Spatial stratification of landscapes allows for the development of efficient sampling surveys,the inclusion of domain knowledge in data-driven modeling frameworks, and the production of information relating the spatial variability of response phenomena to that of landscape processes. This work presents the rassta package as a collection of algorithms dedicated to the spatial stratification of landscapes, the calculation of landscape correspondence metrics across geographic space, and the application of these metrics for spatial sampling and modeling of environmental phenomena. The theoretical background of rassta is presented through references to several studies which have benefited from landscape stratification routines. The functionality of rassta is presented through code examples which are complemented with the geographic visualization of their outputs.
{"title":"rassta: Raster-Based Spatial Stratification Algorithms","authors":"B. Fuentes, Minerva J. Dorantes, John R. Tipton","doi":"10.31223/x50s57","DOIUrl":"https://doi.org/10.31223/x50s57","url":null,"abstract":"Spatial stratification of landscapes allows for the development of efficient sampling surveys,the inclusion of domain knowledge in data-driven modeling frameworks, and the production of information relating the spatial variability of response phenomena to that of landscape processes. This work presents the rassta package as a collection of algorithms dedicated to the spatial stratification of landscapes, the calculation of landscape correspondence metrics across geographic space, and the application of these metrics for spatial sampling and modeling of environmental phenomena. The theoretical background of rassta is presented through references to several studies which have benefited from landscape stratification routines. The functionality of rassta is presented through code examples which are complemented with the geographic visualization of their outputs.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"11 1","pages":"288-309"},"PeriodicalIF":0.0,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82378366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recent work has highlighted the difficulties of estimating difference-in-differences models when treatment timing occurs at different times for different units. This article introduces the R package did2s which implements the estimator introduced in Gardner (2021). The article provides an approachable review of the underlying econometric theory and introduces the syntax for the function did2s. Further, the package introduces a function, event_study, that provides a common syntax for all the modern event-study estimators and plot_event_study to plot the results of each estimator.
{"title":"did2s: Two-Stage Difference-in-Differences","authors":"K. Butts, J. Gardner","doi":"10.32614/RJ-2022-048","DOIUrl":"https://doi.org/10.32614/RJ-2022-048","url":null,"abstract":"Recent work has highlighted the difficulties of estimating difference-in-differences models when treatment timing occurs at different times for different units. This article introduces the R package did2s which implements the estimator introduced in Gardner (2021). The article provides an approachable review of the underlying econometric theory and introduces the syntax for the function did2s. Further, the package introduces a function, event_study, that provides a common syntax for all the modern event-study estimators and plot_event_study to plot the results of each estimator.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"27 1","pages":"162-173"},"PeriodicalIF":0.0,"publicationDate":"2021-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83234916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Itsaso Rodríguez-Moreno, I. Irigoien, B. Sierra, C. Arenas
Common Spacial Patterns (CSP) is a widely used method to analyse electroencephalography (EEG) data, concerning the supervised classification of brain's activity. More generally, it can be useful to distinguish between multivariate signals recorded during a time span for two different classes. CSP is based on the simultaneous diagonalization of the average covariance matrices of signals from both classes and it allows to project the data into a low-dimensional subspace. Once data are represented in a low-dimensional subspace, a classification step must be carried out. The original CSP method is based on the Euclidean distance between signals and here, we extend it so that it can be applied on any appropriate distance for data at hand. Both, the classical CSP and the new Distance-Based CSP (DB-CSP) are implemented in an R package, called dbcsp.
