A Bayesian data combination approach for repeated durations under unobserved missing indicators: Application to interpurchase-timing in marketing

Ryosuke Igari, Takahiro Hoshino

Research output: Contribution to journalArticle

Abstract

Intermittent missingness in repeated duration analysis is common in applied studies, but has not been rigorously considered in statistics. Under intermittent missingness, whether any missing events exist between two observed events is unknown. In other words, the missing indicators are never observed. Thus, if there exist any missing events between two observed events, researchers observe only the cumulative duration of the two or more events. A quasi-Bayes estimation method that utilizes population-level information is used to appropriately estimate the parameters under unobserved intermittent missingness. The proposed model consists of the following: (1) a latent variable model, (2) a latent missing indicator model separating the true and composite durations, (3) mixtures of duration models, and (4) moment restriction from population-level information to deal with nonignorable intermittent missingness. A new estimation procedure is used to simultaneously combine likelihood and the objective function of GMM with the latent variables; this is called Bayesian data combination. The model is applied to the interpurchase duration in database marketing using the purchase history data of Japan; these data capture the purchase incidences and stores.

Original languageEnglish
Pages (from-to)150-166
Number of pages17
JournalComputational Statistics and Data Analysis
Volume126
DOIs
Publication statusPublished - 2018 Oct 1

Fingerprint

Marketing
Timing
Duration Models
Bayes Estimation
Latent Variable Models
Latent Variables
Japan
Data acquisition
Incidence
Likelihood
Objective function
Composite
Statistics
Model
Restriction
Moment
Unknown
Composite materials
Estimate

Keywords

  • Dirichlet process mixture model
  • Intermittent missingness
  • Latent variable modeling
  • Population-level information
  • Quasi-Bayes

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

@article{50a23a45386e422c92934c3b4ed9b94d,
title = "A Bayesian data combination approach for repeated durations under unobserved missing indicators: Application to interpurchase-timing in marketing",
abstract = "Intermittent missingness in repeated duration analysis is common in applied studies, but has not been rigorously considered in statistics. Under intermittent missingness, whether any missing events exist between two observed events is unknown. In other words, the missing indicators are never observed. Thus, if there exist any missing events between two observed events, researchers observe only the cumulative duration of the two or more events. A quasi-Bayes estimation method that utilizes population-level information is used to appropriately estimate the parameters under unobserved intermittent missingness. The proposed model consists of the following: (1) a latent variable model, (2) a latent missing indicator model separating the true and composite durations, (3) mixtures of duration models, and (4) moment restriction from population-level information to deal with nonignorable intermittent missingness. A new estimation procedure is used to simultaneously combine likelihood and the objective function of GMM with the latent variables; this is called Bayesian data combination. The model is applied to the interpurchase duration in database marketing using the purchase history data of Japan; these data capture the purchase incidences and stores.",
keywords = "Dirichlet process mixture model, Intermittent missingness, Latent variable modeling, Population-level information, Quasi-Bayes",
author = "Ryosuke Igari and Takahiro Hoshino",
year = "2018",
month = "10",
day = "1",
doi = "10.1016/j.csda.2018.04.001",
language = "English",
volume = "126",
pages = "150--166",
journal = "Computational Statistics and Data Analysis",
issn = "0167-9473",
publisher = "Elsevier",

}

TY - JOUR

T1 - A Bayesian data combination approach for repeated durations under unobserved missing indicators

T2 - Application to interpurchase-timing in marketing

AU - Igari, Ryosuke

AU - Hoshino, Takahiro

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Intermittent missingness in repeated duration analysis is common in applied studies, but has not been rigorously considered in statistics. Under intermittent missingness, whether any missing events exist between two observed events is unknown. In other words, the missing indicators are never observed. Thus, if there exist any missing events between two observed events, researchers observe only the cumulative duration of the two or more events. A quasi-Bayes estimation method that utilizes population-level information is used to appropriately estimate the parameters under unobserved intermittent missingness. The proposed model consists of the following: (1) a latent variable model, (2) a latent missing indicator model separating the true and composite durations, (3) mixtures of duration models, and (4) moment restriction from population-level information to deal with nonignorable intermittent missingness. A new estimation procedure is used to simultaneously combine likelihood and the objective function of GMM with the latent variables; this is called Bayesian data combination. The model is applied to the interpurchase duration in database marketing using the purchase history data of Japan; these data capture the purchase incidences and stores.

AB - Intermittent missingness in repeated duration analysis is common in applied studies, but has not been rigorously considered in statistics. Under intermittent missingness, whether any missing events exist between two observed events is unknown. In other words, the missing indicators are never observed. Thus, if there exist any missing events between two observed events, researchers observe only the cumulative duration of the two or more events. A quasi-Bayes estimation method that utilizes population-level information is used to appropriately estimate the parameters under unobserved intermittent missingness. The proposed model consists of the following: (1) a latent variable model, (2) a latent missing indicator model separating the true and composite durations, (3) mixtures of duration models, and (4) moment restriction from population-level information to deal with nonignorable intermittent missingness. A new estimation procedure is used to simultaneously combine likelihood and the objective function of GMM with the latent variables; this is called Bayesian data combination. The model is applied to the interpurchase duration in database marketing using the purchase history data of Japan; these data capture the purchase incidences and stores.

KW - Dirichlet process mixture model

KW - Intermittent missingness

KW - Latent variable modeling

KW - Population-level information

KW - Quasi-Bayes

UR - http://www.scopus.com/inward/record.url?scp=85047632446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047632446&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2018.04.001

DO - 10.1016/j.csda.2018.04.001

M3 - Article

AN - SCOPUS:85047632446

VL - 126

SP - 150

EP - 166

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

ER -