Tom'as Capretto, Camen Piho, Ravi Kumar, Jacob Westfall, T. Yarkoni, O. A. Martin
The popularity of Bayesian statistical methods has increased dramatically in recent years across many research areas and industrial applications. This is the result of a variety of methodological advances with faster and cheaper hardware as well as the development of new software tools. Here we introduce an open source Python package named Bambi (BAyesian Model Building Interface) that is built on top of the PyMC probabilistic programming framework and the ArviZ package for exploratory analysis of Bayesian models. Bambi makes it easy to specify complex generalized linear hierarchical models using a formula notation similar to those found in R. We demonstrate Bambi's versatility and ease of use with a few examples spanning a range of common statistical models including multiple regression, logistic regression, and mixed-effects modeling with crossed group specific effects. Additionally we discuss how automatic priors are constructed. Finally, we conclude with a discussion of our plans for the future development of Bambi.
{"title":"Bambi: A Simple Interface for Fitting Bayesian Linear Models in Python","authors":"Tom'as Capretto, Camen Piho, Ravi Kumar, Jacob Westfall, T. Yarkoni, O. A. Martin","doi":"10.18637/jss.v103.i15","DOIUrl":"https://doi.org/10.18637/jss.v103.i15","url":null,"abstract":"The popularity of Bayesian statistical methods has increased dramatically in recent years across many research areas and industrial applications. This is the result of a variety of methodological advances with faster and cheaper hardware as well as the development of new software tools. Here we introduce an open source Python package named Bambi (BAyesian Model Building Interface) that is built on top of the PyMC probabilistic programming framework and the ArviZ package for exploratory analysis of Bayesian models. Bambi makes it easy to specify complex generalized linear hierarchical models using a formula notation similar to those found in R. We demonstrate Bambi's versatility and ease of use with a few examples spanning a range of common statistical models including multiple regression, logistic regression, and mixed-effects modeling with crossed group specific effects. Additionally we discuss how automatic priors are constructed. Finally, we conclude with a discussion of our plans for the future development of Bambi.","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"11 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73026084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces the R package ordinalCont, which implements an ordinal regression framework for response variables which are recorded on a visual analogue scale (VAS). This scale is used when recording subjects' perception of an intangible quantity such as pain, anxiety or quality of life, and consists of a mark made on a linear scale. We implement continuous ordinal regression models for VAS as the appropriate method of analysis for such responses, and introduce smoothing terms and random effects in the linear predictor. The model parameters are estimated using constrained optimization of the penalized likelihood and the penalty parameters are automatically selected via maximization of their marginal likelihood. The estimation algorithm is shown to perform well, in a simulation study. Two examples of application are given: the first involves the analysis of pain outcomes in a clinical trial for laser treatment for chronic neck pain; the second is an analysis of quality of life outcomes in a clinical trial for chemotherapy for the treatment of breast cancer.
{"title":"Continuous Ordinal Regression for Analysis of Visual Analogue Scales: The R Package ordinalCont","authors":"M. Manuguerra, G. Heller, Jun Ma","doi":"10.18637/jss.v096.i08","DOIUrl":"https://doi.org/10.18637/jss.v096.i08","url":null,"abstract":"This paper introduces the R package ordinalCont, which implements an ordinal regression framework for response variables which are recorded on a visual analogue scale (VAS). This scale is used when recording subjects' perception of an intangible quantity such as pain, anxiety or quality of life, and consists of a mark made on a linear scale. We implement continuous ordinal regression models for VAS as the appropriate method of analysis for such responses, and introduce smoothing terms and random effects in the linear predictor. The model parameters are estimated using constrained optimization of the penalized likelihood and the penalty parameters are automatically selected via maximization of their marginal likelihood. The estimation algorithm is shown to perform well, in a simulation study. Two examples of application are given: the first involves the analysis of pain outcomes in a clinical trial for laser treatment for chronic neck pain; the second is an analysis of quality of life outcomes in a clinical trial for chemotherapy for the treatment of breast cancer.","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"21 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82063253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Traditional tools and software for social network analysis are seldom scalable and/or fast. This paper provides an overview of an R package called fastnet, a tool for scaling and speeding up the simulation and analysis of large-scale social networks. fastnet uses multi-core processing and sub-graph sampling algorithms to achieve the desired scale-up and speed-up. Simple examples, usages, and comparisons of scale-up and speed-up as compared to other R packages, i.e., igraph and statnet, are presented.
