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Reliability criteria bolster product classification decisions: A reply to Jones
355
Reliability criteria bolster product classification decisions: A reply to Jones (h+*,c?*+i> should
Siva K. Balasubramanian Vniuersity of Iowa, Iowa City, IA 52242, USA
Amit K. Ghosh CleLleland State University, Cleveland, OH 44115, USA Received
June
1992
We welcome the opportunity to respond to Jones’ comment (Jones, 1992) which, despite its critical stance toward the topic investigated, hardly criticizes our investigation per se. For example, the JCR approach is the central element in our study, and Jones does not question this methodology or the veracity of its empirical application. Neither does he disagree with our fundamental premise that the JCR method is a better basis for product classification decisions (compared to the PE method). On the other hand, Jones expresses thoughtful concern over the implementation potential of the topic, i.e., Easingwood’s (1987) classification scheme. In this response, we provide additional details from our analyses, and conclude that the implementation of Easingwood’s scheme is bolstered by attention to reliability in product classification decisions.
Parameter
instability
The main thrust of Jones’ comment is that the parameter estimate pairs (b,, gtl and
be similar. While we agree with him in principle, we emphasize that this argument applies to data systems that are reasonably long and stable-for example, data with no structural changes over time, and those which do not contain “influential observations” (see Kmenta, 19861. On the contrary, early product sales histories used in diffusion model estimation are notoriously limited in length, and represent dynamic (or evolving) data systems; hence, there is little scope for similarity in diffusion parameters derived from sequentially expanded data samples. Indeed, the diffusion literature recognizes that variations in estimation sample size often trigger parameter instability (e.g., Bass, 19691, and our study was motivated by precisely this reason (see the second paragraph of Balasubramanian and Ghosh, 1992).
Classification
reliability
Given this problem of unstable estimates while working with any diffusion model, a basic question follows: can product classifications be meaningful using the NUI diffusion model? ’ The key to a promising answer lies in assuring the reliability of such classifications. Unlike th PE method used by Easingwood (19871, w4 ich ignores this issue altogether, the JCR method we advocate facilitates attention to the following classification reliability criteria.
Correspondence to: Professor SK. Balasubramanian, College of Business Administration, University of Iowa, 568 Phillips Hall, Iowa City, IA 52242, USA. Intern. J. of Research North-Holland
in Marketing
9 (1992) 355-357
0167-8116/92/$05.00
0 1992 - Elsevier
Science
Publishers
’ Our discussion focuses on whether Easingwood’s scheme is practically meaningful. We (and Jones) are convinced that this scheme is conceptually meaningful.
B.V. All rights
reserved
SK. Balasubramanian, A.K. Ghosh / Reply
356 0.45
0.5
0.6
0.7
0.9
0.8
Parameter delta
-
1949-58
Fig. A. Airconditioners:
+
1949-59
m
1949-60
0
1949-61
Overlap across JCRS.
Criterion A: Confidence
Criterion C: Unique representation
This directly assesses whether the researcher can make a “confident classification decision” for a product using data for a given estimation time-frame. That is, it reliably determines whether all statistically reasonable values of b and 6 (i.e., the corresponding 95% approximate JCR) are located within a single diffusion-map class. Our research demonstrates that at least one confident classification decision is possible for each product analyzed.
For any given product, this criterion checks whether its assigned diffusion-map class is the only one among the nine possible classes that accommodates (at least partially) the JCR for each of the four estimation timeframes analyzed. This criterion was met for all the products included in our study.
Criterion B: Consistency This captures the extent to which confident classification decisions are reliable by being consistent. For example, if confident classification decisions are possible for each of several time-frames for a product, do these decisions always indicate the same diffusionmap class? The JCR method indicates remarkable consistency in this regard (i.e., 100%).
