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Event history, spatial analysis and count data methods for empirical research in information systems

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Abstract

A large number of interesting business and technology problems in IS and e-commerce research center around events and the associated variables that influence them. Researchers are often interested in studying the timing, patterns, and frequencies of events. Some of those events are related to the timing of strategic decisions such as new technology adoption, functionality upgrades to established software products, new outsourcing contracts, and the termination of failing IS projects. Still others are external events that have significant implications on the performance of firms, the structure of industries affected by IT, and the viability of various aspects of the economy. Event history methods, also known as survival analysis and duration analysis methods, spatial analysis, and count data analysis in the medical sciences, public health and biostatistics literature, offer rigorous methods for empirical analysis that can provide rich insights into research issues that arise in association with identifiable events. This article provides a current survey of these methods and in-depth discussion of how researchers can apply them to study technology adoption problems and related issues in IS and e-commerce. We offer a framework for mapping the methods to applicable problems, and discuss the relevant variants of the methods. We also illustrate the range of research questions that can be asked and answered through the use of the methods.

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Notes

  1. For a fuller discussion of semiparametric methods and related regression approaches, the interested reader should see Cameron and Trivedi [36] and Horowitz [89]. In addition to these three basic categories of techniques, there are also advanced models that deal with events driven by multiple competing risks, recurrence of the same event for the subject, heterogeneity of survival patterns among subgroups of subjects, accelerated likelihood of failure due to the impact of the explanatory variables, and long-term survival of a fraction of the population.

  2. Spatial dependence is observed when Cov (Y i , Y j ) ≠ 0, for i ≠ j; where i and j refer to locations and Y is a variable measuring an event of interest.

  3. This commonly is represented in terms of a log-linear function of the explanatory variables of the multiplicative Poisson regression model, with \( \lambda_{i} = \exp \left( {{\beta}_{0} + \sum_{j} {\beta}_{j} x_{ij} } \right). \) The estimated coefficients β j of the independent variables x ij can be interpreted as though they involve an elasticity, with the expected value of y given x j for some value of x j , through log(x j ) in the Poisson regression model. A key issue with Poisson regression is that the dependence of the variance on the mean value of λ is viewed as a strong assumption, diminishing the range of its applicability.

  4. The validity of Poisson regression model maximum likelihood estimation results also is affected by model misspecification. As a result, the literature on count data models has extensively explored and developed models that expand the capabilities of count data modeling, so it is possible to estimate explanatory models to test relevant theory and hypotheses [29, 39, 49, 65].

  5. Although we chose to highlight six levels of analysis, it does not mean that these methods cannot be used to study technology adoption and other phenomena at other levels of analysis. For example, they can be applied to study technology and standards adoption among countries for digital wireless technologies such as the Global System for Mobile Communications (GSM) or the Code Division of Multiple Access (CDMA).

  6. Other nonparametric methods include life tables, which characterize the rate of survivorship in a population at risk, and are helpful for estimating the survival function using intervals of duration. Another is the Nelson-Aalen estimator for the cumulative hazard function [98]. This involves developing a staircase function that specifies when an observation fails or when an event occurs in time, as well as the number of observations for which events have not been observed just prior to the occurrence of event.

  7. In addition to the Cox proportional hazards model, there are other semiparametric survival analysis techniques that are useful, including additive hazards model. With this kind of model, the covariates are assumed to have an additive rather than a multiplicative effect on the hazard rate [90]. Another approach is called rank regression, which is useful for comparing two distributions using the rank of the natural logarithm of the durations [113].

  8. For readers who are interested in exploring the use of event history methods in other disciplines, we offer additional coverage of some of these works in Appendix 1.

