3. The Proposed Model
3.2 Joint-Space Mapping
In order to investigate the interaction between new products released on the market by a multi-products brand at different points in time, this study uses the logit-type market share model (González-Benito et al., 2009) for calculating the price competition index of each product. The competition index serves to calculate the cross-price elasticity in order to determine the relationship between changes in the relative attractiveness of products caused by changes in product prices. This contributes to define the directions toward which the consumer’s compromise tendency moves as
－ － 16
technical progress. A technological trajectory can be represented by the movement of multi-products trade-offs cross over different generations, and the trajectory in the multi-generation space defined by these analyzed price and product attractiveness variables.
To take this one step further, we integrate the competitive interaction model of market sales and the autologistic model of spatial patterns to view the product’s intrinsic growth. The autologistic model is a flexible model for predicting the presence or absence of disease in an agricultural field on the basis of soil variables (Gumpertz, Graham, and Ristaino, 1997). This research applies it to marketing to analyze whether a product possesses attractiveness or not by considering products’ spatial correlation. As shown in Figure 2, the procedure involves three steps. In the first step, we construct a price competition index using the target product’s actual purchase histories by all customers for different generations. This analysis includes prices and sales volumes of each product specification. In the second step, we build an attraction model based on the price competition outcome. As will be seen subsequently, this measure links the estimated purchase odds of the focal product to buying intent or aversion derived from the cross-price elasticity. In the final step, we use the predictive autologistic choice model to forecast the probability that each product specification has an effect as if a tugging action were applied.
Figure 2. Conceptual Overview of Models Logit-Type Market Share Model
Transaction Data －－－－ Equation (1) (2)
Price Competition Index to Reveal Multi-Products Brand Interaction
Attraction Measure
Price Competition Index Outcome －－－－ Equation (3) (4) Cross-Price Elasticity to Determine the Relative Attractiveness Relationship
Autologistic Choice Model for Constructing Joint-Space Map Aggregated Data －－－ Equation (5) －
Products’ Spatial Correlation to Determine the Product Growth Path
－ － 17 3.3 Mathematical Calculations
The logit-type market share model assumes that price is the determining factor in market share; the attractiveness of a particular product is the response variable. It splits the price cross-effects in the market response model into two elements: the first one is the changes in price of other products resulting from the changes in prices of a certain product; the second element is the interaction influence on all other competitive products caused by the price of each product. The subjects in this study are various products modes under a single brand from three generations, so as to transform the original relative attractiveness model among brands into products specially designated to a certain brand category. The analysis of the models is as follows:
' independent of price effects; βjj′stands for the price competition index of product j and
j′; and Pt j( )′ is the price of productj′in period t.
The relative attractiveness of product j in period t can be calculated by formula (1), that is, the ratio of the attraction of product j in a certain time period to its competing products’ attractiveness. The attraction of product j in a certain time period is computed by formula (2); the attraction is divided into two parts: attraction of product j itself without regard to prices and its attraction when influenced by prices. We focus on the latter that discusses the price competition index of product jwhen its attraction is caused by the prices of other existing products in the market.
The attraction model (2) used the logarithm and results in formula (3). The relationship of price and attractiveness can be found by regression estimates according to the products existing in the market at each stage. The price competition index from mutual influences of individual products was obtained, and then the cross-price elasticity from the price competition index was found using formula (4).
－ － 18 of product j′andj′′. The cross elasticity of productjandj′is due to the influence of the price of product j′on the sales of productj, and subtracts the influence of the price of productj′on other products’ attraction. Therefore, considering market competition into consideration, deriving the cross elasticity, and discussing these products enables one to identify substitutes or complementary relationships through the elasticity.
In the autologistic model, the log odds of attraction in a particular quadrat (here meaning product mode or specification) are modeled as a linear combination of high or low attraction in neighboring quadrats as well as the price and memory variables.