{"title":"dbcsp: User-friendly R package for Distance-Based Common Spacial Patterns","authors":"Itsaso Rodríguez-Moreno, I. Irigoien, B. Sierra, C. Arenas","doi":"10.32614/rj-2022-044","DOIUrl":"https://doi.org/10.32614/rj-2022-044","url":null,"abstract":"Common Spacial Patterns (CSP) is a widely used method to analyse electroencephalography (EEG) data, concerning the supervised classification of brain's activity. More generally, it can be useful to distinguish between multivariate signals recorded during a time span for two different classes. CSP is based on the simultaneous diagonalization of the average covariance matrices of signals from both classes and it allows to project the data into a low-dimensional subspace. Once data are represented in a low-dimensional subspace, a classification step must be carried out. The original CSP method is based on the Euclidean distance between signals and here, we extend it so that it can be applied on any appropriate distance for data at hand. Both, the classical CSP and the new Distance-Based CSP (DB-CSP) are implemented in an R package, called dbcsp.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"135 1","pages":"80-94"},"PeriodicalIF":0.0,"publicationDate":"2021-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89071464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Randomized response (RR) designs are used to collect response data about sensitive behaviors (e.g., criminal behavior, sexual desires). The modeling of RR data is more complex since it requires a description of the RR process. For the class of generalized linear mixed models (GLMMs), the RR process can be represented by an adjusted link function, which relates the expected RR to the linear predictor for most common RR designs. The package GLMMRR includes modified link functions for four different cumulative distributions (i.e., logistic, cumulative normal, Gumbel, Cauchy) for GLMs and GLMMs, where the package lme4 facilitates ML and REML estimation. The mixed modeling framework in GLMMRR can be used to jointly analyze data collected under different designs (e.g., dual questioning, multilevel, mixed mode, repeated measurements designs, multiple-group designs). Model-fit tests, tools for residual analyses, and plot functions to give support to a profound RR data analysis are added to the well-known features of the GLM and GLMM software (package lme4). Data of Höglinger and Jann (2018) and Höglinger, Jann, and Diekmann (2014) are used to illustrate the methodology and software.
随机反应(RR)设计用于收集敏感行为(如犯罪行为、性欲)的反应数据。RR数据的建模更为复杂,因为它需要对RR过程进行描述。对于广义线性混合模型(glmm), RR过程可以用一个调整后的链接函数来表示,该函数将期望RR与大多数常见RR设计的线性预测器联系起来。GLMMRR包包含针对glm和glmm的四种不同累积分布(即logistic、累积正态、Gumbel、Cauchy)的修改链接函数,其中包lme4促进了ML和REML的估计。GLMMRR中的混合建模框架可用于联合分析不同设计(如双问、多级、混合模式、重复测量设计、多组设计)下收集的数据。模型拟合检验、残差分析工具和支持深度RR数据分析的绘图函数被添加到GLM和GLMM软件(软件包lme4)的众所周知的功能中。使用Höglinger and Jann(2018)和Höglinger, Jann, and Diekmann(2014)的数据来说明方法和软件。
{"title":"Generalized Linear Randomized Response Modeling using GLMMRR","authors":"J. Fox, K. Klotzke, D. Veen","doi":"10.32614/rj-2021-104","DOIUrl":"https://doi.org/10.32614/rj-2021-104","url":null,"abstract":"Randomized response (RR) designs are used to collect response data about sensitive behaviors (e.g., criminal behavior, sexual desires). The modeling of RR data is more complex since it requires a description of the RR process. For the class of generalized linear mixed models (GLMMs), the RR process can be represented by an adjusted link function, which relates the expected RR to the linear predictor for most common RR designs. The package GLMMRR includes modified link functions for four different cumulative distributions (i.e., logistic, cumulative normal, Gumbel, Cauchy) for GLMs and GLMMs, where the package lme4 facilitates ML and REML estimation. The mixed modeling framework in GLMMRR can be used to jointly analyze data collected under different designs (e.g., dual questioning, multilevel, mixed mode, repeated measurements designs, multiple-group designs). Model-fit tests, tools for residual analyses, and plot functions to give support to a profound RR data analysis are added to the well-known features of the GLM and GLMM software (package lme4). Data of Höglinger and Jann (2018) and Höglinger, Jann, and Diekmann (2014) are used to illustrate the methodology and software.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"50 1","pages":"507"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82372808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Like many predictive models, random forests provide point predictions for new observations. Besides the point prediction, it is important to quantify the uncertainty in the prediction. Prediction intervals provide information about the reliability of the point predictions. We have developed a comprehensive R package, RFpredInterval, that integrates 16 methods to build prediction intervals with random forests and boosted forests. The set of methods implemented in the package includes a new method to build prediction intervals with boosted forests (PIBF) and 15 method variations to produce prediction intervals with random forests, as proposed by Roy and Larocque (2020). We perform an extensive simulation study and apply real data analyses to compare the performance of the proposed method to ten existing methods for building prediction intervals with random forests. The results show that the proposed method is very competitive and, globally, outperforms competing methods.
