VENKATRAM RAMASWAMY, RABIKAR CHATTERJEE, and STEVEN H. COHEN* Walker and Damien (1999) assert that the latent segmentation model developed by Ramaswamy, Chatterjee, and Cohen (1996) is nonidentifi- able. In response, the authors show that this assertion is incorrect, because the model considered by Walker and Damien is not equivalent to Ramaswamy, Chatterjee, and Cohen's model. The authors discuss and clarify issues of identifiability pertaining to latent segmentation models. Reply to "A Note on Ramaswamy, Chatterjee, and Cohen's Latent Joint Segmentation Models" We thank Professors Walker and Damien for raising an important issue that deserves the attention of marketers. There has been substantial research interest in the develop- ment and application of latent segmentation models in mar- keting during the past decade (Wedel and Kamakura 1998). The issue of model identifiability raised by Walker and Damien (1999, hereafter WD) is pertinent to much of this literature, and not limited to Ramaswamy, Chatterjee, and Cohen's (1996) joint segmentation model (hereafter RCC). Thus, our reply to WD provides an opportunity to clarify and elaborate on model identifiability issues pertaining not only to RCC, but also more generally to a class of latent seg- mentation models based on categorical data (see for exam- ple, Dillon and Kumar 1994). We first show that the model considered by WD in their Equations 1-4 is not equivalent to that by RCC. Specifical- ly, the WD model is based on observations from respondents that consist of categorical data on a single variable, whereas the RCC model considers data on multiple categorical vari- ables. It is the information contained in the pattern of data across the variables over the respondents that allows for the identification of latent segments. When multiple categorical variables are collapsed into a single composite categorical variable (e.g., four 2-level categorical variables collapsed into a single 16-level categorical variable), this information *Venkatram Ramaswamy is Associate Professor of Marketing, University of Michigan Business School (e-mail: venkatr@umich.edu). Rabikar Chatterjee is Associate Professor of Business Administration, Katz Graduate School of Business, University of Pittsburgh (e-mail: rabikar@pitt.edu). Steven H. Cohen is President, Stratford Associates, a market research and consulting firm in Newton, Mass. (e-mail: mail@stratfordA.com). The authors thank Gary Russell and Wagner Kamakura for their encouragement and comments on a previous draft of this reply. To interact with colleagues on specific articles in this issue, see "Feedback" on the JMR Web site at www.ama.org/pubs/jmr. 115 is lost. Thus, when WD collapse the multiple categorical variables into a single categorical variable, the resulting likelihood expression, Equation 6, is not the same as Equa- tion 5, which is the correct likelihood expression corre- sponding to Equation 2 in RCC's study. The model represented by WD in Equations 1-4-and the "collapsed" model represented by them in Equations 6-8- does not correspond to an identifiable latent class (LC) mod- el because they consider, in effect, a single multinomial (cat- egorical) observation from each respondent. Thus, though WD are correct in their conclusions about nonestimability of the parameters 8 j and 1tik in their Equation 3 and 8 jj and 1tijc in Equation 7, these conclusions do not necessarily hold for the corresponding parameters of the RCC model (or, for that matter, other latent segmentation models estimated on cate- gorical data). Nevertheless, there are important model identifiability is- sues that are pertinent to latent segmentation models such as RCC's. We discuss these in the second part of this note. In particular, our focus is on motivating the concept of local identifiability (McHugh 1956) and discussing the conditions under which the model parameters are (locally) identified. Our hope is that this discussion will serve to emphasize the steps that must be taken during estimation of such models and the caveats that developers and users of these models should bear in mind. WHY WD IS NOT EQUIVALENT TO RCC An Illustrative Example To motivate the various issues discussed in this note, we use an illustrative example adapted from Stouffer and Toby's (1951) work and later discussed by Goodman (1974). Table 1, Part A represents data from 216 respondents with respect to whether they tend toward universalistic (1) or particularistic (0) values when confronted by each of four different situations of role conflict. Journal of Marketing Research Vol. XXXVI (February 1999), 115-119