{"title":"fastnet: An R Package for Fast Simulation and Analysis of Large-Scale Social Networks","authors":"Xu Dong, Luis E. Castro, N. I. Shaikh","doi":"10.2139/ssrn.3121725","DOIUrl":"https://doi.org/10.2139/ssrn.3121725","url":null,"abstract":"Traditional tools and software for social network analysis are seldom scalable and/or fast. This paper provides an overview of an R package called fastnet, a tool for scaling and speeding up the simulation and analysis of large-scale social networks. fastnet uses multi-core processing and sub-graph sampling algorithms to achieve the desired scale-up and speed-up. Simple examples, usages, and comparisons of scale-up and speed-up as compared to other R packages, i.e., igraph and statnet, are presented.","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"1 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68563997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Discrete choice experiments are widely used in a broad area of research fields to capture the preference structure of respondents. The design of such experiments will determine to a large extent the accuracy with which the preference parameters can be estimated. This paper presents a new R package, called idefix, which enables users to generate optimal designs for discrete choice experiments. Besides Bayesian D-efficient designs for the multinomial logit model, the package includes functions to generate Bayesian adaptive designs which can be used to gather data for the mixed logit model. In addition, the package provides the necessary tools to set up actual surveys and collect empirical data. After data collection, idefix can be used to transform the data into the necessary format in order to use existing estimation software in R.
{"title":"Generating Optimal Designs for Discrete Choice Experiments in R: The idefix Package","authors":"Frits Traets, Danielle Sanchez, M. Vandebroek","doi":"10.18637/jss.v096.i03","DOIUrl":"https://doi.org/10.18637/jss.v096.i03","url":null,"abstract":"Discrete choice experiments are widely used in a broad area of research fields to capture the preference structure of respondents. The design of such experiments will determine to a large extent the accuracy with which the preference parameters can be estimated. This paper presents a new R package, called idefix, which enables users to generate optimal designs for discrete choice experiments. Besides Bayesian D-efficient designs for the multinomial logit model, the package includes functions to generate Bayesian adaptive designs which can be used to gather data for the mixed logit model. In addition, the package provides the necessary tools to set up actual surveys and collect empirical data. After data collection, idefix can be used to transform the data into the necessary format in order to use existing estimation software in R.","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"13 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84399722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce Sim.DiffProc, an R package for symbolic and numerical computations on scalar and multivariate systems of stochastic differential equations (SDEs). It provides users with a wide range of tools to simulate, estimate, analyze, and visualize the dynamics of these systems in both forms, Ito and Stratonovich. One of Sim.DiffProc key features is to implement the Monte Carlo method for the iterative evaluation and approximation of an interesting quantity at a fixed time on SDEs with parallel computing, on multiple processors on a single machine or a cluster of computers, which is an important tool to improve capacity and speed-up calculations. We also provide an easy-to-use interface for symbolic calculation and numerical approximation of the first and central second-order moments of SDEs (i.e., mean, variance and covariance), by solving a system of ordinary differential equations, which yields insights into the dynamics of stochastic systems. The final result object of Monte Carlo and moment equations can be derived and presented in terms of LATEX math expressions and visualized in terms of LATEX tables. Furthermore, we illustrate various features of the package by proposing a general bivariate nonlinear dynamic system of Haken-Zwanzig, driven by additive, linear and nonlinear multiplicative noises. In addition, we consider the particular case of a scalar SDE driven by three independent Wiener processes. The Monte Carlo simulation thereof is obtained through a transformation to a system of three equations. We also study some important applications of SDEs in different fields.
