Latent Class Analysis for Marketing Scales Development

Transcription

1 Workng Paper Seres, N.16, 2009 Latent Class Analyss for Marketng Scales Development Francesca Bass Department of Statstcal Scences Unversty of Padua Italy Abstract: Measurement scales are a crucal nstrument for research n marketng n order to measure unobservable varables as atttudes, opnons, belefs. In usng, evaluatng, or developng mult-tem scales, a number of gudelnes and procedures are recommended to ensure that the measure s psychometrcally robust. These procedures have been outlned n the psychometrc lterature snce the late seventes and are composed of steps whch refer to construct defnton, doman and scale valdty, relablty, dmensonalty, and generalzablty. Varous statstcal nstruments are used n the scale developng process, these almost always refer to metrc varables (nterval or rato scales). Items formng scales are nstead rarely measured on an metrc level, frequently tems are ordnal, n some rare cases, nomnal. In ths paper, t s shown how the mplementaton of latent class analyss may mprove the process of measurement scale development snce t explctly consders that tems generate ordnal or even nomnal varables. Specfcally, applyng approprate latent class models allows to assess scale valdty and relablty more soundly than the methods tradtonally used. Keywords: measurement scales, valdty, relablty, latent class factor model, latent class regresson model, ordnal varables Fnal Verson ( )

2 Latent Class Models for Marketng: An Applcaton to Pharmaceutcals Contents 1. Introducton 1 2. Mult-tem scales development 2 3. A scale to measure customer satsfacton wth reference to experental goods 4 4. Latent class models 6 5. Scale evaluaton Dmensonalty Crteron valdty Construct valdty Conclusons 11 Department of Statstcal Scences Va Cesare Battst, Padua Italy tel: fax: Correspondng author: Frstname Lastname tel: name@unpd.t

3 1 Secton 1. Introducton Latent Class Analyss for Marketng Scales Development Francesca Bass Department of Statstcal Scences Unversty of Padua Italy Abstract: Measurement scales are a crucal nstrument for research n marketng n order to measure unobservable varables as atttudes, opnons, belefs. In usng, evaluatng, or developng mult-tem scales, a number of gudelnes and procedures are recommended to ensure that the measure s psychometrcally robust. These procedures have been outlned n the psychometrc lterature snce the late seventes and are composed of steps whch refer to construct defnton, doman and scale valdty, relablty, dmensonalty, and generalzablty. Varous statstcal nstruments are used n the scale developng process, these almost always refer to metrc varables (nterval or rato scales). Items formng scales are nstead rarely measured on an metrc level, frequently tems are ordnal, n some rare cases, nomnal. In ths paper, t s shown how the mplementaton of latent class analyss may mprove the process of measurement scale development snce t explctly consders that tems generate ordnal or even nomnal varables. Specfcally, applyng approprate latent class models allows to assess scale valdty and relablty more soundly than the methods tradtonally used. Keywords: measurement scales, valdty, relablty, latent class factor model, latent class regresson model, ordnal varables 1. Introducton Measurement scales are a crucal nstrument for research n marketng n order to measure unobservable varables as atttudes, opnons, belefs. Examples of unobservable varables related to marketng are customer satsfacton, purchase nvolvement, brand loyalty, sceptcsm towards advertsng and many others (for a revew, see Bearden and Netemeyer 1998). In usng, evaluatng, or developng mult-tem scales, a number of gudelnes and procedures are recommended to help ensure that the measure s psychometrcally as sound as possble. These procedures are delneated n the psychometrc lterature snce the late seventes. Tradtonally, wth some exceptons, the lterature followed the procedure outlned by Churchll (1979) who dentfes a number of steps to take n developng a measure. These steps refer to construct defnton and doman, and scale valdty, relablty, dmensonalty, and generalzablty. Varous statstcal nstruments are used n the scale developng steps, these almost always refer to varables measured on a metrc scale (examples are correlaton coeffcents, factoral analyss, regresson models). Items formng scales are nstead almost always measured on a level whch s dfferent from the metrc one; often tems are ordnal, n some rare cases, nomnal. Lkert, semantc dfferental, and Staple scales, for example, generate ordnal varables. In ths paper, I show how the mplementaton of latent class analyss (McCoutcheon 1987) may mprove the process of measurement scale development snce t explctly consders that tems generate ordnal or even nomnal varables. Specfcally, applyng approprate latent class models allows to assess scale valdty and relablty more soundly than the methods tradtonally used. The data used n the paper refer to a scale desgned n order to measure customer satsfacton wth reference to an experental good, specfcally a move seen at the cnema (Bass 2010). The proposed procedure can be used to evaluate scales to measure any other construct relevant n marketng. The paper s organzed as follows. Secton 2 revews the lterature on measurement scale development. Secton 3 descrbes the scale under evaluaton, a scale to measure customer satsfacton wth reference to an experental good, the data used n the paper and some prelmnary