  9. Bayesian survival analysis also supports semiparametric and fully-parametric models, as well as more advanced methods, such as the frailty and cure-rate models. In these models, gamma distributions are used for the priors. For the exponential model, we can formulate the prior distribution for the hazard rate λ = φ(x′ β) to be a gamma prior. By specifying the parameters of the gamma prior and our weight or confidence on this prior, we can formulate the posterior distribution π (θ|D) and use the Gibbs sampler to estimate the parameters. For a Weibull model with a shape parameter λ = x′ β and another parameter α, λ and α are treated as independent and specified to follow normal and gamma distributions, respectively. It is common to assume that the βs follow a multivariate normal distribution. By specifying the priors, we can formulate the joint posterior of α and β given D and estimate the parameters. In addition, gamma distributions are often used as prior distributions for the baseline hazard in the Cox proportional hazards model and for the frailty term in shared frailty models.

  10. In the case of the spatial lag model, ordinary least squares (OLS) estimates are biased and inconsistent [5]. So estimation of the spatial lag model needs to be done via maximum likelihood or through the use of instrumental variables. The spatial error model can be estimated via maximum likelihood. The model with both a spatially-lagged dependent variable and spatial dependence in the error term is complicated to estimate, and thus this model is rarely used in practice.

  11. Similar to the cross-sectional spatial models, the estimation of spatial panel models can be performed using maximum likelihood, or instrumental variables and the generalized method of moments (GMM) approaches [10].

  12. Note that, similar to cross-sectional spatial models, constraining the spatial parameters results in three different models. Setting ρ ≠ 0 and γ ≠ 0 results in the mixed spatial lag and error model. Setting γ  = 0 permits estimating the spatial probit lag model only, while setting ρ = 0 is for estimating the spatial error lag model.

  13. The spatial probit model is known to be complex to estimate, however. This is because the joint probabilities in the likelihood function of this model are multi-dimensional multivariate normal probabilities [7]. Four techniques to estimate spatial probit models are: (1) the expectation–maximization (EM) algorithm, (2) the GMM approach, (3) the Gibbs sampling approach, and (4) the recursive importance sampling approach. The EM algorithm uses a two-step process, an expectation step and a maximization step, to estimate the expected likelihood function of the latent model. Pinkse and Slade [137] develop a GMM approach to assess spatial error correlation in a spatial discrete model. Lesage [116] proposes the Bayesian spatial discrete choice methods that uses Gibbs sampling approach to solve a spatial model based on a latent continuous variable. Finally, the recursive importance sampling approach estimator proposed by Beron and Vijverberg [24] uses simulation to estimate the multivariate normal probability function.

  14. We provide a brief summary of other interdisciplinary applications of spatial analysis methods in Appendix 2. For a review of the application of spatial analysis methods in regional economic and social science, see Anselin [6], Anselin et al. [9], Anselin [8], and Goodchild et al. [69].

  15. These include SpaceStat, S+ SpatialStats, GeoDa, PySpace, the Spatial Econometrics Toolbox for MATLAB, R and STATA, and GeoBUGS (for geographical Bayesian inference using the Gibbs sampler).

  16. Similar to the other empirical modeling approaches that we have discussed, there is plentiful software support for count data modeling. See Cameron and Trivedi [35] for Gauss, Limdep and Stata; Liu and Cela [118] for SAS; Venables and Ripley [163] for S, now Spotfire S+; and Zeilis et al. [175] for R.

  17. Greene [72] showed that it is possible to create overdispersion in the negative binomial model. This is because it goes beyond the Poisson model’s representation. It uses a noisy form of the mean function which permits a larger number of zero values for the dependent variable that are predicted. Berk and McDonald [22] caution us about the use of this model, and provide four implications for estimation practice. First, they note that it is critical to specify the full set of explanatory variables for negative binomial regression model estimation, along with an appropriate functional form for the mean value function, similar to the Poisson regression model. Failure to do so creates the omitted variables problem and introduces systematic bias in the estimation results. Second, if the theoretical arguments and knowledge of the empirical regularities of data fail to match the various assumptions of the models, and cause an analyst to lack confidence that the systematic part of the model that is being used is right, then it may not be a good idea to use these models at all. Berk [21] suggests a fallback position involving what he called a descriptive data analysis. Third, even though an analyst may be confident that the systematic part of the model is right, there still is no guarantee that the usual tests of statistical inference are going to be right also. Fourth, though the author suggests the negative binomial model as a workaround, he still reminds us that it may be a stretch to trust the more attractive p-values that the negative binomial produces.