{"title":"RFpredInterval: An R Package for Prediction Intervals with Random Forests and Boosted Forests","authors":"Cansu Alakus, Denis Larocque, A. Labbe","doi":"10.32614/rj-2022-012","DOIUrl":"https://doi.org/10.32614/rj-2022-012","url":null,"abstract":"Like many predictive models, random forests provide point predictions for new observations. Besides the point prediction, it is important to quantify the uncertainty in the prediction. Prediction intervals provide information about the reliability of the point predictions. We have developed a comprehensive R package, RFpredInterval, that integrates 16 methods to build prediction intervals with random forests and boosted forests. The set of methods implemented in the package includes a new method to build prediction intervals with boosted forests (PIBF) and 15 method variations to produce prediction intervals with random forests, as proposed by Roy and Larocque (2020). We perform an extensive simulation study and apply real data analyses to compare the performance of the proposed method to ten existing methods for building prediction intervals with random forests. The results show that the proposed method is very competitive and, globally, outperforms competing methods.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"37 1","pages":"300-320"},"PeriodicalIF":0.0,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74752246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Linear mixed-effects models are commonly used to analyze clustered data structures. There are numerous packages to fit these models in R and conduct likelihood-based inference. The implementation of resampling-based procedures for inference are more limited. In this paper, we introduce the lmeresampler package for bootstrapping nested linear mixed-effects models fit via lme4 or nlme. Bootstrap estimation allows for bias correction, adjusted standard errors and confidence intervals for small samples sizes and when distributional assumptions break down. We will also illustrate how bootstrap resampling can be used to diagnose this model class. In addition, lmeresampler makes it easy to construct interval estimates of functions of model parameters.
{"title":"Bootstrapping Clustered Data in R using lmeresampler","authors":"A. Loy, J. Korobova","doi":"10.32614/rj-2023-015","DOIUrl":"https://doi.org/10.32614/rj-2023-015","url":null,"abstract":"Linear mixed-effects models are commonly used to analyze clustered data structures. There are numerous packages to fit these models in R and conduct likelihood-based inference. The implementation of resampling-based procedures for inference are more limited. In this paper, we introduce the lmeresampler package for bootstrapping nested linear mixed-effects models fit via lme4 or nlme. Bootstrap estimation allows for bias correction, adjusted standard errors and confidence intervals for small samples sizes and when distributional assumptions break down. We will also illustrate how bootstrap resampling can be used to diagnose this model class. In addition, lmeresampler makes it easy to construct interval estimates of functions of model parameters.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"33 1","pages":"103-120"},"PeriodicalIF":0.0,"publicationDate":"2021-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84458796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is dedicated to the R package FMM which implements a novel approach to describe rhythmic patterns in oscillatory signals. The frequency modulated M"obius (FMM) model is defined as a parametric signal plus a gaussian noise, where the signal can be described as a single or a sum of waves. The FMM approach is flexible enough to describe a great variety of rhythmic patterns. The FMM package includes all required functions to fit and explore single and multi-wave FMM models, as well as a restricted version that allows equality constraints between parameters representing a priori knowledge about the shape to be included. Moreover, the FMM package can generate synthetic data and visualize the results of the fitting process. The potential of this methodology is illustrated with examples of such biological oscillations as the circadian rhythm in gene expression, the electrical activity of the heartbeat and neuronal activity.