4 Francesca Bass 2 analyses on t. Secton 4 ntroduces the latent class approach and ts extensons - latent class factor models and latent class regresson models that are especally suted for measurement scale evaluaton. Secton 5 evaluates a scale proposed usng statstcal method that take nto account the unobservable nature of the construct and the fact that tems generate ordnal varables. Secton 6 concludes. 2. Mult-tem scales development Mult-tem measurement scales are largely employed n marketng research for varous reasons (Churchll 1979). Sngle-tem measures (Berkvst & Rosster 207) have consderable unqueness n that each tem tends to have only a low correlaton wth the attrbute beng measured, secondly, sngle tems tend to categorze people nto a relatvely small number of groups, thrd, ndvdual tems typcally have consderable measurement error and, last but not least, many phenomena related to marketng research are multdmensonal and not drectly observable. Many questons n marketng research regard measurng atttudes,.e., psychologcal constructs, ways of conceptualzng ntangble mental states used by ndvduals to structure the way they perceve the envronment and gude the way they respond to t. Examples of atttudes relevant n the feld of marketng research are customer satsfacton, purchase nvolvement, market orentaton, consumer atttude toward marketng, servce qualty. It s unrealstc to measure atttudes towards complex objects wth sngle-tem scales. A large varety of mult-tem scales has been proposed n the marketng lterature n order to measure a sample of belefs about the atttude objects (such as agreement or dsagreement wth a number of statements) and combne the answers n some form of average score. The most frequently employed are the Lkert and the semantc dfferental scale. Lkert scales requre respondents to ndcate a degree of agreement or dsagreement wth a varety of statements, or tems, related to the atttude or object. Often fve ordered response levels are used, but there are Lkert scales also wth seven or nne ordered responses. The scores on ndvdual tems are summed to produce a total score for the respondent; for ths reason, an mportant assumpton of the Lkert scale s that each of the tems measures some aspect of a sngle common factor. In semantc dfferental scales (Snder & Osgood 1969), respondents are asked to rate each atttude object on a number of fve- or seven-pont ratng scales, bounded at each end by polar adjectves or phrases. Each of the seven scale categores s assgned a value form 3 to +3 or from 1 to 7, and the scores across all adjectves pars are summed for each respondent. Staple scales are a smplfed versons of semantc-dfferental scales, whch use only one pole rather tan two. Developng a mult-tem scale s a complex procedure and requres qute a lot of expertse. A large number of papers n the marketng lterature s devoted to ths topc. The frst papers appeared n the seventes, n partcular two semnal works were publshed to whch almost all the followng relevant lterature on the topc refers. Peter (1979) revews tradtonal relablty theory and measurement, dscussng basc concepts and evaluatng assessment procedures for use n marketng research. Peter also ntroduces the generalzablty theory, provdng a unfed conceptual and operatonal approach for addressng relablty ssues. Fnally, the author apples relablty assessment n the area of marketng, specfcally on consumer behavour. Churchll (1979) proposes a framework, a sort of protocol, by whch measures of constructs of nterest to marketers can be developed havng desrable relablty and valdty propertes. Ths framework s stll followed n many studes publshed n the relevant lterature whch propose new or refned nstruments to measure marketng constructs and, for ths reason, deserves our attenton. The procedure proposed by Churchll s artculated n a sequence of steps. The frst step nvolves specfyng the doman and the defnton of the construct. Construct descrpton mples to descrbe what s ncluded n and what s excluded from the doman, and the a

5 3 Secton 2. Mult-tem scales development pror dmensonalty. A thorough revew of the exstng lterature and experts opnon are usually helpful. The second step conssts of generatng tems whch capture the doman as specfed; the followng steps am at purfyng the measure, whch means obtanng a measure whch s vald and relable. Items should exhbt content valdty, that s, they must be consstent wth the theoretcal doman of the construct. To ths am, tems should be screened by judges wth expertse n the reference lterature and undergo several plot tests on samples from the relevant populaton. Items are judged also on ther readablty, clearness and redundancy. On the bases of these crtera, unnecessary tems are elmnated and unclear tems are rewrtten. In ths phase, t s also possble that tems, relevant to the measure but gnored n a precedng step, were ncluded n the scale. The procedure contnues assessng relablty wth new data. A measure s consdered relable to the extent that ndependent but comparable measures of the same trat or construct of a gven object agree. Relablty s a necessary but not suffcent condton of valdty. In order to evaluate relablty, tems are nserted nto a questonnare and admnstered to a sample of respondents. Wth the collected data relablty ndcators are calculated. Hgh nter-tem correlatons, for example, ndcate that tems are drawn from the doman of a sngle construct, low nter-tem correlatons, on the contrary, ndcate that some tems are not drawn from the approprate doman and are producng error. Hgh nter-tem correlatons together wth hgh tem-to-total correlatons show that the scale s nternally consstent. Correlaton between the same person s score on the same set of tems at two ponts n tme s a measure of test-retest relablty. Cronbach s alpha coeffcent (Cronbach, 1951) s recommended as a measure of nternal consstency, together wth other ndexes lke Guttman G and Spearman-Brown Y. In ths phase scale dmensonalty s also evaluated. A construct s doman may be un- or multdmensonal. In ths context, varous nstruments are proposed. Factor analyss s suggested to determne the number of dmensons underlnng the construct. Scale undmensonalty s consdered a prerequste to relablty and valdty; f a scale s multdmensonal, relablty, for example, has to be assessed for each dmenson. Beyond content valdty, dmensonalty, and relablty, a number of other valdty ssues must be consdered n scale development, ncludng construct valdty, whch artculates n convergent and dscrmnant valdty. Determnng the extent to whch the measure correlates wth others desgned to measure the same object generates evdence of convergent valdty; determnng the extent to whch the measure correlates wth measures that are supposed not measurng the same concept generates evdence of dscrmnant valdty, n ths context the nstrument tradtonally proposed s the multtratmultmethod matrx (Campbell and Frske, 1959). Investgatng f the measure behaves as expected n relaton to other constructs evaluates crteron valdty. A fnal step conssts n determnng norms,.e., assessng the poston of the ndvdual on the characterstcs measured by comparng the person s score wth the score acheved by others. Relevant and more recent contrbutons to the topc of scale development are Gerbng and Anderson (1988), Rosster (2002), Fnn and Kayande (2005). Gerbng and Anderson, buldng on the work of Churchll (1979) and Peter (1979), outlne an updated paradgm for scale development that ncorporates confrmatory factor analyss for the assessment of undmensonalty. Rosster proposes a new procedure for the development of scales to measure marketng constructs based on content valdty establshed by experts agreement after pre-ntervews wth target raters. The procedure s labelled C-OAR-SE to reflect ts concern wth construct defnton (C), object classfcaton (O), attrbute classfcaton (A), rater dentfcaton (R), scale formaton (S) and enumeraton and reportng (E). Rosster challenges the tradtonal procedure advocated by Churchll (1979), showng that t s a subset of the C-OAR-SE framework. Fnn and Kayande suggest that multvarate generalzablty theory ntegrates the two competng perspectves (by Churchll and Rosster) by requrng an emphass on conceptual rgor and emprcal evaluaton of constructs. Other nterestng contrbutons are that by Zachkowsky (1985) who develops a protocol to measure

