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"Negative-binomial"
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Research Constituents, Intellectual Structure, and Collaboration Patterns in Journal of International Marketing
by
Donthu, Naveen
,
Kumar, Satish
,
Pandey, Nitesh
in
Bibliometrics
,
Marketing
,
Qualitative research
2021
This study presents a retrospective on Journal of International Marketing using bibliometrics. The study finds that the journal’s run has been characterized by continuous growth in publications and citations, with a dominant contribution base of authors from the United States. Authors have consistently shown a strong preference for quantitative research, with a decline in preference for qualitative research and a negligible increase in preference for mixed-methods research in recent years. The major themes in the journal include global branding, internationalization, cross-cultural marketing, and international relationship marketing. An exploration of the factors affecting article citations reveals that article attributes such as the conceptual method, empirical method, article length, title length, article age, and number of keywords play significant roles in increasing the number of citations. Authors affiliated with nonacademic institutions also have a significant and positive influence on total citations. The article concludes with directions for further research.
Journal Article
A comparison of statistical methods for modeling count data with an application to hospital length of stay
2022
Background
Hospital length of stay (LOS) is a key indicator of hospital care management efficiency, cost of care, and hospital planning. Hospital LOS is often used as a measure of a post-medical procedure outcome, as a guide to the benefit of a treatment of interest, or as an important risk factor for adverse events. Therefore, understanding hospital LOS variability is always an important healthcare focus. Hospital LOS data can be treated as count data, with discrete and non-negative values, typically right skewed, and often exhibiting excessive zeros. In this study, we compared the performance of the Poisson, negative binomial (NB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) regression models using simulated and empirical data.
Methods
Data were generated under different simulation scenarios with varying sample sizes, proportions of zeros, and levels of overdispersion. Analysis of hospital LOS was conducted using empirical data from the Medical Information Mart for Intensive Care database.
Results
Results showed that Poisson and ZIP models performed poorly in overdispersed data. ZIP outperformed the rest of the regression models when the overdispersion is due to zero-inflation only. NB and ZINB regression models faced substantial convergence issues when incorrectly used to model equidispersed data. NB model provided the best fit in overdispersed data and outperformed the ZINB model in many simulation scenarios with combinations of zero-inflation and overdispersion, regardless of the sample size. In the empirical data analysis, we demonstrated that fitting incorrect models to overdispersed data leaded to incorrect regression coefficients estimates and overstated significance of some of the predictors.
Conclusions
Based on this study, we recommend to the researchers that they consider the ZIP models for count data with zero-inflation only and NB models for overdispersed data or data with combinations of zero-inflation and overdispersion. If the researcher believes there are two different data generating mechanisms producing zeros, then the ZINB regression model may provide greater flexibility when modeling the zero-inflation and overdispersion.
Journal Article
Count Regression Models for Analyzing Crime Rates in The East Java Province
2021
Crime rate is the number of reported crimes divided by total population. Several factors could contribute the variability of crime rates among areas. This study aims to model the relationship between crime rates among regencies and cities in the East Java Province (Indonesia) and some potentially explanatory variables based on Statistics Indonesia publication in 2020. The crime rate in the East Java Province was consistently at the top three after DKI Jakarta and North Sumatra during 2017 to 2019. Therefore, it is interesting for us to study further about the crime rate in the East Java. Our preliminary analysis indicates that there is an overdispersion in our sample data. To overcome the overdispersion, we fit Generalized Poisson and Negative Binomial regression. The ratio of deviance and degree of freedom based on Negative Binomial is slightly smaller (1.38) than Generalized Poisson (1.99). The results indicate that Negative Binomial and Generalized Poisson regression, compared to standard Poisson regression, are relatively fit to model our crime rate data. Some factors which contribute significantly (α=0.05) for the crime rate in the East Java Province under Negative Binomial as well as Generalized Poisson regression are percentage of poor people, number of households, unemployment rate, and percentage of expenditure.
Journal Article
Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables
by
Polson, Nicholas G.
,
Scott, James G.
,
Windle, Jesse
in
Approximation
,
Augmentation
,
Bayesian analysis
2013
We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya–Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effect models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple, effective methods for posterior inference that (1) circumvent the need for analytic approximations, numerical integration, or Metropolis–Hastings; and (2) outperform other known data-augmentation strategies, both in ease of use and in computational efficiency. All methods, including an efficient sampler for the Pólya–Gamma distribution, are implemented in the R package BayesLogit . Supplementary materials for this article are available online.