  18. Such models don’t properly capture the structure of the empirical estimation problem, however; there is no assumption with these models that there will be no zeros observed [85]. Instead, it is necessary and logically consistent to eliminate the possibility that any zeros are estimated at all, by adjusting the requirements of the underlying distribution of the observed counts. The approach used involves the application of zero-truncated Poisson models and zero-truncated negative binomial models [35, 169].

  19. Similar to some of the other models that we have discussed, count data models that have an excess number of zeros have also been studied in terms of their robustness and estimation capabilities. For example, there is a score test to evaluate zero inflation in the presence of correlated count data [172]. There is also a test to evaluate the extent to which non-zero count values of the dependent variable are overdispersed in a zero-inflated Poisson mixed regression model [172]. The motivation for this test and model arises in contexts of computer operations that have many small intra-day network service problems, but also major network outages of longer duration. There are other kinds of robustness checks that can be applied that will be useful for research on IT, e-commerce and technology adoption.

  20. The authors point out that the Bayesian nonparametric approach is more effective in fitting the data of the study, and that this is partly due to the fact that an initial parametric model cannot be specified easily based on the data that it estimates. Nevertheless, some specification iteration is to be expected when the analyst identifies the defects of the parametric model that prompt its re-specification.

  21. This has many applications in e-market settings, including in online group-buying Web sites such as Woot! (www.woot.com), DailyDeal (www.dailydeal.com), and ShuangTuan (www.shuangtuan.com) in China, and for social couponing services, including Groupon (www.groupon.com) and its joint venture with TenCent (www. tencent.com) in China called GaoPeng (www.gaopeng.com), as well as LivingSocial (www.livingsocial.com).

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Acknowledgments

The authors would like to thank the guest editor, Christopher Westland, and the anonymous reviewers of this special issue article in Information Technology and Management for their helpful comments and encouragement. Rob Kauffman also thanks Singapore Management University, National Sun Yat-sen University, and the W.P. Carey Chair in IS at Arizona State University for research funding and support.

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Authors and Affiliations

  1. School of Information Systems, and Lee Kong Chian School of Business, Singapore Management University, Singapore, Singapore

    Robert J. Kauffman

  2. Faculty of Business and Law, Auckland University of Technology, Auckland, New Zealand

    Angsana A. Techatassanasoontorn

  3. College of Business, University of Texas-Pan American, Edinburg, TX, USA

    Bin Wang

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  1. Robert J. Kauffman
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  3. Bin Wang
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Correspondence to Robert J. Kauffman.

Appendices

Appendix 1: Interdisciplinary studies illustrating the application of event history methods

We offer a brief summary of additional studies in a number of disciplines beyond IS that illustrate broad applications of event history methods. There are many other applications of event history methods in marketing, human resources and labor economics, and economics that can guide future efforts (see Table 8). A number of articles are worthwhile to briefly discuss for their use of event history methods, since they illustrate the kinds of applications of the modeling and methodological ideas that seem as though they will be most actionable.

Table 8 Representative studies from other disciplines involving event history methods
Full size table

1.1 Marketing

Marketing researchers have used event history methods to examine the adoption of new product and technology innovations [52, 153], a consumer’s decisions to replace an existing durable product [141], the loss of customers by companies [30, 83, 162], and a consumer’s repeat product purchase decisions [99, 123]. The Cox proportional hazards model has been the most often used method, since it allows researchers to examine the factors that affect the underlying failure process that leads to the occurrence of the events. In addition, researchers have used parametric analysis, AFT models, frailty models and Bayesian survival analysis. Using these survival analysis techniques, IS and e-commerce researchers can investigate technology adoption by individuals and organizations, the decision to discontinue using a technology or to replace it with a newer technology, the duration of outsourcing contracts, and the duration a software application remains on the most popular software list on Download.com.