Criterion A applies at the level of each classification decision (i.e., based on a single estimation time-frame), while criteria B and C focus on classification results across several estimation time-frames. Furthermore, criterion B limits attention to time-frames that led to confident classification decisions, while criterion C considers all time frames (regardless of whether they yielded confident classification decisions). Criterion C was not discussed in our study, and its consideration now deserves elaboration. In the worst scenario of extreme parameter instability, the JCRS from sequentially expanded estimation samples will not over-
S.K. Balasubramanian, A.K Ghosh / Reply
lap at all. For our purposes, the extent to which this lack of overlap hinders meaningful product classification indicates the severity of the parameter instability problem. Figure A, for example, provides a visual assessment of this for the airconditioners’ data. The overlap area across JCRS from any three sequential time-frames clearly belongs to Class 3. Although the ideal situation is where all four JCRS overlap, the results in Fig. A are impressive nonetheless. This is because as the estimation sample size increases, the potential for overlap is significantly reduced not only by the diagonal JCR movement toward the lower left (i.e., decrease in the magnitude of b and 6 parameters), but also by the decrease in JCR size. (Because the estimation sample base we started with is quite small, the latter finding suggests that each additional datapoint substantially affects the variance/covariance of b and 6). Although the overlap among JCRs is a reassuring index of the similarity in estimates across sequential samples, one can question whether such overlap is crucial given the somewhat limited objective, i.e., to assign a product to one of nine diffusion classes based on b and 6 parameters. Because each diffusion class accommodates a broad range of b and 6 values, consistent product classification decisions are possible even when there is no overlap, as long as all JCRS are confined within a single class. Our results for each of several products indicate that, besides the absence of perfect overlap, only some (not all four) JCRS are entirely confined within a sin-
357
gle class. In such circumstances, it is useful to verify whether the diffusion-map class chosen for a given product is unique in that it is represented (at least partially) in the JCRS for all four estimation time-frames. The unique representation criterion addresses this. In conclusion, three points deserve emphasis. First, because it is managerially useful to classify early product life cycles (see Easingwood, 19871, research in this area is worthwhile. Second, parameter instability can be a potential problem with Easingwood’s classification scheme. Third, one can determine the severity of this problem by assessing classification reliability, both for results from a single estimation time-frame, and for results across several time-frames. Our work suggests that implementation of Easingwood’s scheme can proceed as long as a reliable classification is possible.
References Balasubramanian, S.K. and A.K. Ghosh, 1992. Classifying early product life cycle forms via a diffusion model: Problems and prospects, International Journal of Research in Marketing 9, 345-352. Bass, F.M., 1969. A new product growth model for consumer durables. Management Science 15 (Jan.), 215-227. Easingwood, C.J., 1987. Early product life cycle forms for infrequently purchased major products. International Journal of Research in Marketing 4, 3-9. Jones, J.M., 1992. A comment on “Classifying early product life cycle forms via a diffusion model: Problems and prospects” by Balasubramanian and Ghosh. International Journal of Research in Marketing 9, 353-354. Kmenta, J., 1986. Elements of econometrics, 2nd ed. New York: Macmillan.
Reliability criteria bolster product classification decisions: A reply to Jones (h+*,c?*+i> should
Siva K. Balasubramanian Vniuersity of Iowa, Iowa City, IA 52242, USA
Amit K. Ghosh CleLleland State University, Cleveland, OH 44115, USA Received
June
1992
We welcome the opportunity to respond to Jones’ comment (Jones, 1992) which, despite its critical stance toward the topic investigated, hardly criticizes our investigation per se. For example, the JCR approach is the central element in our study, and Jones does not question this methodology or the veracity of its empirical application. Neither does he disagree with our fundamental premise that the JCR method is a better basis for product classification decisions (compared to the PE method). On the other hand, Jones expresses thoughtful concern over the implementation potential of the topic, i.e., Easingwood’s (1987) classification scheme. In this response, we provide additional details from our analyses, and conclude that the implementation of Easingwood’s scheme is bolstered by attention to reliability in product classification decisions.
Parameter
instability
The main thrust of Jones’ comment is that the parameter estimate pairs (b,, gtl and
be similar. While we agree with him in principle, we emphasize that this argument applies to data systems that are reasonably long and stable-for example, data with no structural changes over time, and those which do not contain “influential observations” (see Kmenta, 19861. On the contrary, early product sales histories used in diffusion model estimation are notoriously limited in length, and represent dynamic (or evolving) data systems; hence, there is little scope for similarity in diffusion parameters derived from sequentially expanded data samples. Indeed, the diffusion literature recognizes that variations in estimation sample size often trigger parameter instability (e.g., Bass, 19691, and our study was motivated by precisely this reason (see the second paragraph of Balasubramanian and Ghosh, 1992).
Classification
reliability
Given this problem of unstable estimates while working with any diffusion model, a basic question follows: can product classifications be meaningful using the NUI diffusion model? ’ The key to a promising answer lies in assuring the reliability of such classifications. Unlike th PE method used by Easingwood (19871, w4 ich ignores this issue altogether, the JCR method we advocate facilitates attention to the following classification reliability criteria.