6 Francesca Bass 4 purchase nvolvement and that by De Vells (1991) who refnes the procedure to obtan vald, relable and generalzable measurement scales. Very recent ones are Coelho and Esteves (2007) who face the problem of the optmal number of response alternatves to an tem and Treblanche and Boshoff (2008) who show how structural equaton modellng mproves construct valdty. The topc of marketng scale development occupes a relevant porton of space n the lterature: a complaton of mult-tem, self-reported measures developed and used n consumer research and market behavour s n the handbook by Bearden and Netemeyer (1998). The handbook refers to papers publshed n the most mportant journals n the areas of marketng and consumer behavour research. The majorty of scales s developed followng the lnes outlned above, based on the semnal works of Peter (1979) and Churchll (1979). 3. A scale to measure customer satsfacton wth reference to experental goods The data used n ths paper was collected wth a scale proposed to measure customer satsfacton wth reference to experental goods (Bass, 2010). The pecular nature of these goods means that both the classcal theory of consumer behavour and tradtonal marketng need revson and extenson. Experence may be defned as an event that nvolves a person n a memorable way (Pne and Glmore, 1999). Ths means that experental goods cannot be treated wth tradtonal crtera (for example, utltaran), snce they nvolve a greater affectve component, hedonstc crtera, and customers personal characterstcs (Babn et al., 1994). The scale was desgned wthn a research project whch ams at measurng customer satsfacton by consderng all aspects nvolved n a consumpton experence (Bass and Gudo, 2006). The scale was tested on a convenence sample and ts relablty and valdty were evaluated followng the protocol proposed by Zachowsky (1985) whch s nested n the procedure for scale development proposed by Churchll (1979). The product chosen was a flm seen at the cnema. The method used to buld the scale started wth an exploratory research n order to defne the object to be measured. Items were then generated by means of a lterature revew and an exploratory survey wth two focus groups and ntervews wth an open-queston questonnare. Items were frst evaluated and selected wth reference to ther representatveness and consstency wth the concept to be measured, and then on the bases of valdty and relablty (Ltwn, 1995). The tradtonal dsconfrmaton paradgm defnes customer satsfacton as the result of an evaluaton whch compares product performance, as perceved by customers, wth ther expectatons and desres (Spreng et al., 1997). In our approach, the nature of the concept s mantaned as an evaluaton dervng from a comparatve process, but the terms wth whch expectatons and desres are compared are extended: from product performance to consumpton experence. Customer satsfacton s defned as an evaluaton emergng from a comparson between expectatons and performance of aspects relevant to the entre consumpton experence. Items were generated wth reference to the varous phases of a consumpton experence, focusng on experental goods wth relatve aspects connected to purchase. Items were suggested by a lterature revew (coverng customer behavour, experental goods, development of scales, and customer satsfacton), focus groups wth consumers and a survey wth an open-queston questonnare on a convenence sample of customers. Items were evaluated as regards content valdty on the bass of two crtera: () the representatveness of the concept to be measured, and () comparson of aspects emergng from the lterature wth those expressed n the focus groups and questonnares. Twenty selected tems composed the fnal scale (see Appendx). Respondents were requested to express ther judgement on each tem wth reference to ther expectatons and desres on a fve-pont scale rangng from much less than expected to much more than expected. Items 1-3 refer to the need recognton phase of the consumpton experence, tems 4-7 to nformaton search, tems 8-10