{"title":"FMM: An R Package for Modeling Rhythmic Patterns in Oscillatory Systems","authors":"Itziar Fernández, Alejandro Rodríguez-Collado, Yolanda Larriba, Adrián Lamela, Christian Canedo, Cristina Rueda","doi":"10.32614/RJ-2022-015","DOIUrl":"https://doi.org/10.32614/RJ-2022-015","url":null,"abstract":"This paper is dedicated to the R package FMM which implements a novel approach to describe rhythmic patterns in oscillatory signals. The frequency modulated M\"obius (FMM) model is defined as a parametric signal plus a gaussian noise, where the signal can be described as a single or a sum of waves. The FMM approach is flexible enough to describe a great variety of rhythmic patterns. The FMM package includes all required functions to fit and explore single and multi-wave FMM models, as well as a restricted version that allows equality constraints between parameters representing a priori knowledge about the shape to be included. Moreover, the FMM package can generate synthetic data and visualize the results of the fitting process. The potential of this methodology is illustrated with examples of such biological oscillations as the circadian rhythm in gene expression, the electrical activity of the heartbeat and neuronal activity.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"60 1","pages":"361-380"},"PeriodicalIF":0.0,"publicationDate":"2021-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80532832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H.Sherry Zhang, D. Cook, U. Laa, Nicolas Langren'e, Patricia Men'endez
A guided tour helps to visualise high-dimensional data by showing low-dimensional projections along a projection pursuit optimisation path. Projection pursuit is a generalisation of principal component analysis, in the sense that different indexes are used to define the interestingness of the projected data. While much work has been done in developing new indexes in the literature, less has been done on understanding the optimisation. Index functions can be noisy, might have multiple local maxima as well as an optimal maximum, and are constrained to generate orthonormal projection frames, which complicates the optimization. In addition, projection pursuit is primarily used for exploratory data analysis, and finding the local maxima is also useful. The guided tour is especially useful for exploration, because it conducts geodesic interpolation connecting steps in the optimisation and shows how the projected data changes as a maxima is approached. This work provides new visual diagnostics for examining a choice of optimisation procedure, based on the provision of a new data object which collects information throughout the optimisation. It has helped to diagnose and fix several problems with projection pursuit guided tour. This work might be useful more broadly for diagnosing optimisers, and comparing their performance. The diagnostics are implemented in the R package, ferrn.
{"title":"Visual Diagnostics for Constrained Optimisation with Application to Guided Tours","authors":"H.Sherry Zhang, D. Cook, U. Laa, Nicolas Langren'e, Patricia Men'endez","doi":"10.32614/RJ-2021-105","DOIUrl":"https://doi.org/10.32614/RJ-2021-105","url":null,"abstract":"A guided tour helps to visualise high-dimensional data by showing low-dimensional projections along a projection pursuit optimisation path. Projection pursuit is a generalisation of principal component analysis, in the sense that different indexes are used to define the interestingness of the projected data. While much work has been done in developing new indexes in the literature, less has been done on understanding the optimisation. Index functions can be noisy, might have multiple local maxima as well as an optimal maximum, and are constrained to generate orthonormal projection frames, which complicates the optimization. In addition, projection pursuit is primarily used for exploratory data analysis, and finding the local maxima is also useful. The guided tour is especially useful for exploration, because it conducts geodesic interpolation connecting steps in the optimisation and shows how the projected data changes as a maxima is approached. This work provides new visual diagnostics for examining a choice of optimisation procedure, based on the provision of a new data object which collects information throughout the optimisation. It has helped to diagnose and fix several problems with projection pursuit guided tour. This work might be useful more broadly for diagnosing optimisers, and comparing their performance. The diagnostics are implemented in the R package, ferrn.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"88 1","pages":"542"},"PeriodicalIF":0.0,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85947585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Machine learning decision systems are getting omnipresent in our lives. From dating apps to rating loan seekers, algorithms affect both our well-being and future. Typically, however, these systems are not infallible. Moreover, complex predictive models are really eager to learn social biases present in historical data that can lead to increasing discrimination. If we want to create models responsibly then we need tools for in-depth validation of models also from the perspective of potential discrimination. This article introduces an R package fairmodels that helps to validate fairness and eliminate bias in classification models in an easy and flexible fashion. The fairmodels package offers a model-agnostic approach to bias detection, visualization and mitigation. The implemented set of functions and fairness metrics enables model fairness validation from different perspectives. The package includes a series of methods for bias mitigation that aim to diminish the discrimination in the model. The package is designed not only to examine a single model, but also to facilitate comparisons between multiple models.