{"title":"Performing Parallel Monte Carlo and Moment Equations Methods for Itô and Stratonovich Stochastic Differential Systems: R Package Sim.DiffProc","authors":"A. Guidoum, Kamal Boukhetala","doi":"10.18637/jss.v096.i02","DOIUrl":"https://doi.org/10.18637/jss.v096.i02","url":null,"abstract":"We introduce Sim.DiffProc, an R package for symbolic and numerical computations on scalar and multivariate systems of stochastic differential equations (SDEs). It provides users with a wide range of tools to simulate, estimate, analyze, and visualize the dynamics of these systems in both forms, Ito and Stratonovich. One of Sim.DiffProc key features is to implement the Monte Carlo method for the iterative evaluation and approximation of an interesting quantity at a fixed time on SDEs with parallel computing, on multiple processors on a single machine or a cluster of computers, which is an important tool to improve capacity and speed-up calculations. We also provide an easy-to-use interface for symbolic calculation and numerical approximation of the first and central second-order moments of SDEs (i.e., mean, variance and covariance), by solving a system of ordinary differential equations, which yields insights into the dynamics of stochastic systems. The final result object of Monte Carlo and moment equations can be derived and presented in terms of LATEX math expressions and visualized in terms of LATEX tables. Furthermore, we illustrate various features of the package by proposing a general bivariate nonlinear dynamic system of Haken-Zwanzig, driven by additive, linear and nonlinear multiplicative noises. In addition, we consider the particular case of a scalar SDE driven by three independent Wiener processes. The Monte Carlo simulation thereof is obtained through a transformation to a system of three equations. We also study some important applications of SDEs in different fields.","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"123 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75809179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Emily, Nicolas Sounac, F. Kroell, Magalie Houée-Bigot
GeneGeneInteR is an R package dedicated to the detection of an association between a case-control phenotype and the interaction between two sets of biallelic markers (single nucleotide polymorphisms or SNPs) in case-control genome-wide associations studies. The development of statistical procedures for searching gene-gene interaction at the SNP-set level has indeed recently grown in popularity as these methods confer advantage in both statistical power and biological interpretation. However, all these methods have been implemented in home made softwares that are for most of them available only on request to the authors and at best have a web interface. Since the implementation of these methods is not straightforward, there is a need for a user-friendly tool to perform gene-based genegene interaction. The purpose of GeneGeneInteR is to propose a collection of tools for all the steps involved in gene-based gene-gene interaction testing in case-control association studies. Illustrated by an example of a dataset related to rheumatoid arthritis, this paper details the implementation of the functions available in GeneGeneInteR to perform an analysis of a collection of SNP sets. Such an analysis aims at addressing the complete statistical pipeline going from data importation to the visualization of the results through data manipulation and statistical analysis.