Correspondence to: Professor SK. Balasubramanian, College of Business Administration, University of Iowa, 568 Phillips Hall, Iowa City, IA 52242, USA. Intern. J. of Research North-Holland
in Marketing
9 (1992) 355-357
0167-8116/92/$05.00
0 1992 - Elsevier
Science
Publishers
’ Our discussion focuses on whether Easingwood’s scheme is practically meaningful. We (and Jones) are convinced that this scheme is conceptually meaningful.
B.V. All rights
reserved
SK. Balasubramanian, A.K. Ghosh / Reply
356 0.45
0.5
0.6
0.7
0.9
0.8
Parameter delta
-
1949-58
Fig. A. Airconditioners:
+
1949-59
m
1949-60
0
1949-61
Overlap across JCRS.
Criterion A: Confidence
Criterion C: Unique representation
This directly assesses whether the researcher can make a “confident classification decision” for a product using data for a given estimation time-frame. That is, it reliably determines whether all statistically reasonable values of b and 6 (i.e., the corresponding 95% approximate JCR) are located within a single diffusion-map class. Our research demonstrates that at least one confident classification decision is possible for each product analyzed.
For any given product, this criterion checks whether its assigned diffusion-map class is the only one among the nine possible classes that accommodates (at least partially) the JCR for each of the four estimation timeframes analyzed. This criterion was met for all the products included in our study.
Criterion B: Consistency This captures the extent to which confident classification decisions are reliable by being consistent. For example, if confident classification decisions are possible for each of several time-frames for a product, do these decisions always indicate the same diffusionmap class? The JCR method indicates remarkable consistency in this regard (i.e., 100%).
Criterion A applies at the level of each classification decision (i.e., based on a single estimation time-frame), while criteria B and C focus on classification results across several estimation time-frames. Furthermore, criterion B limits attention to time-frames that led to confident classification decisions, while criterion C considers all time frames (regardless of whether they yielded confident classification decisions). Criterion C was not discussed in our study, and its consideration now deserves elaboration. In the worst scenario of extreme parameter instability, the JCRS from sequentially expanded estimation samples will not over-
S.K. Balasubramanian, A.K Ghosh / Reply
lap at all. For our purposes, the extent to which this lack of overlap hinders meaningful product classification indicates the severity of the parameter instability problem. Figure A, for example, provides a visual assessment of this for the airconditioners’ data. The overlap area across JCRS from any three sequential time-frames clearly belongs to Class 3. Although the ideal situation is where all four JCRS overlap, the results in Fig. A are impressive nonetheless. This is because as the estimation sample size increases, the potential for overlap is significantly reduced not only by the diagonal JCR movement toward the lower left (i.e., decrease in the magnitude of b and 6 parameters), but also by the decrease in JCR size. (Because the estimation sample base we started with is quite small, the latter finding suggests that each additional datapoint substantially affects the variance/covariance of b and 6). Although the overlap among JCRs is a reassuring index of the similarity in estimates across sequential samples, one can question whether such overlap is crucial given the somewhat limited objective, i.e., to assign a product to one of nine diffusion classes based on b and 6 parameters. Because each diffusion class accommodates a broad range of b and 6 values, consistent product classification decisions are possible even when there is no overlap, as long as all JCRS are confined within a single class. Our results for each of several products indicate that, besides the absence of perfect overlap, only some (not all four) JCRS are entirely confined within a sin-
357
gle class. In such circumstances, it is useful to verify whether the diffusion-map class chosen for a given product is unique in that it is represented (at least partially) in the JCRS for all four estimation time-frames. The unique representation criterion addresses this. In conclusion, three points deserve emphasis. First, because it is managerially useful to classify early product life cycles (see Easingwood, 19871, research in this area is worthwhile. Second, parameter instability can be a potential problem with Easingwood’s classification scheme. Third, one can determine the severity of this problem by assessing classification reliability, both for results from a single estimation time-frame, and for results across several time-frames. Our work suggests that implementation of Easingwood’s scheme can proceed as long as a reliable classification is possible.
References Balasubramanian, S.K. and A.K. Ghosh, 1992. Classifying early product life cycle forms via a diffusion model: Problems and prospects, International Journal of Research in Marketing 9, 345-352. Bass, F.M., 1969. A new product growth model for consumer durables. Management Science 15 (Jan.), 215-227. Easingwood, C.J., 1987. Early product life cycle forms for infrequently purchased major products. International Journal of Research in Marketing 4, 3-9. Jones, J.M., 1992. A comment on “Classifying early product life cycle forms via a diffusion model: Problems and prospects” by Balasubramanian and Ghosh. International Journal of Research in Marketing 9, 353-354. Kmenta, J., 1986. Elements of econometrics, 2nd ed. New York: Macmillan.