{"title":"fairmodels: A Flexible Tool For Bias Detection, Visualization, And Mitigation","authors":"Jakub Wi'sniewski, P. Biecek","doi":"10.32614/rj-2022-019","DOIUrl":"https://doi.org/10.32614/rj-2022-019","url":null,"abstract":"Machine learning decision systems are getting omnipresent in our lives. From dating apps to rating loan seekers, algorithms affect both our well-being and future. Typically, however, these systems are not infallible. Moreover, complex predictive models are really eager to learn social biases present in historical data that can lead to increasing discrimination. If we want to create models responsibly then we need tools for in-depth validation of models also from the perspective of potential discrimination. This article introduces an R package fairmodels that helps to validate fairness and eliminate bias in classification models in an easy and flexible fashion. The fairmodels package offers a model-agnostic approach to bias detection, visualization and mitigation. The implemented set of functions and fairness metrics enables model fairness validation from different perspectives. The package includes a series of methods for bias mitigation that aim to diminish the discrimination in the model. The package is designed not only to examine a single model, but also to facilitate comparisons between multiple models.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"51 1","pages":"227-243"},"PeriodicalIF":0.0,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82663985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R package krippendorffsalpha provides tools for measuring agreement using Krippendorff's Alpha coefficient, a well-known nonparametric measure of agreement (also called inter-rater reliability and various other names). This article first develops Krippendorff's Alpha in a natural way, and situates Alpha among statistical procedures. Then the usage of package krippendorffsalpha is illustrated via analyses of two datasets, the latter of which was collected during an imaging study of hip cartilage. The package permits users to apply the Alpha methodology using built-in distance functions for the nominal, ordinal, interval, or ratio levels of measurement. User-defined distance functions are also supported. The fitting function can accommodate any number of units, any number of coders, and missingness. Bootstrap inference is supported, and the bootstrap computation can be carried out in parallel.
{"title":"krippendorffsalpha: An R Package for Measuring Agreement Using Krippendorff's Alpha Coefficient","authors":"John Hughes","doi":"10.32614/rj-2021-046","DOIUrl":"https://doi.org/10.32614/rj-2021-046","url":null,"abstract":"R package krippendorffsalpha provides tools for measuring agreement using Krippendorff's Alpha coefficient, a well-known nonparametric measure of agreement (also called inter-rater reliability and various other names). This article first develops Krippendorff's Alpha in a natural way, and situates Alpha among statistical procedures. Then the usage of package krippendorffsalpha is illustrated via analyses of two datasets, the latter of which was collected during an imaging study of hip cartilage. The package permits users to apply the Alpha methodology using built-in distance functions for the nominal, ordinal, interval, or ratio levels of measurement. User-defined distance functions are also supported. The fitting function can accommodate any number of units, any number of coders, and missingness. Bootstrap inference is supported, and the bootstrap computation can be carried out in parallel.","PeriodicalId":20974,"journal":{"name":"R J.","volume":"26 1","pages":"413"},"PeriodicalIF":0.0,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90806068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}