7 5 Secton 3. A scale to measure customer satsfacton wth reference to experental goods to evaluaton of alternatves, tems to purchase decson, and tems to consumpton and post-purchase evaluaton. In a precedng work (Bass, 2010) scale propertes were evaluated usng data collected on a convenence sample of 100 respondents. Item to total correlaton coeffcents were hgher than 0.5, except for tems 1, 2, 3, 4, 6, 7, 10, 13 and 20; n partcular, tem 7-to-total correlaton coeffcent was not statstcally dfferent from 0 at a sgnfcance level of α=0.05. It was therefore concluded that tems 1 to 7, referrng to the two frst phases of the consumpton experence, are not completely sutable for measurng customer satsfacton wth reference to a flm seen at the cnema, and must be better formulated. Factor analyss confrmed ths hypothess: one domnatng egenvalue was found, wth a factor correlated to all tems except 1, 2, 5 and 7. There was one factor explanng 24% of total varance not a very hgh percentage, but sgnfcant n confrmng the nternal relablty of tems. Coeffcents whch measure nternal scale relablty showed satsfactory levels of nternal consstency: Spearman-Brown (0.65), Guttman (0.64) and Cronbach s alpha (0.81) coeffcents were calculated and showed a satsfactory level of nternal consstency In order to evaluate scale relablty over smlar condtons, the sample was randomly dvded nto two groups. A t-test showed not only that the means n the two groups were not sgnfcantly dfferent, but also that the nternal relablty coeffcents had smlar, and hgh, values n the two random subsamples. Crteron valdty s the degree of correspondence between a measure and a crteron varable, usually assessed by ther correlaton. To assess crteron valdty, we need a varable that gves us a standard wth whch to compare our measure. In the fnal part of the questonnare, one addtonal tem (A1) was ntroduced, askng respondents to express ther satsfacton wth the entre consumpton experence a flm seen at the cnema - on a fve-pont scale. Ths tem was our crteron varable. The correlaton coeffcent between the average scale value and the crteron varable was not very hgh, but suffcent to ensure valdty. Unvarate analyss of varance (ANOVA; for the method, see Malhotra, 1999 ), wth the total score as dependent varable and the crteron varable as factor, showed that the average total score was sgnfcantly dfferent among the fve levels of the crteron varable. Construct valdty assesses whether a measure relates to other observed varables n a way that s consstent wth theoretcally derved predctons. In order to evaluate construct valdty, three more addtonal tems were ntroduced nto the fnal part of the questonnare, descrbng aspects assumed to be postvely correlated wth the overall satsfacton level: A2. I would lke to see ths flm agan. A3. I wll speak well about ths flm and ths cnema. A4. I do not have any complant about the consumpton experence. Respondents were asked to answer on a fve-pont scale. Correlaton coeffcents between average total score and scores on the three addtonal tems were 0.5, 0.5 and 0.4, respectvely; all statstcally dfferent from 0. Our scale total score was classfed nto three categores: low (total score 63), medum (64-72) and hgh ( 73), accordng to the quartles of the dstrbuton. Three ANOVAs, one per addtonal tem, were conducted n order to evaluate dfferences among means per satsfacton level. Only for the frst two addtonal tems were means statstcally dfferent. Ths result, together wth the fact that the thrd tem also showed the lowest correlaton wth the total score, casts some doubt on ts specfcaton. It s, n effect, dffcult for a customer not to have one sngle complant about such a complex experence. Nevertheless, these complants may not nfluence the overall satsfacton level. Multvarate analyss of varance (MANOVA, for the method, see Malhotra, 1999) evaluated all three tems together wth reference to satsfacton level. The means of the three addtonal tems were sgnfcantly dfferent across total score levels. Ths result means that respondents wth a low scale score assgned scores to the three addtonal tems dfferent from those assgned by respondents havng medum or hgh total scores whch s another proof of scale construct valdty.

8 Francesca Bass 6 Accordng to the recommendatons developed n the lterature, startng from Churchll s (1979) framework, the analyses descrbed above evaluate the scale to measure customer satsfacton wth reference to an experental good to be undmensonal, vald and relable. In ths paper I want to dscuss ths result startng from the consderaton that n the scale development procedure outlned above, scale propertes have been judged applyng statstcal technques whch assume that varables generated by the Lkert tems are measured on a metrc scale. In the followng, I show how latent class analyss, whch explctly consders the ordnal nature of observed varables may mprove scale evaluaton. Another advantage of LC analyss s that t allows to consder the object that the scale ams at measurng, customer satsfacton, s not drectly observable. Three aspects of the scale development procedure wll deserve attenton. In the assessment of scale dmensonalty, factor analyss, tradtonally employed and recommended (see, for example, the work by Gerbng and Anderson, 1988) s more approprately replaced by an extenson of latent class models denomnated latent class factor model (Magdson and Vermunt, 2001). For the assessment of crteron valdty, I propose an approach that takes explctly nto account the fact that the object under measurement s not drectly observable. In the assessment of construct valdty, correlaton coeffcents are more approprately replaced by latent class regresson models (Magdson and Vermunt, 2004). In order to estmate latent class models, the scale was admnstered to a new convenence sample of 800 respondents. 4. Latent class models The basc notons of latent class (LC) analyss were developed by Lazarsfeld (1950) and hs assocates (Lazarsfeld and Henry, 1968). Credt for feasble and flexble algorthms for testng the valdty of a wde varety of latent class models (LCM) and estmatng ther parameters s due especally to Goodman (1974) and Haberman (1979). Introducton to more recent developments are provded by Clogg (1982), Forman (1985) and Hagenaars (1990). There are two knds of varables n LCM: drectly observed manfest varables, also called ndcators, and not drectly observed latent varables. Both types of varables are treated as nomnallevel, but there exst approprate extensons of the latent class approach that treat varables as ordnal-level. Categores of the latent varables are called latent classes. In the latent class approach, respondents scores on ndcators are a drect result of ther belongng to one of the latent classes. However, the relaton between the latent varable and ts ndcators s not determnstc, but probablstc. Furthermore, t s assumed that the scores on the manfest varables do not nfluence each other drectly, all the manfest varables have n common s ther beng ndcators of the same latent varable. The manfest varables are correlated wth each other, but ths correlaton dsappears when the latent varable s held constant. Ths s the assumpton of local ndependence. A latent class model for four nomnal manfest varables A, B, C and D, and one latent varable, s defned as: = ABCD jklt t A t B jt C kt D lt where ABCD jklt s the proporton of unts n the fve-way contngency table, t s the probablty of beng n latent class t=1,2,,t of varable ; A t s the probablty of obtanng the th,, =1,2,,I, response to tem A, from members of latent class t; B C D jt, kt, lt, j=1,2,,j, k=1,2,,k, l=1,2,,l, are the condtonal probabltes of tems B, C and D, respectvely. Observed responses to ndcators A, B, C and D are mutually ndependent, gven the latent varable, as the local ndependence assumpton mples.

