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: An R Package for Bayesian Multilevel Models Using Stan","{\"openalex\":\"W2749069611\",\"doi\":\"10.18637/jss.v080.i01\"}","openalex","2026-05-14T00:51:39.020950163","2026-05-21T02:28:06.183259993","doi","10.18637/jss.v080.i01","arxivId","openalexId","W2749069611","title","abstractText","The brms package implements Bayesian multilevel models in R using the probabilistic programming language Stan. A wide range of distributions and link functions are supported, allowing users to fit - among others - linear, robust linear, binomial, Poisson, survival, ordinal, zero-inflated, hurdle, and even non-linear models all in a multilevel context. Further modeling options include autocorrelation of the response variable, user defined covariance structures, censored data, as well as meta-analytic standard errors. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their beliefs. In addition, model fit can easily be assessed and compared with the Watanabe-Akaike information criterion and leave-one-out cross-validation.","publishedDate","2017-01-01","publishedYear",2017,"venue","Journal of Statistical Software","citationCount",9129,"authors","keywords",[30,142,143],"pdfUrl","https://www.jstatsoft.org/index.php/jss/article/view/v080i01/v80i01.pdf","topVenue",true,"Data Analysis with R","Economic and Environmental Valuation","paper_W2090330784","Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study","{\"openalex\":\"W2090330784\",\"doi\":\"10.1080/10705510701575396\"}","2026-05-14T00:49:55.419288812","2026-05-21T02:23:26.19725628","10.1080/10705510701575396","W2090330784","Abstract Mixture modeling is a widely applied data analysis technique used to identify unobserved heterogeneity in a population. Despite mixture models' usefulness in practice, one unresolved issue in the application of mixture models is that there is not one commonly accepted statistical indicator for deciding on the number of classes in a study population. This article presents the results of a simulation study that examines the performance of likelihood-based tests and the traditionally used Information Criterion (ICs) used for determining the number of classes in mixture modeling. We look at the performance of these tests and indexes for 3 types of mixture models: latent class analysis (LCA), a factor mixture model (FMA), and a growth mixture models (GMM). We evaluate the ability of the tests and indexes to correctly identify the number of classes at three different sample sizes (n = 200, 500, 1,000). Whereas the Bayesian Information Criterion performed the best of the ICs, the bootstrap likelihood ratio test proved to be a very consistent indicator of classes across all of the models considered. ACKNOWLEDGMENTS Karen L. Nylund's research was supported by Grant R01 DA11796 from the National Institute on Drug Abuse (NIDA) and Bengt O. Muthén's research was supported by Grant K02 AA 00230 from the National Institute on Alcohol Abuse and Alcoholism (NIAAA). We thank Mplus for software support, Jacob Cheadle for programming expertise, and Katherine Masyn for helpful comments. Notes 1In general, the within-class covariance structure can be freed to allow within-class item covariance. a Item probabilities for categorical LCA models are specified by the probability in each cell, and the class means for the continuous LCA are specified by the value in parentheses. 2The number random starts for LCA models with categorical outcomes was specified to be \"starts = 70 7;\" in Mplus. The models with continuous outcomes had differing numbers of random starts. 3It is important to note that when coverage is studied, the random starts option of Mplus should not be used. If it is used, label switching may occur, in that a class for one replication might be represented by another class for another replication, therefore distorting the estimate. 4The models that presented convergence problems were those that were badly misspecified. For example, for the GMM (true k = 3 class model) for n = 500, the convergence rates for the three-, four-, and five-class models were 100%, 87%, and 68%, respectively.","2007-10-23",2007,"Structural Equation Modeling A Multidisciplinary Journal",10712,[30,157,158],"Bayesian Methods and Mixture Models","Statistical Methods and Inference","paper_W2156267802","Missing data: Our view of the state of the art.","{\"openalex\":\"W2156267802\",\"doi\":\"10.1037/1082-989x.7.2.147\"}","2026-05-14T00:42:07.293037266","2026-05-21T02:21:58.182464464","10.1037/1082-989x.7.2.147","W2156267802","Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, discourage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR. Although not yet in the mainstream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art.","2002-01-01",2002,"Psychological