{"title":"Gene-Based Methods to Detect Gene-Gene Interaction in R: The GeneGeneInteR Package","authors":"M. Emily, Nicolas Sounac, F. Kroell, Magalie Houée-Bigot","doi":"10.18637/jss.v095.i12","DOIUrl":"https://doi.org/10.18637/jss.v095.i12","url":null,"abstract":"GeneGeneInteR is an R package dedicated to the detection of an association between a case-control phenotype and the interaction between two sets of biallelic markers (single nucleotide polymorphisms or SNPs) in case-control genome-wide associations studies. The development of statistical procedures for searching gene-gene interaction at the SNP-set level has indeed recently grown in popularity as these methods confer advantage in both statistical power and biological interpretation. However, all these methods have been implemented in home made softwares that are for most of them available only on request to the authors and at best have a web interface. Since the implementation of these methods is not straightforward, there is a need for a user-friendly tool to perform gene-based genegene interaction. The purpose of GeneGeneInteR is to propose a collection of tools for all the steps involved in gene-based gene-gene interaction testing in case-control association studies. Illustrated by an example of a dataset related to rheumatoid arthritis, this paper details the implementation of the functions available in GeneGeneInteR to perform an analysis of a collection of SNP sets. Such an analysis aims at addressing the complete statistical pipeline going from data importation to the visualization of the results through data manipulation and statistical analysis.","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"33 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77796451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Many popular nonparametric inferential methods are based on ranks. Among the most commonly used and most famous tests are for example the Wilcoxon-Mann-Whitney test for two independent samples, and the Kruskal-Wallis test for multiple independent groups. However, recently, it has become clear that the use of ranks may lead to paradoxical results in case of more than two groups. Luckily, these problems can be avoided simply by using pseudo-ranks instead of ranks. These pseudo-ranks, however, suffer from being (a) at first less intuitive and not as straightforward in their interpretation, (b) computationally much more expensive to calculate. The computational cost has been prohibitive, for example, for large-scale simulative evaluations or application of resampling-based pseudorank procedures. In this paper, we provide different algorithms to calculate pseudo-ranks efficiently in order to solve problem (b) and thus render it possible to overcome the current limitations of procedures based on pseudo-ranks.
{"title":"Pseudo-Ranks: How to Calculate Them Efficiently in R","authors":"Martin Happ, G. Zimmermann, E. Brunner, A. Bathke","doi":"10.18637/jss.v095.c01","DOIUrl":"https://doi.org/10.18637/jss.v095.c01","url":null,"abstract":"Many popular nonparametric inferential methods are based on ranks. Among the most commonly used and most famous tests are for example the Wilcoxon-Mann-Whitney test for two independent samples, and the Kruskal-Wallis test for multiple independent groups. However, recently, it has become clear that the use of ranks may lead to paradoxical results in case of more than two groups. Luckily, these problems can be avoided simply by using pseudo-ranks instead of ranks. These pseudo-ranks, however, suffer from being (a) at first less intuitive and not as straightforward in their interpretation, (b) computationally much more expensive to calculate. The computational cost has been prohibitive, for example, for large-scale simulative evaluations or application of resampling-based pseudorank procedures. In this paper, we provide different algorithms to calculate pseudo-ranks efficiently in order to solve problem (b) and thus render it possible to overcome the current limitations of procedures based on pseudo-ranks.","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"9 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84770972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Survival analysis features heavily as an important part of health economic evaluation, an increasingly important component of medical research. In this setting, it is important to estimate the mean time to the survival endpoint using limited information (typically from randomized trials) and thus it is useful to consider parametric survival models. In this paper, we review the features of the R package survHE, specifically designed to wrap several tools to perform survival analysis for economic evaluation. In particular, survHE embeds both a standard, frequentist analysis (through the R package flexsurv) and a Bayesian approach, based on Hamiltonian Monte Carlo (via the R package rstan) or integrated nested Laplace approximation (with the R package INLA). Using this composite approach, we obtain maximum flexibility and are able to pre-compile a wide range of parametric models, with a view of simplifying the modelers' work and allowing them to move away from non-optimal work flows, including spreadsheets (e.g., Microsoft Excel).
{"title":"survHE: Survival Analysis for Health Economic Evaluation and Cost-Effectiveness Modeling","authors":"G. Baio","doi":"10.18637/jss.v095.i14","DOIUrl":"https://doi.org/10.18637/jss.v095.i14","url":null,"abstract":"Survival analysis features heavily as an important part of health economic evaluation, an increasingly important component of medical research. In this setting, it is important to estimate the mean time to the survival endpoint using limited information (typically from randomized trials) and thus it is useful to consider parametric survival models. In this paper, we review the features of the R package survHE, specifically designed to wrap several tools to perform survival analysis for economic evaluation. In particular, survHE embeds both a standard, frequentist analysis (through the R package flexsurv) and a Bayesian approach, based on Hamiltonian Monte Carlo (via the R package rstan) or integrated nested Laplace approximation (with the R package INLA). Using this composite approach, we obtain maximum flexibility and are able to pre-compile a wide range of parametric models, with a view of simplifying the modelers' work and allowing them to move away from non-optimal work flows, including spreadsheets (e.g., Microsoft Excel).","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"48 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76911960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
mlogit is a package for R which enables the estimation of random utility models with choice situation and/or alternative specific variables. The main extensions of the basic multinomial model (heteroscedastic, nested and random parameter models) are implemented.