9 7 Secton 4. Latent class models Any LC model s equvalent to a loglnear model wth latent varables (Haberman, 1979); n the case of four ndcators and one latent varable, n loglnear terms, we have: ln F ABCD jklt = λ t A B j C k D l A t B jt C kt D lt where λ t, ABCD F jklt s the absolute frequency n the generc cell of a fve-way contngency table; A λ, B λ j, C λ k and D λ l denote frst-order effects; A B C D λ t, λ jt, λ kt and λ lt denote second-order effects. The assumpton of local ndependence s mposed by the omsson of all nteracton terms pertanng to the assocatons between the ndcators. A For example, condtonal probablty may be wrtten as: t A t = I A exp( λ r= 1 A exp( λ r A t ) A rt ) (1) A When the ndcators are ordnal, the second-order effect n equaton (1) becomes λ t = λt, where s the score assgned to tem A. Ths yelds the adjacent-category ordnal logt model (Goodman, 1979). One goal of tradtonal LC analyss s to determne the smallest number of latent classes T whch s suffcent to explan the assocatons observed among the manfest varables. The fnal step of LC analyss s to use the results of the model to classfy unts nto the approprate latent class. For any gven response pattern (, j, k, l), estmates for the posteror membershp probabltes may be obtaned through the Bayes theorem. Cases are then assgned to the class for whch the posteror probablty s hghest. Magdson and Vermunt (2001) refer to ths as an LC cluster model because the goal of classfcaton nto T homogeneous groups s dentcal to that of cluster analyss. Cases n the same latent class are smlar because ther responses are generated by the same probablty dstrbuton. Rejecton of a T-class LCM due to lack of ft means that the local ndependence assumpton does not hold. The tradtonal model-fttng strategy s to ft a T+1-class model to the data, but alternatve strateges may be consdered, to see f they lead to more parsmonous models, as well as models more congruent wth ntal hypotheses. Magdson and Vermunt (2001) show that, by ncreasng dmensonalty by addng latent varables rather than latent classes, the resultng LC factor model often fts data better than the LC cluster model wth the same number of parameters. In addton, LC factor models are dentfed n some stuatons when the tradtonal LCM s not. Certan tradtonal LCMs contanng four or more classes may be nterpreted n terms of two or more component latent varables (factors). For example, a latent varable consstng of four classes can be represented n terms of two dchotomous latent varables V and W, usng the followng correspondences: =1 corresponds wth V=1 and W=1; =2 wth V=1 and W=2; =3 wth V=2 and W=1; =4 wth V=2 and W=2. Formally, for four nomnal varables, the four-class LCM may be reparametersed as an unrestrcted LC factor model wth two dchotomous latent varables, as follows: = = ABCDVW jklrs VW rs ABCDVW jklrs VW rs AVW rs BVW jrs CVW krs DVW lrs and n loglnear terms:

10 Francesca Bass 8 ln ABCDVW F jklrs DV lr AW s = λ BW js V r W s CW ks VW rs DW ls A AVW rs B j C k BVW jrs D l CVW krs AV r DVW lrs BV jr CV kr + (2) The basc R-factor LCM contans R dchotomous latent varables whch are mutually ndependent of each other and whch exclude hgher-order nteractons from the condtonal response probabltes. Specfcally, the basc R-factor model s obtaned by mposng approprate restrctons on the unrestrcted LC factor model. In the case of R=2, from equaton (2), we have: ln ABCDVW F jklrs AW s BW js = λ CW ks V r W s DW ls A B j C k D l AV r BV jr CV kr DV lr + where the two-varable terms become: λ = λ A AV AW, 2( r 1)+ s r s, λ = λ B j,2( r 1)+ s BV jr BW js AV AW For varable A, λ r represents the loadng of A on factor V and λ s the loadng of A on factor W. Fxng the three-varable terms equal to 0 mples that each of the factors may have an nfluence on each ndcator, but there s no nteracton. Mutual ndependence between latent varables make the model smlar to exploratory factor analyss. Magdson and Vermunt (2001) show that the basc LC factor model wth R ndependent factors has the same number of dstnct parameters as a tradtonal LC cluster model wth R+1 classes. Ths offers a great advantage n parsmony and results are often easer to nterpret. 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 correct 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 and Kamakura, 2000). form: The most general probablty structure for a LC regresson model takes on the followng f ( y z cov, z pred ) = K T cov P( z ) x= 1 t= 1 f ( y t, z pred t ) 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 ; z s a vector of covarates; cov pred z s a vector of predctors; s sngle nomnal latent varable wth K categores, or classes. 5. Scale evaluaton The protocol for scale valuaton, descrbed n Secton 3, was appled to the data collected on the new convenence sample of 800 respondents. Obtaned results are substantally the same as those llustrated n Secton 3. In the followng, I refer on the analyses conducted wth the new