Methods",10853,[30,157,158],"paper_W2158196600","Multimodel Inference","{\"openalex\":\"W2158196600\",\"doi\":\"10.1177/0049124104268644\"}","2026-05-14T00:41:36.189547062","2026-05-21T02:20:18.278634368","10.1177/0049124104268644","W2158196600","The model selection literature has been generally poor at reflecting the deep foundations of the Akaike information criterion (AIC) and at making appropriate comparisons to the Bayesian information criterion (BIC). There is a clear philosophy, a sound criterion based in information theory, and a rigorous statistical foundation for AIC. AIC can be justified as Bayesian using a “savvy” prior on models that is a function of sample size and the number of model parameters. Furthermore, BIC can be derived as a non-Bayesian result. Therefore, arguments about using AIC versus BIC for model selection cannot be from a Bayes versus frequentist perspective. The philosophical context of what is assumed about reality, approximating models, and the intent of model-based inference should determine whether AIC or BIC is used. Various facets of such multimodel inference are presented here, particularly methods of model averaging.","2004-11-01",2004,"Sociological Methods & Research",11464,[185,157,30],"Bayesian Modeling and Causal Inference","paper_W2057765075","Discussion on the paper by Spiegelhalter, Best, Carlin and van der Linde","{\"openalex\":\"W2057765075\",\"doi\":\"10.1111/1467-9868.00353\"}","2026-05-14T00:40:39.239495348","2026-05-21T02:17:52.201456505","10.1111/1467-9868.00353","W2057765075","no abstract","ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)",12712,[30,157,158],"paper_W2115098571","mice: Multivariate Imputation by Chained Equations inR","{\"openalex\":\"W2115098571\",\"doi\":\"10.18637/jss.v045.i03\"}","2026-05-14T00:40:12.26985759","2026-05-21T02:16:52.217648119","10.18637/jss.v045.i03","W2115098571","The R package mice imputes incomplete multivariate data by chained equations. The software mice 1.0 appeared in the year 2000 as an S-PLUS library, and in 2001 as an R package. mice 1.0 introduced predictor selection, passive imputation and automatic pooling. This article documents mice, which extends the functionality of mice 1.0 in several ways. In mice, the analysis of imputed data is made completely general, whereas the range of models under which pooling works is substantially extended. mice adds new functionality for imputing multilevel data, automatic predictor selection, data handling, post-processing imputed values, specialized pooling routines, model selection tools, and diagnostic graphs. Imputation of categorical data is improved in order to bypass problems caused by perfect prediction. Special attention is paid to transformations, sum scores, indices and interactions using passive imputation, and to the proper setup of the predictor matrix. mice can be downloaded from the Comprehensive R Archive Network. This article provides a hands-on, stepwise approach to solve applied incomplete data problems.","2011-01-01",2011,13337,[142,209,30],"Metabolomics and Mass Spectrometry Studies","paper_W2158672897","Hierarchical Linear Models: Applications and Data Analysis Methods","{\"openalex\":\"W2158672897\",\"doi\":\"10.1198/jasa.2003.s288\"}","2026-05-14T00:39:36.36880966","2026-05-21T02:15:33.18216421","10.1198/jasa.2003.s288","W2158672897","(2003). Hierarchical Linear Models: Applications and Data Analysis Methods. Journal of the American Statistical Association: Vol. 98, No. 463, pp. 767-768.","2003-09-01",2003,"Journal of the American Statistical Association",13911,[30,223,157],"Statistical Methods and Applications","paper_W2148534890","Inference from Iterative Simulation Using Multiple Sequences","{\"openalex\":\"W2148534890\",\"doi\":\"10.1214/ss/1177011136\"}","2026-05-14T00:38:04.456839655","2026-05-21T02:12:27.211948396","10.1214/ss/1177011136","W2148534890","The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give misleading answers. Our methods are simple and generally applicable to the output of any iterative simulation; they are designed for researchers primarily interested in the science underlying the data and models they are analyzing, rather than for researchers interested in the probability theory underlying the iterative simulations themselves. Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution. At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely. Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations. The methods are illustrated on a random-effects mixture model applied to experimental measurements of reaction times of normal and schizophrenic patients.","1992-11-01",1992,"Statistical Science",16607,[157,30,238],"https://projecteuclid.org/journals/statistical-science/volume-7/issue-4/Inference-from-Iterative-Simulation-Using-Multiple-Sequences/10.1214/ss/1177011136.pdf","Gaussian Processes and Bayesian Inference","paper_W2774486220","lmerTest Package: Tests in Linear Mixed Effects Models","{\"openalex\":\"W2774486220\",\"doi\":\"10.18637/jss.v082.i13\"}","2026-05-14T00:30:30.282038599","2026-05-21T02:06:39.190253174","10.18637/jss.v082.i13","W2774486220","One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get p values for the F and t tests for objects returned by lmer? The lmerTest package extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects. We have implemented the Satterthwaite's method for approximating degrees of freedom for the t and F tests. We have also implemented the construction of Type I - III ANOVA tables. Furthermore, one may also obtain the summary as well as the anova table using the Kenward-Roger approximation for denominator degrees of freedom (based on the KRmodcomp function from the pbkrtest package). Some other convenient mixed model analysis tools such as a step method, that performs backward elimination of nonsignificant effects - both random and fixed, calculation of population means and multiple comparison tests together with plot facilities are provided by the package as well.",22905,[30,250,142],"https://www.jstatsoft.org/index.php/jss/article/view/v082i13/v82i13.pdf","Advanced Statistical Methods and Models","paper_W1951724000","Fitting Linear Mixed-Effects Models Using lme4","{\"openalex\":\"W1951724000\",\"doi\":\"10.18637/jss.v067.i01\"}","2026-05-14T00:27:22.418091264","2026-05-21T02:01:03.181232379","10.18637/jss.v067.i01","W1951724000","Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.","2015-01-01",2015,84083,[142,30,264],"https://www.jstatsoft.org/index.php/jss/article/view/v067i01/v67i01.pdf","Mental Health Research Topics",{"_58":266,"_60":267},[],[268],{"_63":269,"_65":270,"_67":271,"_69":272},1780547146295,{"_72":274,"_74":75,"_76":269,"_77":-5,"_78":26,"_79":26,"_80":26,"_81":-5,"_82":-5,"_83":84,"_35":85,"_86":87},[71,273],"[\"portal\",\"industries\"]","industries",[275,276,277,278,279,280,281,282,283,284,285,286],{"_15":346,"_29":347,"_31":-5,"_32":348,"_33":349,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":350,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":347,"_57":349},{"_15":342,"_29":343,"_31":-5,"_32":-5,"_33":344,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":345,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":343,"_57":344},{"_15":336,"_29":337,"_31":-5,"_32":338,"_33":339,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":340,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":337,"_57":339},{"_15":332,"_29":333,"_31":-5,"_32":-5,"_33":334,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":335,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":333,"_57":334},{"_15":328,"_29":329,"_31":-5,"_32":-5,"_33":330,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":331,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":329,"_57":330},{"_15":322,"_29":323,"_31":-5,"_32":324,"_33":325,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":326,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":323,"_57":325},{"_15":318,"_29":319,"_31":-5,"_32":-5,"_33":320,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":321,"_299":26,"_300":141,"_301":26,"_101":-5,"_56":319,"_57":320},{"_15":314,"_29":315,"_31":-5,"_32":-5,"_33":316,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":317,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":315,"_57":316},{"_15":310,"_29":311,"_31":-5,"_32":-5,"_33":312,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":313,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":311,"_57":312},{"_15":306,"_29":307,"_31":-5,"_32":-5,"_33":308,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":309,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":307,"_57":308},{"_15":302,"_29":303,"_31":-5,"_32":-5,"_33":304,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":305,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":303,"_57":304},{"_15":287,"_29":288,"_31":-5,"_32":-5,"_33":289,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":290,"_42":-5,"_44":-5,"_291":292,"_293":-5,"_294":75,"_295":296,"_297":298,"_299":26,"_300":84,"_301":26,"_101":-5,"_56":288,"_57":289},"tax_ind_smartphone","智能手机","Smartphone","manual","taxonomyType","INDUSTRY","code","level","parentId","tax_ind_root","path","科技行业/智能手机","sortOrder","isLeaf","entityCount","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_quantum","量子计算","Quantum Computing","科技行业/量子计算","tax_ind_blockchain","区块链",[327],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[341],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[351,352],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_355":24},"SITE_BASE_URL"]

Statistical Methods and Bayesian Inference 技术

Statistical Methods and Bayesian Inference · 相关文章