1.2 Human resources and labor economics

Researchers have used survival analysis to examine employee turnover [86, 130, 158], the decision to quit on the part of employees and managers [117], and the duration of unemployment [11]. In addition to the Cox proportional hazards model, this stream of research also uses recurrent event survival analysis, since researchers often observe multiple instances of turnover and unemployment on the same individual. Similar research issues in the IS and e-commerce area include IT professionals’ turnover and duration of unemployment.

1.3 Economics

Survival analysis, especially the Cox proportional hazards model, has been frequently used in empirical analyses of the diffusion of new technologies [143, 147] and firm survival [14, 88]. Parametric and semiparametric proportional hazards models have been leveraged, allowing researchers to examine the impact of a set of explanatory variables on the adoption decisions or firm survival. These studies provide IS and e-commerce researchers with examples for how different survival analysis techniques can be applied to examine the adoption and diffusion of new technologies and survival of IT and e-commerce firms.

Appendix 2: Interdisciplinary studies illustrating the application of spatial analysis methods

There are also many areas of application for spatial analysis methods that occur in sociology and criminology, political science and political economy, and trade and economics, among others. We will cover a representative sample of the different kinds of applications (see Table 9).

Table 9 Representative studies from other disciplines involving spatial analysis methods
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2.1 Sociology and criminology

Three studies in sociology examine neighborhood effects in population dynamics, child development, and violence. Morenoff and Sampson [129] looked at the effects of homicide and ecological factors (socioeconomic disadvantage, ethnicity, age composition, and residential stability) on changes in the neighborhood population in Chicago from 1970 to 1990. They tested the hypothesis that neighborhood population change is a contagion-bearing process, so a change in one area is likely to affect other close-by neighborhoods. The results suggest the extent of spatial interactions on the diffusion of violent crime and population change. The higher the crime in the surrounding neighborhood of a given area, the greater will be its population loss. Sampson et al. [148] used the spatial lag model to study the spatial dynamics in social processes that produce collective efficacy for children in Chicago area. They found that neighborhoods benefit from being in proximity to those that have high levels of adult-child exchange and shared expectations for child social control.

Tolnay et al. [157] studied the lynching of African Americans across counties in ten southern U.S. states. They test two competing theories that might explain the spatial dependence of lynchings. Contagion theory predicts that lynchings in one area increase the likelihood that they will occur in other nearby areas. Deterrence theory predicts that the probability of such events declines when they occurred in other areas. Their findings support the deterrence model of spatial dependence. Similarly, IS and e-commerce researchers can examine contagion effects in IT adoption in different regions, the provision of outsourcing services in neighboring cities and countries, the emergence of IT and e-commerce firms in different cities, states, or countries, and the migration of IT professionals in the marketplace.

2.2 Political science

Two studies look at spatial effects in war involvement and political campaign donations. Ward and Gleditsch [165] modeled the dependence of the likelihood of a country’s war involvement on the war involvement of other proximate countries using an autologistic model and the MCMC estimation method. Autologistic models have found much use in the evaluation of Markov random field theory and spatial correlation representations for pixel locations in computer and robotic vision [25]. Ward and Gleditsch’s [165] model shows good predictive ability in an out-of-sample forecast for countries that were drawn into civil wars and international conflicts in the 1989–1998 period. Cho [41] estimated spatial effects in campaign donations in the U.S. from 1980 to 1998. The results suggest that campaign donations from Asian American contribution networks are spatially-clustered with both spatial dependence and spatial heterogeneity. This research offers analogies for IS and e-commerce modeling, including the spatial clustering of competition among similar business models in a variety of industry sectors that have been major areas of technological innovation, capital investment and business development.