11 9 Secton 5. Scale evaluaton approach to evaluate the scale wth specal reference to dmensonalty, crteron valdty and construct valdty Dmensonalty Factor analyss s largely employed n measurement scale evaluaton, especally n order to verfy the dmensonalty of the construct descrbed by a set of tems. Even f t s largely known that factor analyss s a statstcal nstrument approprate to metrc varables, t s nevertheless used also when tems generate ordnal varables. In ths case, estmaton results may be based and also ndexes of model ft may gve msleadng results. Table 1. Factor loadngs Item Factor 1 Factor 2 Factor 3 I1-0,4054 0,2832-0,2373 I2-0,5464 0,3657-0,2836 I3-0,2186 0,2153 0,2471 I4-0,4278 0,3742-0,0682 I5-0,5434 0,4343-0,0205 I6-0,3978 0,4353 0,0255 I7-0,2273 0,4320-0,0426 I8-0,4458 0,0587 0,4792 I9-0,1907 0,4076 0,2644 I10-0,2139 0,1780 0,1142 I11-0,0472 0,4098 0,1462 I12-0,0809 0,4290 0,0782 I13-0,1949 0,3922-0,0253 I14-0,2125 0,5333 0,1006 I15-0,5037 0,3386 0,2755 I16-0,2768 0,0253 0,4977 I17-0,1142 0,1479 0,4290 I18-0,3831 0,0703 0,4044 I19-0,3514 0,0268 0,5142 I20-0,1434 0,1128 0,3087 The LC factor model, nstead, s approprate to treat nomnal and ordnal varables n the case of dmensonalty evaluaton. For what concerns our scale to measure customer satsfacton wth reference to a move seen at the cnema, factor analyss on the new sample of 800 respondents confrmed the exstence of 1 latent factor, explanng 20.5% of total varance and wth factor loadngs hgher then 0.30 wth all tems. Ths result leads to conclude that the measurement scale s undmensonal. Estmatng on the same data a LC factor model whch consders observed varables as ordnal revealed 3 latent factors. The LC factor model whch showed the best ft to the data (lookng at the BIC ndex 1 ) s the one wth 3 bnary latent factors. Estmated factor loadngs (Table 1) descrbe the three factors. The frst factor s lnked to tems 1, 2, 3, 4, 5, 10 and 15 referrng to nformaton search; the second factor loads on tems 6, 7, 9, 11, 12, 13 and 14 that regard the cnema and ts characterstcs; the thrd factor s lnked to remanng tems that descrbe the move. The measurement scale results tr-dmensonal, made up of three components that determne customer satsfacton: one referrng to nformaton, advertsng ncluded, collected before the move 1 The Bayesan Informaton Crteron (BIC) ndex s an nstrument used to select among alternatve non-nested models. It s a functon of the lkelhood-rato goodness-of-ft value and the number of degrees of freedom to take nto account the parsmony of the model. The model wth the lowest BIC ndex has the best ft to the data.

12 Francesca Bass 10 s seen; a second one that comprses the cnema and all ts features: envronment, personnel, cost; and a thrd one regardng the product move tself and especally ts ablty to nvolve the vewer Crteron valdty In ths paper an alternatve approach to evaluate crteron valdty of a measurement scale s proposed. Ths approach consders both the fact that the object to be measured s not drectly observable and that the tems generate varables wth an ordnal nature. Wth reference to our example, estmatng a LC cluster model wth 1, 2 and 3 latent classes revealed that the scale dentfes 3 latent segments of customers wth dfferent levels of satsfacton towards the product chosen the move seen at the cnema. The LC cluster model wth 3 latent classes showed the best ft to the data accordng to the BIC ndex 2. Another nterestng result from model estmaton s that all tems (except for tem 3 n segment 1) are statstcally sgnfcant n dentfyng latent groups. The frst segment (group 1) s composed of 14% of the sample and dentfes respondents wth hghest levels of satsfacton on all tems (the average satsfacton level s 3,80). The second segment (group 2) contans 78% of the sample and refers to customers wth a medum level of satsfacton (3,27). In the thrd segment (8%) we fnd customers least satsfed (average level on the scale s 2,66). The proposed procedure to evaluate crteron valdty compares the latent varable wth the crteron varable (addtonal tem A1), reorganzed n three classes. Some ndces of agreement between the two measures (latent varable and addtonal tem) were calculated: the percentage of unts consstently classfed s equal to 84%, Cohen s Kappa coeffcent s equal to 0.285, Somers D to All these values cast some doubts on the property of crteron valdty for our scale Construct valdty Also to evaluate construct valdty, n ths paper a new approach s proposed. Usually, to ths am, correlaton coeffcents are calculated, ths nstrument s better suted for metrc varable. The proposed procedure consders ordnal observed varables and, agan, the fact that the object under measurement s not drectly observable. Table 2. Regresson coeffcents and z statstcs for LC regresson models wth 3 latent classes and A2, A3, and A4 as dependent varables. Class 1 Class 2 Class 3 2 R S2 coeffcent 25,79 7,24-0,74 0,57 Z 5,06 2,15-1,36 S3 coeffcent 11,75-0,34 17,64 0,52 z 0,01-0,44 2,31 S4 coeffcent ,51 4,98 0,82 z -2,41 3,31 4,27 LC regresson models, as antcpated n secton 4, estmate a casual relatonshp among one or more predctve varables and one dependent varable, takng nto account that ths relaton may dffer across latent classes. The dfference wth the tradtonal regresson model, where all predctors all observed, s n the fact that, n the LC regresson model, one or more latent varables nteract wth the observed ndependent varables. 2 The BIC ndex for the LC cluster model wth 3 latent classes s lower than that of the LC cluster model wth 2 latent classes but slghtly hgher than that wth 4 latent classes. The percentage of classfcaton errors,.e., the proporton of cases erroneously classfed assgnng each unt to the class wth hgher posteror probablty, s the lowest for the LC cluster model wth 3 latent classes.

