NBD Regression

The degree of distribution intensity is the realized result the companies decide to enter and create, so do BDI. That is why some argue that they cannot use BDI as a determinant for distribution intensity directly. In this section, we will test two possible determinants, market growth and distribution capabilities, as major influential covariates analysis of distribution intensity. By adding such deterministic heterogeneity to NBD model for distribution intensity distribution, we can deeply understand how well-developed the performance and influence of market growth and distribution capabilities are in a certain market.

As shown in equation (10), the negative binomial regression model (NBRM) incorporates observed and unobserved heterogeneity into the conditional mean. In this section, we assume two predictors for distribution intensity in emerging China. CDI is used to evaluate market growth of a product category in a particular market. On the other hand, the ratio of the BDI divided by the corresponding number of resident intermediaries indicates their management capability in that city. This will be the one for representing the distribution capabilities.

In NBD regression model, we assume distribution intensity is distributed as a Poisson random variable with mean λ, which has a gamma distribution across all cities and test whether λ is related to these two predictors .However, the Poisson

regression model (PRM) has the same conditional mean and variance (equidispersion).

When it is invalid, the conditional variance of y becomes larger than its conditional mean; thus, we are said to have overdispersion data (Long, 1997). Considering two regression models, the likelihood ratio test, , is developed to examine the null hypothesis of no overdispersion. If the null hypothesis is rejected, the NBRM is in favor of the PRM, that is, shape parameter α≠0. In fact, PRM rarely fits in practice due to overdispersion. As shown in Table 5.7, all shape parameter α in different models is significant from 0. In Figure 5.1, we have shown goodness-of-fit between NBD model and data. In the bottom of Table 5.6, we also run a restricted model without regressors in order to conduct the likelihood ratio test for improvement for the explaining power of covariates (all p-values < 0.01).

Table 5.6 NBD regression estimates of distribution intensity

PLC 3C leader Haier(TV) Nokia(Mobile phone) Lenovo(PC) Parameters Coefficient

BDI/channel members -7.086*** 0.636 -10.855*** 0.696 -11.311*** 0.821 Log Likelihood (unrestricted) 11270.59 9273.78 11361.68 Log Likelihood (restricted) 11216.87 9146.62 11183.19 Likelihood Ratio for

Covariates 107.44*** 254.32*** 356.98***

1.*at 0.1 level of significant, ** at 0.05 level of significant, *** at 0.01 level of significant.

Table 5.6 also provides NBD regression estimates of distribution intensity of 3C leaders. Since HP does not enter into some markets, we will further discuss its details

( )

2 LL_NBD−LL_poisson

in Table5.7. In Table 5.6, although most parameters are significant among brands, we still discover some interesting patterns from the results. One is the variable representing the distribution capability that shows negative impact on distribution intensity among different models. The other one is the variable CDI, which is not significant in the model of Haier only. This phenomenon might result from TV in its saturation stage of product life cycle.

From the results, we can conclude that distribution capability is more likely an important covariate, which will be considered when making distribution strategies, even in different stages of 3C product life cycle. Besides, CDI is still one of the criteria for brands except for Haier. This result shows that when the industry is still in growth stage, it is better for companies to put their marketing channel resources into the market where industry and brand are well developed. But, when the category is now in saturation stage or even decline, it is better to put the resources into the market according to capable distributors.

Table 5.7 NBD regression estimates ofdistribution intensity in different city-tier samples_HP

PLC Introduction stage

3C leader HP (Printer)

city-tier (Ⅱ) (Ⅲ) (Ⅳ)

Parameters Coefficient Std Error Coefficient

Std

Error Coefficient Std Error shape parameter α 0.286*** 0.097 0.644*** 0.177 1.930*** 1.064

Intercept 2.235*** 0.259 -0.297*** 0.206 -3.416*** 0.833

CDI 0.475*** 0.148 0.963*** 0.220 4.507*** 1.632

BDI/channel members -3.145** 1.439 1.933** 0.933

*at 0.1 level of significant, ** at 0.05 level of significant, *** at 0.01 level of significant.

As shown in Table 5.7, we conduct NBD regression to examine distribution intensity of printer for HP among different city-tier city samples, and ask a key question, “While introducing a new product, such as printer, how to decide market entry strategy among different city-tier markets?” It is apparent that excluding trivial cases in the first city-tier cities, HP decides to enter cities with different market-penetration level. Some interesting patterns from Table 5.7 will be revealed.

One is the variable representing the distribution capability that shows negative impact on distribution intensity only in the second city-tier cities model. But it is not significant on the condition of four-tier markets due to many non-entry data over there.

More interestingly, distribution capability has positive impacts on distribution intensity in the third-tier cities model. This result shows that very few distributors are in third-tier cities. Hence, distribution capability should be approximated to BDI. It is shown that BDI is positively correlated to the number of local distributors. HP in third-tier markets tends to allocate more marketing channel resources in the cities where the brand has already been appreciated by the residences. In contrast, CDI plays a role in introduction stage of 3C product life cycle. As shown in Table 5.7, CDI has a significantly positive influence on distribution intensity across different models.

To sum up, all of the shape parameter αs in different models are significant from 0. In addition, we observe that in saturated markets and reluctant markets in introduction stage, their shape parameter αs are bigger than those in other stages of PLC. It means more concentrated distribution intensity happen in the whole range from growth to mature stages adjusted for market growth and distribution capability.

Substituting NBD regression estimates into Equation (9), and yields the expected distribution intensity. We can further infer that the negative residuals (observed minus expected) of fitting NBD regression model will indicate where the cities are unmet distribution intensity area for these 3C benchmark brands. For instance, the

corresponding top three cites priorities for market entry connected with significantly negative residuals for analysis of Nokia, such as Shen Zhen,Zhu Hai and Fu Zhou, indicating that each of Nokia’s channel intensities among these three cities is much lower than the ideal numbers of intermediaries in that local market. On the other hand, the residual analysis can also identify the place which has oversaturated distribution intensity.