Journal Article
Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression
by
Green, James A.
in
Advanced Methods in Health Psychology and Behavioral Medicine
,
Binomial distribution
,
Count data
2021
Dependent variables in health psychology are often counts, for example, of a behaviour or number of engagements with an intervention. These counts can be very strongly skewed, and/or contain large numbers of zeros as well as extreme outliers. For example, 'How many cigarettes do you smoke on an average day?' The modal answer may be zero but may range from 0 to 40+. The same can be true for minutes of moderate-to-vigorous physical activity. For some people, this may be near zero, but take on extreme values for someone training for a marathon. Typical analytical strategies for this data involve explicit (or implied) transformations (smoker v. non-smoker, log transformations). However, these data types are 'counts' (i.e. non-negative whole numbers) or quasi-counts (time is ratio but discrete minutes of activity could be analysed as a count), and can be modelled using count distributions - including the Poisson and negative binomial distribution (and their zero-inflated and hurdle extensions, which alloweven more zeros).
In this tutorial paper I demonstrate (in R, Jamovi, and SPSS) the easy application of these models to health psychology data, and their advantages over alternative ways of analysing this type of data using two datasets - one highly dispersed dependent variable (number of views on YouTube, and another with a large number of zeros (number of days on which symptoms were reported over a month).
The negative binomial distribution had the best fit for the overdispersed number of views on YouTube. Negative binomial, and zero-inflated negative binomial were both good fits for the symptom data with over-abundant zeros.
In both cases, count distributions provided not just a better fit but would lead to different conclusions compared to the poorly fitting traditional regression/linear models.
Journal Article
Evaluating the performance of different Bayesian count models in modelling childhood vaccine uptake among children aged 12–23 months in Nigeria
by
Fagbamigbe, A. F.
,
Lawal, T. V.
,
Atoloye, K. A.
in
Bayes Theorem
,
Bayesian statistical decision theory
,
Biostatistics
2023
Background
Choosing appropriate models for count health outcomes remains a challenge to public health researchers and the validity of the findings thereof. For count data, the mean–variance relationship and proportion of zeros is a major determinant of model choice. This study aims to compare and identify the best Bayesian count modelling technique for the number of childhood vaccine uptake in Nigeria.
Methods
We explored the performances of Poisson, negative binomial and their zero-inflated forms in the Bayesian framework using cross-sectional data pooled from the Nigeria Demographic and Health Survey conducted between 2003 and 2018. In multivariable analysis, these Bayesian models were used to identify factors associated with the number of vaccine uptake among children. Model selection was based on the -2 Log-Likelihood (-2 Log LL), Leave-One-Out Cross-Validation Information Criterion (LOOIC) and Watanabe-Akaike/Widely Applicable Information Criterion (WAIC).
Results
Exploratory analysis showed the presence of excess zeros and overdispersion with a mean of 4.36 and a variance of 12.86. Observably, there was a significant increase in vaccine uptake over time. Significant factors included the mother’s age, level of education, religion, occupation, desire for last-child, place of delivery, exposure to media, birth order of the child, wealth status, number of antenatal care visits, postnatal attendance, healthcare decision maker, community poverty, community illiteracy, community unemployment, rural proportion and number of health facilities per 100,000. The zero-inflated negative binomial model was best fit with -2Log LL of -27171.47, LOOIC of 54464.2, and WAIC of 54588.0.
Conclusion
The Bayesian zero-inflated negative binomial model was most appropriate to identify factors associated with the number of childhood vaccines received in Nigeria due to the presence of excess zeros and overdispersion. Improving vaccine uptake by addressing the associated risk factors should be promptly embraced.
Journal Article
Influence of Sociodemographic, Premorbid, and Injury-Related Factors on Post-Concussion Symptoms after Traumatic Brain Injury
2020
Background: Post-concussion symptoms (PCS) are often reported as consequences of mild and moderate traumatic brain injury (TBI), but these symptoms are not well documented in severe TBI. There is a lack of agreement as to which factors and covariates affect the occurrence, frequency, and intensity of PCS among TBI severity groups. The present study therefore aims to examine the association between sociodemographic, premorbid, and injury-related factors and PCS. Methods: A total of 1391 individuals (65% male) from the CENTER-TBI study were included in the analyses. The occurrence, frequency (number of PCS), and intensity (severity) of PCS were assessed using the Rivermead Post-concussion Symptoms Questionnaire (RPQ) at six months after TBI. To examine the association between selected factors (age, sex, living situation, employment status, educational background, injury and TBI severity, and premorbid problems) and PCS, a zero-inflated negative binomial model (ZINB) for occurrence and frequency of PCS and a standard negative binomial regression (NB) for intensity were applied. Results: Of the total sample, 72% of individuals after TBI reported suffering from some form of PCS, with fatigue being the most frequent among all TBI severity groups, followed by forgetfulness, and poor concentration. Different factors contributed to the probability of occurrence, frequency, and intensity of PCS. While the occurrence of PCS seemed to be independent of the age and sex of the individuals, both the frequency and intensity of PCS are associated with them. Both injury and TBI severity influence the occurrence and frequency of PCS, but are associated less with its intensity (except “acute” symptoms such as nausea, vomiting, and headaches). Analyses focusing on the mTBI subgroup only yielded results comparable to those of the total sample. Discussion: In line with previous studies, the results support a multifactorial etiology of PCS and show the importance of differentiating between their occurrence, frequency, and intensity to better provide appropriate treatment for individual subgroups with different symptoms (e.g., multiple PCS or more intense PCS). Although PCS often occur in mild to moderate TBI, individuals after severe TBI also suffer from PCS or post-concussion-like symptoms that require appropriate treatment. The chosen statistical approaches (i.e., ZINB and NB models) permit an ameliorated differentiation between outcomes (occurrence, frequency, and intensity of PCS) and should be used more widely in TBI research.