13 11 Secton 5. Scale evaluaton On our data, three LC regresson models were estmated havng all as predctor the overall level of satsfacton measured wth the scale and as dependent varables the answers to the 3 addtonal tems A2 (I wll see the flm agan), A3 (I wll speak well about the flm and the cnema) and A4 (I do not have any complants about the consumpton experence). In all three models the best ft (lookng at the BIC ndex) was obtaned wth 3 latent classes, as was expected from the results obtaned verfyng the property of crteron valdty. LC regresson models estmaton results are lsted n Table 2. They are a bt surprsng especally consderng that, usng the tradtonal approach and calculatng correlaton coeffcents between the observed level of satsfacton and the three addtonal tems, the measurement scale was judged to have the property of construct valdty. The relatonshp between the average score obtaned wth the scale and the ntenton to see the move agan s estmated sgnfcantly dfferent n the three latent classes. In two groups (class 2: medum level of satsfacton and class 1: hgh level of satsfacton) ths relaton s postve, n the thrd group (low level of satsfacton) the relatons s estmated not sgnfcantly dfferent from 0. For what concerns the relatonshp between the observed level of satsfacton and the fact to be wllng to speak postvely about the consumpton experence, the estmated regresson coeffcent has been estmated statstcally sgnfcant and postve only n the frst latent class, where customers are the least satsfed. Fnally, the observed level of satsfacton s a statstcally sgnfcant predctor of the fact not to have complants about the consumpton experence n all three groups. In the latent classes wth low and medum satsfacton level the relaton s postve, n the thrd class, the relaton s negatve. The above results cast some doubt on crteron valdty for our measurement scale. 6. Conclusons In ths paper t has been shown how LC analyss allows to mprove the tradtonal approach to develpo and valdate measurement scales. The LC approach, specfcally, takes nto account the facts that data collected wth tems are often ordnal and that the objects that the scale ams at measurng are not drectly observable. The data used n ths work was obtaned admnsterng a scale to measure customer satsfacton wth reference to an experental good: a move seen at the cnema to a sample of respondents. The scale was develpoed n order to take nto account all phases of the consumpton experence. Tradtonal (cluster) LC models were used to evaluate crteron valdty. LC class factor models were estmated n order to evaluate scale dmensonalty and LC regresson models were appled to assess construct valdty. All models take nto account the facts that customer satsfacton s not drectly observable and has to be represented by a latent varable and that observed varables have an ordnal nature. Model estmaton results do not always confrm the evdences obtaned evaluatng the scale wth tradtonal methods of analyss and show the potentaltes of these nstruments nsde the protocols to develop measurement scales. These results encourage applcaton of the method n ths fled and suggest further research work.