{"title":"Estimation of Random Utility Models in R: The mlogit Package","authors":"Y. Croissant","doi":"10.18637/jss.v095.i11","DOIUrl":"https://doi.org/10.18637/jss.v095.i11","url":null,"abstract":"mlogit is a package for R which enables the estimation of random utility models with choice situation and/or alternative specific variables. The main extensions of the basic multinomial model (heteroscedastic, nested and random parameter models) are implemented.","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"17 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90720025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Clustered covariances or clustered standard errors are very widely used to account for correlated or clustered data, especially in economics, political sciences, or other social sciences. They are employed to adjust the inference following estimation of a standard least-squares regression or generalized linear model estimated by maximum likelihood. Although many publications just refer to "the" clustered standard errors, there is a surprisingly wide variety of clustered covariances particularly due to different flavors of bias corrections. Furthermore, while the linear regression model is certainly the most important application case, the same strategies can be employed in more general models (e.g. for zero-inflated, censored, or limited responses). In R, functions for covariances in clustered or panel models have been somewhat scattered or available only for certain modeling functions, notably the (generalized) linear regression model. In contrast, an object-oriented approach to "robust" covariance matrix estimation - applicable beyond lm() and glm() - is available in the sandwich package but has been limited to the case of cross-section or time series data. Now, this shortcoming has been corrected in sandwich (starting from version 2.4.0): Based on methods for two generic functions (estfun() and bread()), clustered and panel covariances are now provided in vcovCL(), vcovPL(), and vcovPC(). These are directly applicable to models from many packages, e.g., including MASS, pscl, countreg, betareg, among others. Some empirical illustrations are provided as well as an assessment of the methods' performance in a simulation study.
{"title":"Various Versatile Variances: An Object-Oriented Implementation of Clustered Covariances in R","authors":"A. Zeileis, Susanne Köll, N. Graham","doi":"10.18637/JSS.V095.I01","DOIUrl":"https://doi.org/10.18637/JSS.V095.I01","url":null,"abstract":"Clustered covariances or clustered standard errors are very widely used to account for correlated or clustered data, especially in economics, political sciences, or other social sciences. They are employed to adjust the inference following estimation of a standard least-squares regression or generalized linear model estimated by maximum likelihood. Although many publications just refer to \"the\" clustered standard errors, there is a surprisingly wide variety of clustered covariances particularly due to different flavors of bias corrections. Furthermore, while the linear regression model is certainly the most important application case, the same strategies can be employed in more general models (e.g. for zero-inflated, censored, or limited responses). In R, functions for covariances in clustered or panel models have been somewhat scattered or available only for certain modeling functions, notably the (generalized) linear regression model. In contrast, an object-oriented approach to \"robust\" covariance matrix estimation - applicable beyond lm() and glm() - is available in the sandwich package but has been limited to the case of cross-section or time series data. Now, this shortcoming has been corrected in sandwich (starting from version 2.4.0): Based on methods for two generic functions (estfun() and bread()), clustered and panel covariances are now provided in vcovCL(), vcovPL(), and vcovPC(). These are directly applicable to models from many packages, e.g., including MASS, pscl, countreg, betareg, among others. Some empirical illustrations are provided as well as an assessment of the methods' performance in a simulation study.","PeriodicalId":17237,"journal":{"name":"Journal of Statistical Software","volume":"41 1","pages":""},"PeriodicalIF":5.8,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77953816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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