Journal Article
Faster permutation inference in brain imaging
by
Winkler, Anderson M.
,
Smith, Stephen M.
,
Ridgway, Gerard R.
in
Algorithms
,
Binomial distribution
,
Brain - diagnostic imaging
2016
Permutation tests are increasingly being used as a reliable method for inference in neuroimaging analysis. However, they are computationally intensive. For small, non-imaging datasets, recomputing a model thousands of times is seldom a problem, but for large, complex models this can be prohibitively slow, even with the availability of inexpensive computing power. Here we exploit properties of statistics used with the general linear model (GLM) and their distributions to obtain accelerations irrespective of generic software or hardware improvements. We compare the following approaches: (i) performing a small number of permutations; (ii) estimating the p-value as a parameter of a negative binomial distribution; (iii) fitting a generalised Pareto distribution to the tail of the permutation distribution; (iv) computing p-values based on the expected moments of the permutation distribution, approximated from a gamma distribution; (v) direct fitting of a gamma distribution to the empirical permutation distribution; and (vi) permuting a reduced number of voxels, with completion of the remainder using low rank matrix theory. Using synthetic data we assessed the different methods in terms of their error rates, power, agreement with a reference result, and the risk of taking a different decision regarding the rejection of the null hypotheses (known as the resampling risk). We also conducted a re-analysis of a voxel-based morphometry study as a real-data example. All methods yielded exact error rates. Likewise, power was similar across methods. Resampling risk was higher for methods (i), (iii) and (v). For comparable resampling risks, the method in which no permutations are done (iv) was the absolute fastest. All methods produced visually similar maps for the real data, with stronger effects being detected in the family-wise error rate corrected maps by (iii) and (v), and generally similar to the results seen in the reference set. Overall, for uncorrected p-values, method (iv) was found the best as long as symmetric errors can be assumed. In all other settings, including for familywise error corrected p-values, we recommend the tail approximation (iii). The methods considered are freely available in the tool PALM — Permutation Analysis of Linear Models.
•Permutation methods can be accelerated through additional statistical approaches.•Six approaches are described and assessed.•Methods can be 100 times faster than in the non-accelerated case.•Recommendations are provided for various common scenarios.
Journal Article
Quality control, modeling, and visualization of CRISPR screens with MAGeCK-VISPR
by
Liu, X. Shirley
,
Xu, Han
,
Köster, Johannes
in
Algorithms
,
Animal Genetics and Genomics
,
Bayesian analysis
2015
High-throughput CRISPR screens have shown great promise in functional genomics. We present MAGeCK-VISPR, a comprehensive quality control (QC), analysis, and visualization workflow for CRISPR screens. MAGeCK-VISPR defines a set of QC measures to assess the quality of an experiment, and includes a maximum-likelihood algorithm to call essential genes simultaneously under multiple conditions. The algorithm uses a generalized linear model to deconvolute different effects, and employs expectation-maximization to iteratively estimate sgRNA knockout efficiency and gene essentiality. MAGeCK-VISPR also includes VISPR, a framework for the interactive visualization and exploration of QC and analysis results. MAGeCK-VISPR is freely available at
http://bitbucket.org/liulab/mageck-vispr
.
Journal Article
Observation weights unlock bulk RNA-seq tools for zero inflation and single-cell applications
by
Risso, Davide
,
Dudoit, Sandrine
,
Perraudeau, Fanny
in
Animal Genetics and Genomics
,
binomial distribution
,
Bioinformatics
2018
Dropout events in single-cell RNA sequencing (scRNA-seq) cause many transcripts to go undetected and induce an excess of zero read counts, leading to power issues in differential expression (DE) analysis. This has triggered the development of bespoke scRNA-seq DE methods to cope with zero inflation. Recent evaluations, however, have shown that dedicated scRNA-seq tools provide no advantage compared to traditional bulk RNA-seq tools. We introduce a weighting strategy, based on a zero-inflated negative binomial model, that identifies excess zero counts and generates gene- and cell-specific weights to unlock bulk RNA-seq DE pipelines for zero-inflated data, boosting performance for scRNA-seq.
Journal Article