Nalini Ravishanker

Multichannel Shopping: Causes and Consequences

The authors explore the drivers of multichannel shopping and the impact of multichannel shopping on customer profitability. Through a longitudinal analysis, the authors provide evidence that multichannel shopping is associated with higher customer profitability. Using the social exchange theory, they develop hypotheses regarding the impact of several customer–firm interaction characteristics on customer channel adoption duration. They propose a shared-frailty hazard model for testing the proposed hypotheses. They use the customer database of an apparel manufacturer that sells through three distinct channels for the empirical analysis and find that frequency-related interaction characteristics have the greatest influence on second-channel adoption duration. In contrast, proportion of returns, a purchase-related interaction characteristic, has the greatest influence on third-channel adoption duration. Variation across customers in purchase-related attributes has a greater impact on the duration to adopt the second channel than the duration to adopt the third channel. In contrast, variation across customers in the channel-related attributes has a greater impact on the third-channel adoption duration than on the second-channel adoption duration. The customer–firm interaction characteristics identified in this study and the proposed model framework allow for forward-looking allocation of multichannel marketing resources.

Selecting exposure measures in crash rate prediction for two-lane highway segments

A critical part of any risk assessment is identifying how to represent exposure to the risk involved. Recent research shows that the relationship between crash count and traffic volume is non-linear; consequently, a simple crash rate computed as the ratio of crash count to volume is not proper for comparing the safety of sites with different traffic volumes. To solve this problem, we describe a new approach for relating traffic volume and crash incidence. Specifically, we disaggregate crashes into four types: (1) single-vehicle, (2) multi-vehicle same direction, (3) multi-vehicle opposite direction, and (4) multi-vehicle intersecting, and define candidate exposure measures for each that we hypothesize will be linear with respect to each crash type. This paper describes initial investigation using crash and physical characteristics data for highway segments in Michigan from the Highway Safety Information System (HSIS). We use zero-inflated-Poisson (ZIP) modeling to estimate models for predicting counts for each of the above crash types as a function of the daily volume, segment length, speed limit and roadway width. We found that the relationship between crashes and the daily volume (AADT) is non-linear and varies by crash type, and is significantly different from the relationship between crashes and segment length for all crash types. Our research will provide information to improve accuracy of crash predictions and, thus, facilitate more meaningful comparison of the safety record of seemingly similar highway locations.

Bayesian analysis of autoregressive fractionally integrated moving-average processes

For the autoregressive fractionally integrated moving‐average (ARFIMA) processes which characterize both long‐memory and short‐memory behavior in time series, we formulate Bayesian inference using Markov chain Monte Carlo methods. We derive a form for the joint posterior distribution of the parameters that is computationally feasible for repetitive evaluation within a modified Gibbs sampling algorithm that we employ. We illustrate our approach through two examples.

Dynamic Reliability Models for Software Using Time-Dependent Covariates

This article presents a new model for software reliability characterization using a growth curve formulation that allows model parameters to vary as a function of covariate information. In the software reliability framework, covariates may include such things as the number of lines of code for a product throughout its development cycle and the number of customer licenses sold over the field life of a product. We describe a Bayesian framework for inference and model assessment, using Markov chain Monte Carlo techniques, that allows for incorporation of subjective information about the parameters through the assumed prior distributions. The methods are illustrated using simulated defect data and defect data collected during development for two large commercial software products.

Analysis of driver and passenger crash injury severity using partial proportional odds models

The question of whether crash injury severity should be modeled using an ordinal response model or a non-ordered (multinomial) response model is persistent in traffic safety engineering. This paper proposes the use of the partial proportional odds (PPO) model as a statistical modeling technique that both bridges the gap between ordered and non-ordered response modeling, and avoids violating the key assumptions in the behavior of crash severity inherent in these two alternatives. The partial proportional odds model is a type of logistic regression that allows certain individual predictor variables to ignore the proportional odds assumption which normally forces predictor variables to affect each level of the response variable with the same magnitude, while other predictor variables retain this proportional odds assumption. This research looks at the effectiveness of this PPO technique in predicting vehicular crash severities on Connecticut state roads using data from 1995 to 2009. The PPO model is compared to ordinal and multinomial response models on the basis of adequacy of model fit, significance of covariates, and out-of-sample prediction accuracy. The results of this study show that the PPO model has adequate fit and performs best overall in terms of covariate significance and holdout prediction accuracy. Combined with the ability to accurately represent the theoretical process of crash injury severity prediction, this makes the PPO technique a favorable approach for crash injury severity modeling by adequately modeling and predicting the ordinal nature of the crash severity process and addressing the non-proportional contributions of some covariates.

NHPP models with Markov switching for software reliability

We describe the use of a latent Markov process governing the parameters of a nonhomogeneous Poisson process (NHPP) model for characterizing the software development defect discovery process. Use of a Markov switching process allows us to characterize non-smooth variations in the rate at which defects are found, better reflecting the industrial software development environment in practice. Additionally, we propose a multivariate model for characterizing changes in the distribution of defect types that are found over time, conditional on the total number of defects. A latent Markov chain governs the evolution of probabilities of the different types. Bayesian methods via Markov chain Monte Carlo facilitate inference. We illustrate the efficacy of the methods using simulated data, then apply them to model reliability growth in a large operating system software component-based on defects discovered during the system testing phase of development.

Bayesian Inference for Time Series with Stable Innovations

This paper describes Bayesian inference for a linear time series model with stable innovations. An advantage of the Bayesian approach is that it enables the simultaneous estimation of the parameters characterizing the stable law and the parameters of the linear autoregressive moving-average model. Our approach uses a Metropolis–Hastings algorithm to generate samples from the joint posterior distribution of all the parameters and subsequent inference is based on these samples. We illustrate our approach using data simulated from three linear processes with stable innovations and a real data set

Bayesian modelling of ARFIMA processes by Markov chain Monte Carlo methods

This article describes Bayesian inference for autoregressive fractionally integrated moving average (ARFIMA) models using Markov chain Monte Carlo methods. The posterior distribution of the model parameters, corresponding to the exact likelihood function is obtained through the partial linear regression coefficients of the ARFIMA process. A Metropolis-Rao-Blackwellizallization approach is used for implementing sampling-based Bayesian inference. Bayesian model selection is discussed and implemented.

Bayesian prediction for vector ARFIMA processes

Abstract We provide explicit formulae for the joint predictive distribution of a Gaussian vector autoregressive fractionally integrated moving average (VARFIMA) process and describe a Bayesian method for its feasible evaluation. Inference for the parameters in the Bayesian framework is based on the joint posterior distribution of the model parameters using the exact likelihood function, as described in Ravishanker and Ray [ Australian Journal of Statistics 23 (1997) 295–312]. Markov chain Monte Carlo methods are used to generate samples from the joint predictive distributions of unknown future realizations conditional on the observed data. The means or medians of the sampled predictions provide point forecasts of the future realizations, while the sample prediction quantiles provide prediction intervals. The approach is illustrated using sea surface temperatures along the California coast at three locations.

Multivariate Survival Models with a Mixture of Positive Stable Frailties

In this paper, we describe models for dependent multivariate survival data using finite mixtures of positive stable frailty distributions. We investigate the cross-ratio function as a local measure of association. We estimate the parameters in the stable mixture together with the parameters of the (conditional) proportional hazards model in a Bayesian framework using Markov chain Monte Carlo algorithms. We illustrate the methodology using data on kidney infections.