2.3 Political economy

Case et al. [38] analyzed the impact of state budgets on the expenditures of other nearby states. Their theoretical perspective is based on the effects of spillovers between states that are in close proximity or share similar economic characteristics and demographic qualities. For example, school expenditures in the Washington, DC area may have provided the impetus for Maryland and Virginia, since they are neighboring states, to spend more. The authors found that state government fiscal decisions are influenced significantly by the budgeting actions of nearby states. Another interesting study is by Novo [134], who used a spatial probit model to study the contagion effects among European countries in the 1992 currency crisis. The author’s findings confirm that problems with perceptions about the strengths and weaknesses of currencies were transmitted through the community’s trade channels.

2.4 Economics

Several studies in various sub-fields of economics have investigated spatial dependence in other contexts. For example, Basu and Thibodeau [19] examined spatial autocorrelation in the prices of single-family properties in Dallas, Texas between 1991 and 1993. They found that structural characteristics (lot characteristics, neighborhood amenities, accessibility to other locations) did not explain all of the variation in transaction prices. Instead, there was strong evidence of spatial autocorrelation in transaction prices across submarkets. Cohen and Paul [44] attempted to answer why manufacturing activities seem to concentrate in a few regions. In particular, they examined the contribution of spatial spillovers and agglomeration economies on the performance of the food manufacturing industry in the U.S. Their results suggest that the geographic concentration of food manufacturers is motivated by cost considerations from locating close to suppliers and markets. The agglomeration of IT companies and outsourcing service providers can also be examined using similar methods.

Appendix 3: Interdisciplinary studies illustrating the application of count data methods

We will discuss a number of application areas of count data methods including: transportation, criminal recidivism, healthcare, manufacturing and factory processes, the creation of patents in research and development activities, and labor and unemployment issues (see Table 10).

Table 10 Representative studies from other disciplines involving count data methods
Full size table

3.1 Transportation accidents

One of the well-known application areas for count data modeling is motivated by the study of the frequency of airline accidents and incidents, including the work of Rose [142] and Dionne et al. [59]. The original work by Rose [142] explores data on 16 American passenger airlines between 1957 and 1986 that involved the incidence of aircraft damage and human injuries and deaths. Dionne et al.’s [59] research explored similar issues for 120 Canadian airlines during the 1976–1987 period. In both instances, a problem arose with correlation between the incidence of accidents and the actions of regulatory authorities to require the airlines to implement improved practices that were intended to diminish the likelihood of accidents.

Chib and Winkelmann [39] examined this kind of data using a model that represents the accident count correlations using correlated latent effects. They estimate the data based on a model with Poisson counts and latent effects that follow a multivariate Gaussian distribution, and a number of context-relevant covariates. The latter include: the number of an airline’s departures, the operating margin to gauge an airline’s profitability, the average stage length of an airline’s city-pair routes, the airline’s cumulative experience in terms of miles flown, and the extent to which the airline’s flights had international components, as well as airline firm and year fixed effects. The authors used Markov chain Monte Carlo (MCMC) methods, a Bayesian simulation-based approach.

A number of interesting applications of count data estimation models cluster in the area of vehicle accidents. For example, Houston [91] modeled youth motorcycle fatalities for 15 to 20-year olds from 1974 to 2004 using a family of negative binomial regression models as a basis for understanding the relevant explanatory factors. By using a variety of fixed effects in their models, the authors were able to show regional and temporal variations in the incidence of deaths. They also were able to evaluate the beneficial impacts of mandatory universal helmet laws versus partial coverage helmet laws at the state level in the U.S. The authors’ methodology and careful consideration of estimation bias was relatively effective in how it addressed omitted variables and unobserved heterogeneity, even though the fixed effects modeling specification assumed that there was temporal stability with respect to the effects of the stratifying variables. This work offers a useful analogy for how IS researchers might conduct empirical studies of a spectrum of issues that arise with respect to the incidence of customer information privacy breaches, corporate information breaches, and a variety of related problems that arise on the effectiveness of what organizations do to safeguard sensitive information for their stakeholders.