14 Francesca Bass 12 References Babn, B.J., Darden, W.R. & Grffn, M. (1994) Work and/or fun: measurng hedonc and utltaran shoppng value. Journal of Consumer Research, 20, 4, pp Bass, F. (2010). Experental goods and customer satsfacton: an applcaton to moves. Qualty Technology & Quanttatve Management, 7, 1. Bass, F., & Gudo, G. (2006). Measurng customer satsfacton: from product performance to consumpton experence, Journal of Consumer Satsfacton, Dssatsfacton and Complanng Behavor, 19, Bearden W.O & Netemeyer R.G. (1998). Handbook of Marketng Scales. Thousand Oaks, CA: Sage. Bergkvst, L. and Rosster, J.R. (2007). The predctve valdty of multple-tem versus sngle-tem measures of the same construct. Journal of Marketng research, 44, May, Campbell, D.R. & Frske, D.W. (1959). Convergent and dscrmnant valdaton by the multtratmultmethod matrx. Psychologcal Bulletn, 56, pp Churchll, G.A. (1979). A paradgm for developng better measures of marketng constructs. Journal of Marketng Research, 16, 1, pp Coelho, P.S. & Esteves, S.P. (2007). The choce between a fve-pont and a ten-pont scale n the framework of customer satsfacton measurement. Internatonal Journal of Marketng Research, 49, 3, Clogg, C.C. (1981). Latent structure models for moblty. Amercan Journal of Socology, 86, Cronbach, L.J. (1951). Coeffcent Alpha and the nternal structure of tests. Psychometrka, 16, pp Fnn, A. & Kayande, U. (2005). How fne s C-OAR-SE? A generalzablty theory perspectve on Rosster s procedure. Internatonal Journal of Research n Marketng, 22, pp Gerbng, D.W. & Anderson, J.C. (1988) An updated paradgm for scale development ncorporatng undmensonalty and ts assessment. Journal of Marketng Research, 25, 2, pp Goodman, L.A. (1974). The analyss of systems of qualtatve varables when some of the varables are unobservable: part I. A modfed latent structure approach. Amercan Journal of Socology, 79, Goodman L.A. (1979). Smple models for the analyss of assocaton n corss-classfcatons havng ordered categores. Journal of the Amercan Statstcal Assocaton, 74, Haberman, S. J. (1979). Analyss of Qualtatve Data, Vol.2. New York: Academc Press. Hagenaars, J.A. (1990). Categorcal Longtudnal Data: Loglnear Panel, Trend and Cohort Analyss. Newbury Park: Sage. Lazarsfeld, P.F. (1950). The Interpretaton and Logcal Foundaton of Latent Structure Analyss. In Stoufer S., (eds.), Measurement and Predcton. NJ: Prnceton Unversty Press. Lazarsfeld, P.F. & Henry N.W. (1968). Latent Structure Analyss. Boston: Houghton Muffln. Ltwn, M.S. (1995). How to Measure Survey Relablty and Valdty. New York: Sage. Magdson, J. & Vermunt, J.K. (2001). Latent class factor and cluster models, b-plots and related graphcal dsplays. Socologcal Methodology, 31, pp Magdson, J. & Vermunt, J.K. (2004). Latent class models. In Kaplan D. (ed.) The Sage Handbook of Quanttatve Methodology for the Socal Scences, Chapter 10. Thousand Oaks: Sage, pp Malhotra, N.K. (1999). Marketng Research. London: Prentce Hall. McCoutcheon, A.L. (1987), Latent Class Analyss. Newbury Park: Sage. Peter, J.P. (1979). Relablty: a revew of psychometrc bascs and recent marketng practces. Journal of Marketng Research, 16, 1, pp

15 13 Secton References Pne, B.J. & Glmore, J.H. (1999). The Experence Economy: Work s Theatre and Every Busness a Stage. Harvard: Harvard Busness School Publshng. Popper, R., Kroll, J., & Magdson, J. (2004). Applcaton of latent class models to food product development: a case study. Sawthooth Conference Proceedngs, pp Rosster, J.R. (2002), The C-OAR-SE procedure for scale development n marketng. Journal of Research n Marketng, 19, pp Snder, J.G. & Osgood, C.E. (1969). Semantc Dfferental Technques: A sourcebook. Chcago: Aldne. Spreng, R.A., Mackenze, S.B. & Olshavsky, R.W. (1996). A re-examnaton of the determnants of consumer satsfacton. Journal of Marketng, 60, 3, pp Thurstone, L.L. (1928). Atttudes can be measured. Amercan Journal of Socology, 33, pp Treblanche, N.S., Boshoff, C. (2007). Improved scale development n marketng. Internatonal Journal of Research n Marketng, 50, 1, Wedel, M., & Kamakura, W. A. (2000). Market Segmentaton: Concepts and Methodologcal Foundatons. Boston: Kluwer Academc. Zachkowsky, J.L. (1985). Measurng the nvolvement construct. Journal of Consumer Research. 12, 3, pp

16 Francesca Bass 14 Appendx FINAL QUESTIONNAIRE PERSONAL INFORMATION: SE: F M F F AGE: CONDITION: F Student F Worker Thnk of a flm you saw at the cnema that nvolved you partcularly. Express your judgement about t, wth reference to your expectatons and wshes, regardng the followng aspects on the fve-pont scale below: Much less than Less than As More than Much more than expected expected expected expected expected Tck your choce 1. To what extent advertsng stmulated your curosty n the flm. 2. To what extent advertsng gave you a real dea of the flm. 3. Flm vdeo and audo qualty at the cnema wth respect to home TV. 4. Correctness of nformaton collected from frends who had already seen the flm 5. Correctness of nformaton collected from advertsng on the story, actors, drector, and soundtrack. 6. Correctness of nformaton on new shootng, photographc or cuttng technques used for the flm. 7. Correctness of nformaton on cnema prces and tmetable, and other servces costs. 8. Your judgement on the potentalty of the flm to be enthrallng, wth reference to other moves avalable. 9. Your judgement on a sutable prce wth respect to your experence at that cnema. 10. Flm avalablty at other cnemas.

17 15 Secton Appendx 11. Audo and vdeo qualty, seatng comfort and cleanness of audtorum. 12. Envronmental potental to nvolve customers postvely (atmosphere, furnshngs, etc.) 13. Helpfulness of personnel. 14. Tcket prce n relaton to overall cnema offer. 15. Confrmaton of nformaton collected (story, soundtrack, specal effects, etc.). 16. Orgnalty of the story. 17. The flm was not borng. 18. How the flm nvolved you, dstractng you from problems. 19. Your feelngs dd not fnsh n the cnema, but contnued after the flm. 20. Capablty of the flm to arouse dscusson. A1. How satsfed are you wth the entre consumpton experence? Not at all Slghtly Nether unsatsfed Moderately Very satsfed satsfed nor satsfed satsfed satsfed Express your agreement wth the followng tems on the fve-pont scale: Total Dsagreement Nether dsagreement Agreement Total dsagreement nor agreement agreement A2. I would lke to see the flm agan. A3. I wll speak well about the flm and the cnema. A4. I do not have any complants about the consumpton experence.

18 Francesca Bass 16 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: