The diffusion of a new service: Combining service consideration and brand choice

We propose an individual-level model of a two-stage service diffusion process. In the first stage, customers decide whether to "consider" joining the service. This (Consideration) stage is modeled by a hazard model. Customers who decide to consider the service move on to the Choice stage, wherein they choose among the service alternatives and an outside No Choice option. This stage is modeled by a conditional Multinomial Logit model. The service provider does not observe the transition in the first stage of potential customers who have yet to choose a brand. Such potential customers may have started to consider joining the service, yet chose the outside alternative in each period thereafter. One of the main contributions of the model is its ability to distinguish between these two non-adopter types. We estimated the model using data on the adoption process of newly introduced service plans offered by a commercial bank. We employed the hierarchical Bayes Monte Carlo Markov Chain procedure to estimate individual as well as population parameters. The empirical results indicate that the model outperforms competing models in breadth of analysis, model fit, and prediction accuracy

Comparison of two dependent within subject coefficients of variation to evaluate the reproducibility of measurement devices

<p>Abstract</p> <p>Background</p> <p>The within-subject coefficient of variation and intra-class correlation coefficient are commonly used to assess the reliability or reproducibility of interval-scale measurements. Comparison of reproducibility or reliability of measurement devices or methods on the same set of subjects comes down to comparison of dependent reliability or reproducibility parameters.</p> <p>Methods</p> <p>In this paper, we develop several procedures for testing the equality of two dependent within-subject coefficients of variation computed from the same sample of subjects, which is, to the best of our knowledge, has not yet been dealt with in the statistical literature. The Wald test, the likelihood ratio, and the score tests are developed. A simple regression procedure based on results due to Pitman and Morgan is constructed. Furthermore we evaluate the statistical properties of these methods via extensive Monte Carlo simulations. The methodologies are illustrated on two data sets; the first are the microarray gene expressions measured by two plat- forms; the Affymetrix and the Amersham. Because microarray experiments produce expressions for a large number of genes, one would expect that the statistical tests to be asymptotically equivalent. To explore the behaviour of the tests in small or moderate sample sizes, we illustrated the methodologies on data from computer-aided tomographic scans of 50 patients.</p> <p>Results</p> <p>It is shown that the relatively simple Wald's test (WT) is as powerful as the likelihood ratio test (LRT) and that both have consistently greater power than the score test. The regression test holds its empirical levels, and in some occasions is as powerful as the WT and the LRT.</p> <p>Conclusion</p> <p>A comparison between the reproducibility of two measuring instruments using the same set of subjects leads naturally to a comparison of two correlated indices. The presented methodology overcomes the difficulty noted by data analysts that dependence between datasets would confound any inferences one could make about the differences in measures of reliability and reproducibility. The statistical tests presented in this paper have good properties in terms of statistical power.</p

A Choice-Based Approach to the Diffusion of a Service: Forecasting Fax Penetration by Market Segments

Motivated by poor performance of standard estimation methods in our application, the problem of modeling the diffusion of a new service (or a product) is considered without the assumption of a homogeneous population. The model consists of a two-stage procedure where customers receive purchase occasions according to a conventional diffusion model and at each purchase occasion they buy according to a binary choice model. This approach permits explicit incorporation of individual customer demographics and product attributes, whence one can study changes in diffusion as a function of changes in product attributes, prices, advertising, and customer demographics. The model has provided excellent results in a number of applications including the one on fax penetration reported here. In our applications this approach has been useful in market segmentation, studying the effect of marketing strategies, and in evaluating the effects of new service features. A limited validation is carried out to judge the forecasting performance of the model used in the fax example. A simulation study is carried out to compare the proposed solution with the result obtained by fitting the Bass model to a set of market segments separately. The simulation indicates that the proposed approach substantially improves over the aggregate fitting.diffusion of innovations, customer choice models, purchase incentives, product attributes

Some approximations for the moments of a process used in diffusion of new products

We consider approximations for the moments of a well known birth process commonly used in a variety of applications involving diffusion of new products and services. This process also has applications in Epidemiology and Social Sciences. The available approximation for the mean function involves the use of a well known population dynamics model. Direct substitution of this formula in the mean variance relationship leads to an identically zero variance function. We propose an improvement for approximating the mean function. Further, we propose two nontrivial approximations for the variance function. Both of the approximations are evaluated in a limited simulation study. As a extension, the problem of approximating the correlation function is also considered.Epidemic models Bass Model variance function correlation function

Inference on Reliability in Two-parameter Exponential Stress–strength Model

Coverage probability, Generalized confidence limit, Generalized p-value, Location-scale invariance, Pareto distribution, Power distribution, Size,