Neighboring quadrats can be defined as adjacent quadrats within a generation, quadrats in adjacent generations, quadrats two generations away, and so on. There are three features of the autologistic model that make it well suited to the study of spatial patterns of attractiveness: (1) it applies specifically to binary response variables such as high or low attraction; (2) explanatory variables can be incorporated into the model; and (3) the probability of high attraction in a quadrat depends explicitly on whether the neighboring plots are attracted.
Traditionally, logistic regression is often used to model nonspatial binary data (Gumpertz et al., 1997). This research incorporates spatial correlation into logistic regression models by modeling the probability of high attraction in a given quadrat (product mode) as dependent on the attraction status of neighboring quadrats. This method was originally developed by physicists to model an electron spin at each site in a magnetic field (Cressie, 1991). It has also been extended to ordered categorical data, such as disease ratings on a scale of 1 to 4 (Strauss, 1992); similarly, we rated a categorical scale of product memory attributes as independent variables since the marketing communication mechanism lies in capacity attributes, especially in regard to technology goods.
For rectangular lattices, there are some standard systems of neighbors (Besag,
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1972). We applied and modified it as a first-order system includes only the four adjacent quadrats in the set of neighbors—two within the generation and two in adjacent generations; a second-order system includes the four diagonal neighbors in addition to the quadrats of the first-order system; a third-order system includes quadrats two generations or columns away, shown in Figure 3.
＊ Figure 3. Modified Standard Systems of Spatial Mapping
A set of products can be defined for each quadrat in the lattice; if quadrat i is a neighbor of quadrat j, the converse is also true. For binary data, if the response at site i depends in a pairwise fashion on the observed number of neighbors with attraction presence and on covariates, then the conditional probability of a particular response,
i 1 1 if the attraction is high, the log of the odds of attraction being present is expressed in formula (5). of high attractions in the four neighbors. The parameters β quantify the effects of the k
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covariates given the attraction status of the neighbors. For instance, if price is a covariate, its parameter would measure the log of the increase in odds of high attraction that was due to increasing price, after accounting for the effect of attraction in any neighboring quadrats. This type of model has flexibility in that neighbors may be defined in any way that makes sense. If spatial correlation is present, the covariates alone are not sufficient to account for the observed spatial variability. In some settings, spatial correlations can be completely eliminated by regression on covariates. In the present application, however, attractiveness is actually spread or whittled away from one product to another, so it is likely that, even after considering the variables, the attractiveness status of the neighboring quadrats could be an important predictor of attractiveness presence.
3.4 Lifetime Distributions
As the study concerns the duration of product mode after market entry, and these products become competitive at different times, lifetime data analysis is proposed for attractive comparison. Assuming that T is a nonnegative lifetime random variable, functions of T are summarized as follows:
Probability density function: f t( ), ∀ ≥t 0 (6) given that the product survives till time t. These functions can provide mathematically equivalent specifications of the distribution of T. This means that if any of them are known, the others are uniquely specified.
The lifetime of a product is said to be censored when its end-point of interests has
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not been observed, but is known to have occurred at certain interval. There are several types of censoring: (1) right censoring- the observed lifetime is less than or equal to the actual but unknown lifetime, in brief, not experiencing the event at the end or termination; (2) left censoring- the actual lifetime is less than that observed—this situation is encountered when experiencing the event before the start of study or when the only thing for sure is the event occurring at or before the observed time; (3) interval censoring- the event has occurred within an interval of time, but the exact time point is unknown.
Two methods can be employed to estimate the survival function. First, the life table method is a modification of the frequency table to deal with censored data and is a widely used method of portraying lifetime data. This method emphasizes estimation of the conditional probability of death in an interval given surviving to the start of that interval and the probability of surviving past the end of an interval. Assumptions for the life table method are as follows: (1) censored event times are independent of their real lifetimes; and (2) the censoring times and failure times are uniformly distributed with each interval. The second method is product limit estimate, also called Kaplan-Meier estimate. To obtain this estimate of survival, the lifetimes for those experiencing the specified event are first ranked in increasing order. If both censorings and failures occur at the same time, then the censorings are assumed to occur after the failure time. The Kaplan-Meier method assumes that all of the subjects with censored times were at risk at the time of the failures.
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4. Empirical Application
4.1 Industry Property and Data Sources
The target industry is that of the MP3 (MPEG-1 AUDIO LYER3) music player, a market that has already entered the saturation phase in a majority of developed countries.
Following the first purchase, product sales become dependent on the consumers’
purchasing related, upgraded products or on discarding old products in favor of repurchase. Therefore, compared to PLC, using PEC can provide a more comprehensive perspective for understanding the interaction and competition among products in each evolutionary cycle. This understanding can provide a basis for determining the future development trends of products when formulating marketing strategies.
MP3 is a kind of digital audio encoding and destructive compression format developed by MPEG (Motion Picture Experts Group). It is designed to reduce the amount of audio data, filter out the voices that people cannot accept when listening to music. In applying psychological acoustics to determine whether the audio composition can be discarded, the MP3 format for music compression does not differ much from the CD format of music storage as far as the human ear is concerned. The first MP3 music player in the world was manufactured by Saehan Information Systems in Korea in 1998 and its subsequent product sales grew exponentially each year.
Currently, the globally competitive, major vendors in the market are Apple, Creative, Samsung, Sony, SanDisk, Microsoft, iRiver, etc. Industrial concentration is low. With the introduction of its iPod series products, Apple has achieved leadership; its global market share was 26.7% in 2007, and over 20% in 2009, whereas other manufacturers have less than 10% market share. In the US market alone, its market share was 70% in 2010 (Yoffie and Kim, 2010). Nevertheless, an analysis of the PLC of the global MP3 music player shows its introductory stage was from 1998 to 2001, at which time there were only a few R&D manufacturers; 2002 to 2006 saw the growth stage; in 2007, it matured, and since then, the growth rate has gradually declined and has become negative. Even with the economy’s rebound in 2010, market growth is still limited. It is predicted that the product will enter a decline in the future because of market saturation.
In addition to the declining quantity of MP3 products delivered as a result of
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market saturation, there will be further decline due to MP3 music phones absorbing most of the original market. As with personal computers, consumers’ first purchase will not be the main source of sales in the future; rather, product sales will depend on consumers purchasing related upgraded products or discarding old or damaged products in favor of repurchase. Firms must provide more powerful product features, for example, advanced wireless connectivity and high-end displays to attract consumers to buy the new products (iSuppli, 2008). At present, Apple, Samsung, Microsoft, and iRiver have adjusted their strategic direction to pursue the development of multimedia products; they no longer manufacture just the MP3 pure play music products but have introduced more polybasic PMP-related (portable multimedia player) products, using innovation to stimulate a market in which growth is limited.
The transaction data for Taiwan’s market leader is analyzed. Following the leading brand, MSI, Creative, and Panasonic have the sequence market shares. The analysis can be extrapolated to analyze the music industry. This research endeavors to examine MP3 products among which the brand in Taiwan was the leader, in the context of the global MP3 player’s industrial development, and then to explore the competition among various types of music players.
4.2 Database Description
This study probes the effect of the price of different product modes belonging to a single brand category on the relative attractiveness of other products. To measure the relative attractiveness of specific brand products, this study used existing data on market transactions. Using the database systems of certain distributors in Taiwan, 15 months of sales records on MP3 transaction data were collected: a total of 7,936 entries of observed data for 53,197 units sold. The authors analyzed the price competition among nine different product types launched on the Taiwan market by the leading brand. The influence of the prices of specific products on the sales of other products was used to reflect the relative attractiveness of this brand’s products. This study discusses the brand in three stages from the PEC perspective, and uses the research results to determine the structure of market competition.
Information on the different product types selling in the observation period include
－ － 24
product memory, mode, buyers’ name, and purchasing time. Drafting the sales revenue and sales volume of all products with respect to selling time fails to show a simple-four cycle distribution of introduction, growth, maturity, and decline as expected in PLC. The survival time observed for each mode of product in the market is from 7 to 16 months;
the shortest is for mode 720 (7 months from February 2005 to August 2005) and the longest is for modes 200 and 210 (both 16 months from December 2004 to February 2006). Meanwhile, although memory DRAM (dynamic random access memory) was expensive both before and after 2004, it can store more capacity, and the size of memory capacity, therefore, became the greatest force that pushed consumers to make purchases at that time (Yoffie and Kim, 2010). The follow-up products discussion is divided into three stages because makers of MP3 continue to introduce new products, as they have a short life cycle. To maintain the accuracy of the study estimates, the products are classified according to the PEC concept. The first phase of product specifications is 128/256MB, the second is 256MB products, and the third phase consists of 512MB, 1G, and 5G memory.
The average price and sales volume of each product specification according to PEC stages are displayed in Table 1. Firms adjusted the product price over time. Moreover, the total sales of existing products also change in the light of new product launches.
Corporations use the product mode as their communication mechanism in advertising and promotion, while modes are prioritized according to memory capacity, and organized by their launch dates. Therefore, consumers’ purchases also depend on the order of mode, apart from the memory capacity.
Table 1. Product Price and Sale in Each PEC (Price Unit: NT dollar)
PEC Mode 110 120 150 102 180 130 200 210 720
Average Price 3155 4061 5180 2950 4715 Sales Volume 2345 3594 694 650 1365 Third
November 2004 to May 2005
Average Price 4407 2693 3700 3668 4835 3309 7578
Sales Volume 321 360 415 2319 4366 10583 68
－ － 25 4.3 Joint-Space Reasoning
The first PEC includes the 128MB generation; the firm sold modes 110, 120, and 150. This research infers that the relationship between the sales volume of 110 and the average prices of 120 and 150 has significant relevance; likewise, the relationship between the sales of mode 120 and the average prices of 110 and 150; and that between the sales of mode 150 and the average prices of 110 and 120. The entire ratiocination proposes that there exists significant association between the sales of each product mode and the average prices of other modes in the first PEC stage. Similarly, firms lead in 256MB-generation sales in the second PEC phrase, with product specifications for 102, 110, 120, 150, and 180. A correlation may be inferred between the sales of 102 and the prices of 110, 120, 150, and 180. The rest may be deduced by analogy, resulting in a total of five relationships. The overall proposed ratiocination is that there exists significant association between the sales of each product mode and the average prices of other modes in the second PEC stage.
The third PEC is a complete product line generation, having product specifications for 102, 130, 150, 180, 200, 210, and 720. There is evidence of a correlation between the sales of 102 and the prices of 130, 150, 180, 200, 210, and 720. The rest may be deduced by analogy; a total of seven relationships ought to be significant and it is inferred that there exists significant association between the sales of each product mode and the average prices of other modes in the third PEC stage. We can then investigate the causation of compromise effect through price elasticity’s influence on choice or attraction’s influence on market share.
4.4 Product Price Competition
All the regression equations were derived using formula (3) for the relations between the sales of each product and the prices of other product modes targeted at each evolution stage. The results are summarized in Table 2, and most of the reasoning is supported. The indices in the first PEC stage all reach statistical significance. By observing the positive or negative sign, we can discern the intra-brand interaction. For example, for the sales attraction of mode 110, the price of mode 120 has a negative influence on the sales of mode 110, that is, mode 120 weakened the appeal of mode 110.
On the other hand, the price of mode 150 has a positive influence on the sales of mode
－ － 26
110, that is, mode 150 increased the attractiveness of mode 110; the equation is as follows:
Compared to the first stage, another two product modes were promoted in the second PEC, namely, 102 and 180. Mode 102 is low-priced in the product set; the price of mode 180 is between 120 and 150. Observing the firm’s pricing adjustments, the average price of the existing products in the first phase (mode 110, 120, and 150) was seen to descend in the second stage. In the third PEC stage, two products dropped out
Compared to the first stage, another two product modes were promoted in the second PEC, namely, 102 and 180. Mode 102 is low-priced in the product set; the price of mode 180 is between 120 and 150. Observing the firm’s pricing adjustments, the average price of the existing products in the first phase (mode 110, 120, and 150) was seen to descend in the second stage. In the third PEC stage, two products dropped out