Another work in the transportation safety area is suggestive of a different kind of analogy for the development of useful research in the IS discipline based on the characteristics of different technologies, applications and systems, users and adopter groups, business processes, and business partners. Shively et al. [149] used a Bayesian semiparametric model to evaluate the relationship between the characteristics of more than 7,700 two-lane rural roadways and roadway segments, and vehicle crash counts that occurred on them in the state of Washington in 2002. The authors’ approach brings a set of continuous variables into their model via unknown functional forms and a second set of categorical variables via linear functions. They use measures such as speed limits, average annualized daily traffic, roadway width, degree of road curvature, and vertical grade, among other variables, to predict the number of crashes. Their approach goes beyond prior and more standard approaches involving panel data negative binomial regression models with covariate effects that are modeled in linear form [109, 127], incorporate random effects [40, 111], and employ Bayesian approaches to the estimation of the data [122]. Taken together, these different works that extend the negative binomial regression model’s assumptions and estimation approach offer a useful roadmap for the application of these methods in IS research involving such issues as the occurrence of defects related to the characteristics of software applications, development teams, project development tools and organizational environments.

3.2 Public transportation

Another area of study that IS researchers can learn from the application of count data modeling approaches is in the area of public transportation. This area has become increasingly important as oil and energy resource prices have steadily risen, reflecting the need for greater awareness of business policies that emphasize resource sustainability. Research that demonstrates the application of zero-inflated count data models in this area is attributable to Frondel and Vance [64], although its basis is on earlier work that pioneered zero-inflated Poisson models in the estimation of manufacturing defects [112] and in the more general areas of zero-inflated models and zero-inflated negative binomial models that we discussed earlier. The need for such models arises when the analyst observes many zeros for the dependent variable in a count data model. The authors investigate public transportation use in Germany during the five-day work-week, and how it is influenced by vehicle fuel prices and transit fares. The zeros arise because the authors modeled individual riders in the catchment areas of potential public transportation users that are served. On any given day, many do not use public transportation, and others never use it at all. The authors’ approach permitted them to model the effects of key covariates while controlling for individual-level user attributes, as well as the characteristics of the system as a whole.

The public transportation context suggests the presence of two latent regimes: one involving users and the other involving non-users. We see similar problems in IS research including the use of virus scanning software and PC firewalls, choices to opt out or opt into corporate information privacy programs, the non-adoption versus adoption and use of a variety of social networking tools and environments, and online news and advertising services (e.g., Facebook and LinkedIn, RSS and other pushed Internet news services, and Groupon, Social Living and other online purchase opportunity awareness building services). The opportunity to leverage zero-inflated models also is likely to occur in the context of music and video downloads among free and fee-based online streaming digital media services for the study of users who consume digital media contents differently via different distribution channels. A similar analogy applies to consumers whose travel-related purchase patterns for airline tickets and hotel stays, where there is significant interest in issues of information transparency [71], alternative channel strategies [31] and product and service decommoditization [70].

3.3 Healthcare

There have been other efforts made to model a variety of healthcare issues using count data modeling approaches. Another aspect of Chib and Winkelmann’s [39] research involves the application of their MCMC approach to explain patient visits for different healthcare services (including doctor’s office visits, non-doctor office visits, hospital outpatient visits, emergency room visits and so on). Although they specifically considered the possibility of correlated visit outcomes based on different provisions for healthcare insurance, prior research viewed the different outcomes as independent [56, 133]. These approaches offer almost immediate translation for application in the technology adoption arena, when firms experience new regulatory requirements for accounting process changes and information requirements that require multiple changes and adjustments to their systems requiring modifications and choices of new kinds of supporting technologies.

The research of Deb and Trivedi [56, 57], Bago d’Uva [15, 16], and Gurmu and Elder [78] offers useful guidance for IS researchers who wish to distinguish between adopters who are frequent users versus infrequent users, as opposed to adopters versus non-adopters. This is true for healthcare services, for example, where few people are non-users, even though not many people are likely to be frequent users. Gurmu and Elder [78] explored empirical count data models that involve two kinds of zeros: one type is the choices that consumers, technology adopters, or users make, and the other is measurement error where the analyst is unable to record relevant count-related behaviors. This occurs with research scientists who apply for patents and do not receive them, and for other research scientists who obtain patents for their inventions outside the observation time window [155].

The methods and empirical work that these authors present use the negative binomial model as a foundation. Their work suggests that hurdle models for count data analysis do not offer sufficient structure to take into account frequent versus infrequent use, and so they propose the use of another class of models called finite mixture models. The method involves the identification of latent classes. In the healthcare context, this could be something like a person’s long-term unobservable health status (e.g., related to advancing problems with diabetes, heart disease or other issues). In the IS context, latent classes may arise with respect to technology adoption due to changes in the functionality of the available technologies, evolving business practices and business models, and so on, that cause individuals to be differentially pre-disposed to higher or lower levels of technology usage. This kind of modeling approach, according to Bago d’Uva [16], can be applied in such a way that it is possible to allow or disallow the parameters in the model that address overdispersion to vary with the latent classes.

The reader shouldn’t conclude that only more complex count data models are useful in empirical research in healthcare. An important problem in the treatment of women’s health involves diagnosing breast cancer from axillary dissection of cancerous breast tissue. This helps clinicians to determine the counts of involved nodes to set up a basis for assessing the severity of the illness, the likelihood of survival, and the appropriate treatment for their patients. Dwivedi et al. [60] evaluated the Poisson, zero-inflated Poisson, negative binomial, and zero hurdle/negative binomial regression models for the extent to which visible skin changes, location and tumor size were associated with cancerous nodes for 1,152 Indian women from 1983 to 2005.

Two results are interesting to consider for IS researchers, since they illustrate the sophistication of observation that is possible with this kind of econometric analysis. First, the researchers found that the negative binomial model fits the data better than any of the other models that were used, which is consistent with the large number of uninvolved nodes (the zeros, in this case) that often are present when the cancer is diagnosed early. The zero-inflated negative binomial and the hurdle regression models predicted the number of involved nodes better though. The conclusion the authors drew was that the prediction of involved nodes was a by-product of the overdispersion of uninvolved nodes, as well as some other unobserved heterogeneity that was not captured by the explanatory variables. They recommend that doctors base their treatment on the results of zero-inflated negative binomial regression estimates, since it permits the analysis to focus on uninvolved nodes that are at high risk of becoming cancerous.

The work of Rose et al. [144] is similar in its comparisons of these kinds of models in a study of vaccine-averse patient event count data for at-risk and not-at-risk populations. The issue is whether it is appropriate to permit zeroes to arise from both the at-risk (what they call sample zeroes) and the not-at-risk groups (what they call structural zeroes). The authors conclude that overdispersion of zero outcomes may not always be sufficient cause for the analyst to choose zero-inflated negative binomial regression or hurdle regression. They show empirically, based on their data, that when at-risk and not-at-risk patients are considered (the sample and structural zeroes together), then a zero-inflated negative binomial regression is better. When estimating data with only at-risk patients, hurdle regression seems to work better.

3.4 Unemployment

To wrap up our discussion of applied contexts that may offer useful modeling analogies for IS researchers who are interested in the application of count data modeling, we will next consider three studies that deal with labor and employment. (For a more in-depth review, see [169].) There is a substantial literature available that offers useful research designs, modeling structures, and estimation approach choices in which various count data models are employed.

