DeSarbo, W. S., Wedel, M., Vrens, M. & Ramaswamy, V. (1992) Latent class metrc conjont analyss. Marketng Letters, vol. 3, pp Dllon, W. R., & Mulan, N. (1984). LADI: a latent dscrmnant model for analysng marketng research data. Multvarate Behavoral Research, vol. 19, pp

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12 Francesca Bass 10 Workng Paper Seres Department of Statstcal Scences, Unversty of Padua You may order copes of the workng papers from by emalng to Most of the workng papers can also be found at the followng url: