A Hierarchical Model of Nonhomogeneous Poisson Processes for Twitter Retweets

Lee, Clement; Wilkinson, Darren J.

doi:10.1080/01621459.2019.1585358

Cited by 13 publications

(4 citation statements)

References 42 publications

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“…Here, we consider two crucial dimensions on which researchers have to make a decision when applying a cognitive model: They need to decide how they take into account similarities and differences between units of observation (i.e., pooling of data), and whether they want to estimate model parameters in a frequentist or in a Bayesian statistical framework. As with any result in psychological research, parameter estimates from cognitive models should ideally be reproducible and robust across these modeling decisions (C. Lee & Wilkinson, 2019;Vandekerckhove et al, 2019). We focus on the level of pooling and the statistical framework, because a researcher can hardly avoid deliberating on these two aspects, whereas for other aspects (e.g., prior distributions) the researcher can resort to standards.…”

Section: Cognitive Modeling Decisionsmentioning

confidence: 99%

Evaluating the Robustness of Parameter Estimates in Cognitive Models: A Meta-Analytic Review of Multinomial Processing Tree Models Across the Multiverse of Estimation Methods

Singmann,

Heck,

Barth

et al. 2024

Preprint

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Researchers have become increasingly aware that data-analysis decisions affect results. Here, we examine this issue systematically for multinomial processing tree (MPT) models, a popular class of cognitive models for categorical data. Specifically, we examine the robustness of MPT model parameter estimates that arise from two important decisions: the level of data aggregation (complete pooling, no pooling, or partial pooling) and the statistical framework (frequentist or Bayesian). These decisions span a multiverse of estimation methods. We synthesized the data from 13,956 participants (164 published data sets) with a meta-analytic strategy and analyzed the magnitude of divergence between estimation methods for the parameters of nine popular multinomial processing tree (MPT) models in psychology (e.g., process dissociation, source monitoring). We further examined moderators as potential sources of divergence. We found that the absolute divergence between estimation methods was small on average (< .04; with MPT parameters ranging between 0 and 1); in some cases, however, divergence amounted to nearly the maximum possible range (.97). Divergence was partly explained by few moderators (e.g., the specific MPT model parameter, uncertainty in parameter estimation), but not by other plausible candidate moderators (e.g., parameter trade-offs, parameter correlations) or their interactions. Partial-pooling methods showed the smallest divergence within and across levels of pooling and thus seem to be an appropriate default method. Using MPT models as an example, we show how transparency and robustness can be increased in the field of cognitive modeling.

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Section: Cognitive Modeling Decisionsmentioning

confidence: 99%

Evaluating the Robustness of Parameter Estimates in Cognitive Models: A Meta-Analytic Review of Multinomial Processing Tree Models Across the Multiverse of Estimation Methods

Singmann,

Heck,

Barth

et al. 2024

Preprint

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“…The dissemination of information through social media, especially Twitter, is very fast, especially conversations between netizens. Use of a non-homogeneous Poisson process (NHPP) to define the retweet hierarchy of the original tweet data (Gu and Kurov, 2020) set where all retweet processes are placed on a single hierarchical model so that information can be collect to estimate a parameter (Lee and Wilkinson, 2020). In determining the estimate for the application for non-life insurance data, NHPP is used as a method of solution to analyze data within a certain period of time (Vedyushenko, 2018).…”

Section: Introductionmentioning

confidence: 99%

Probability distributions of COVID-19 tweet posted trends uses a nonhomogeneous Poisson process

Munandar

Supian

Subiyanto

2020

ijqrm

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The influence of social media in disseminating information, especially during the COVID-19 pandemic, can be observed with time interval, so that the probability of number of tweets discussed by netizens on social media can be observed. The nonhomogeneous Poisson process (NHPP) is a Poisson process with dependent on time parameters and the exponential distribution having unequal parameter values and, independently of each other. The probability of no accurence an event in the initial state is one and the probability of an event in initial state is zero. Using of non-homogeneous Poisson in this paper aims to predict and count the number of tweet posts with the keyword coronavirus, COVID-19 with set time intervals every day. Posting of tweets from one time each day to the next do not affect each other and the number of tweets is not the same. The dataset used in this study is crawling of COVID-19 tweets three times a day with duration of 20 minutes each crawled for 13 days or 39 time intervals. Result of this study obtained predictions and calculated for the probability of the number of tweets for the tendency of netizens to post on the situation of the COVID-19 pandemic.

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“…However, as far as we know there are not many applications of independent Poisson clocks into modelling in social science. Many existing social science models do not address independence of arrivals of events explicitly [19,61,67,89,107]. Stochastic models are increasingly applied as a tool to social sciences, e.g., urban structure, disease transmission and networks ( [24,33,34]).…”

Section: Introductionmentioning

confidence: 99%

A stochastic-statistical residential burglary model with independent Poisson clocks

et al. 2020

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Residential burglary is a social problem in every major urban area. As such, progress has been to develop quantitative, informative and applicable models for this type of crime: (1) the Deterministic-time-step (DTS) model [Short, D’Orsogna, Pasour, Tita, Brantingham, Bertozzi & Chayes (2008) Math. Models Methods Appl. Sci.18, 1249–1267], a pioneering agent-based statistical model of residential burglary criminal behaviour, with deterministic time steps assumed for arrivals of events in which the residential burglary aggregate pattern formation is quantitatively studied for the first time; (2) the SSRB model (agent-based stochastic-statistical model of residential burglary crime) [Wang, Zhang, Bertozzi & Short (2019) Active Particles, Vol. 2, Springer Nature Switzerland AG, in press], in which the stochastic component of the model is theoretically analysed by introduction of a Poisson clock with time steps turned into exponentially distributed random variables. To incorporate independence of agents, in this work, five types of Poisson clocks are taken into consideration. Poisson clocks (I), (II) and (III) govern independent agent actions of burglary behaviour, and Poisson clocks (IV) and (V) govern interactions of agents with the environment. All the Poisson clocks are independent. The time increments are independently exponentially distributed, which are more suitable to model individual actions of agents. Applying the method of merging and splitting of Poisson processes, the independent Poisson clocks can be treated as one, making the analysis and simulation similar to the SSRB model. A Martingale formula is derived, which consists of a deterministic and a stochastic component. A scaling property of the Martingale formulation with varying burglar population is found, which provides a theory to the finite size effects. The theory is supported by quantitative numerical simulations using the pattern-formation quantifying statistics. Results presented here will be transformative for both elements of application and analysis of agent-based models for residential burglary or in other domains.

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A Hierarchical Model of Nonhomogeneous Poisson Processes for Twitter Retweets

Cited by 13 publications

References 42 publications

Evaluating the Robustness of Parameter Estimates in Cognitive Models: A Meta-Analytic Review of Multinomial Processing Tree Models Across the Multiverse of Estimation Methods

Evaluating the Robustness of Parameter Estimates in Cognitive Models: A Meta-Analytic Review of Multinomial Processing Tree Models Across the Multiverse of Estimation Methods

Probability distributions of COVID-19 tweet posted trends uses a nonhomogeneous Poisson process

A stochastic-statistical residential burglary model with independent Poisson clocks

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