An example of the issues and estimation structures that are employed is found in the work of Andress [4], who studied the recurrence of unemployment among West German men between 1977 and 1982. The author points out the contrast between having access to event data, which are more micro-level and more informative, in comparison to count data, which are more aggregative and less informative. He also points out three other issues: problems with underestimation of counts due to the use of retrospective data and only registered instances of unemployment, the sampling of employment status as an endogenous variable (which raises the question of the underlying structural model, and leaves the analysis open to over-sampling of higher-risk groups), one-shot observations of independent variables that actually are changing over time, and panel attrition of participants across the timeline of the study. The author distinguishes between two useful concepts. One is statistical dependence, which occurs when “events appear to be dynamically dependent, but in fact, some individuals have higher risks of experiencing an event than others” [4] due to some unobserved heterogeneity. The other is causal dependence, which occurs when there is something beyond the individual that is a clear driver of the outcome that is counted. In this context, an example is that prior spells of unemployment might drive the observation of recurring unemployment; in other words, there is some causal link. The author extends the Poisson regression model with a gamma mixing distribution to permit overdispersion of zero event counts. He refers to his approach as an apparent contagion model or a spurious occurrence dependence model, with the idea of emphasizing the effort they have made to sort out causal and statistical dependence.

Numerous observers have suggested that unemployment tends to predispose people to healthcare problems, since they are less likely to be able to visit the doctor or receive the appropriate kinds of hospital treatment that are called for in funded health insurance programs. Danö [53] evaluated causality in this setting, with panel data from 1981 to 1996 with a 10% sample of the entire population of Denmark, based on the frequency of doctor visits and consultations. The author uses multiple count data estimation approaches, two of which involve the negative binomial regression model with fixed effects and a Mundlak formulation random effects specification [132]. The latter formulation permits individual-specific effects to be correlated with time-varying explanatory variables in the model—something that was not possible with fixed effects at the time the author did this research. An interesting outcome of this research, which illustrates the power that refined econometric models have for challenging the conventional wisdom of an area, is that the authors found no significant effects of unemployment for health among men and women—even after correcting for the possible correlations between individual-specific effects and the relevant explanatory variables. A requirement of all of the count data models that the authors used was the assumption of exogenous explanatory variables, so they also estimated a reduced generalized method of moments (GMM) model that didn’t require this assumption, and they still were able to establish the same general results. This approach in empirical research with count data models further emphasizes how it is possible with post-estimation robustness checks to increase the perceived reliability of the statistical findings.

3.5 Political economy

Another interesting work in the labor and political economy area explores the connection between the results of a variety of count data models with other associated events that occur later, but are subject to unknown lags. This is a useful method for IS and e-commerce researchers, since it is often the case that the observation of one kind of event, or a cluster of events, may be tied to other events that come later. An example is in the context of the signing on or the departure of members of a firm’s top management team, once the chief executive officer resigns. Honaker [87] also estimated a family of count data models in order to make the case that there is a causal link between the unemployment level in the population and the number of instances of political violence in Northern Ireland. In this research, the author employed several different models, including Poisson, negative binomial, zero-inflated Poisson and hurdle regression, and again shows the different efficacies of the various formulations based on the estimation outcomes. The author’s estimation approach also involved the modeling of instances when one side retaliates against a violent attack by the other side, by building a lag structure for violence into a count data estimation model.

An important observation in this research, and one that should be relevant to other IS researchers who undertake e-commerce and technology adoption studies, is that lagging the dependent variable further increases the number of zero-valued dependent variable counts. The workaround suggested by the author is to compute a rolling average of the events over some period of time that makes sense for the study context. A second key observation that is useful for IS research, e-commerce and technology adoption modeling settings is to recognize that there will be a most likely time to the observation of the lagged event associated with the initial event. It may be typical to assume, as the author has, that the likelihood of a tied event diminishes after the occurrence of the first event. This observation may be helpful for those who are interested in studying time-clustered technology adoption that is subject to contagion effects from prior adoption events [124]. Honaker [87] evaluated the retaliation events with geometrically-distributed and quadratically-distributed lags, which are well-suited to creating reaction curves of the appropriate shape. This approach also provides a micro-level foundation for the theoretical explanation of aggregate behavior.

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Kauffman, R.J., Techatassanasoontorn, A.A. & Wang, B. Event history, spatial analysis and count data methods for empirical research in information systems. Inf Technol Manag 13, 115–147 (2012). https://doi.org/10.1007/s10799-011-0106-5

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