[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-529284-105":59,"doc-detail-529284-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","a-bayesian-hierarchical-selection-model-for-academic-growth-with-missing-data","A Bayesian Hierarchical Selection Model for Academic Growth with Missing Data","","A Bayesian hierarchical selection model is developed to analyze academic growth using annually administered grade 9–11 assessments linked through a latent growth curve framework. Student intercepts and slopes are nested within schools, while missed assessments—caused by mobility, dropout, absenteeism, or other factors—are treated as informative missingness. Missingness indicators are modeled via logistic regression using grade-9 and potentially unobserved growth covariates. School effects on growth and missingness are estimated and compared against a model that ignores the missing-data mechanism.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/a-bayesian-hierarchical-selection-model-for-academic-growth-with-missing-data/529284/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/a-bayesian-hierarchical-selection-model-for-academic-growth-with-missing-data/529284.png","ImageObject",300,407,{"name":92,"@type":93},"Mary Man","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-14","2026-10-09",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does the paper address in longitudinal academic assessments?","Question",{"text":112,"@type":113},"It addresses missing primary-outcome data in longitudinal assessments, where missingness may depend on unobserved academic achievement rather than only observed responses and covariates.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the proposed model treat missed assessments?",{"text":117,"@type":113},"It jointly models academic growth and the missing-data process under a hierarchical selection framework, explicitly linking missingness to latent growth information via logistic regression.",{"name":119,"@type":110,"acceptedAnswer":120},"How are the results evaluated?",{"text":121,"@type":113},"The selection model’s estimates of school effects on academic growth are compared with a simpler model that ignores the missing-data process.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},529284,1791557198,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},7421720224475,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","A Bayesian Hierarchical Selection Model for Academic Growth with Missing Data  \nJeff Allen  \nWP-2015-04 April, 2015  \nACT Working Paper Series   \nACT working papers document preliminary research. The papers are intended to promote discussion and feedback before formal publication. The research does not necessarily reflect the views of ACT.  \nA Bayesian Hierarchical Selection Model for Academic Growth with Missing Data  \nJeff Allen  \nApril 2015  \nAbstract  \nUsing a sample of schools testing annually in grades 9-11 with a vertically-linked series of assessments, a latent growth curve model is used to model test scores with student interceptsand slopes nested within school. Missed assessments can occur because of student mobility, student dropout, absenteeism, and other reasons. Missing data indicators are modeled using logistic regression, with grade 9 and potentially unobserved growth scores used as covariates. Under a hierarchical selection model, estimates of school effects on academic growth and missingness are obtained. The results from the selection model are compared to a model that ignores the missing data process.  \nThe author would like to acknowledge Ruitao Liu and Justine Radunzel for their review and helpful comments on this report.  \nKEY WORDS: selection model, latent growth curve, hierarchical model, not missing at random, informative missingness, school effectiveness, Bayesian analysis, WinBUGS  \nIntroduction  \nEducators, researchers, and policymakers are increasingly interested in measures of academic growth for purposes of monitoring student progress, evaluating interventions, and measuring school or teacher effectiveness. Growth models require longitudinal data systems that track assessment data over time and link the data to individual students, teachers, and schools. Not unlike longitudinal data in other disciplines, missing data are common with academic assessment because of student migration out of the school system, sickness, truancy, and student dropout, among other reasons.  \nCustomary methods for analyzing longitudinal data assume that data are missing at random – that is, missingness depends only on the observed responses and covariates. However, in the case of longitudinal assessment data, it is plausible that missingness is related to unobserved level of academic achievement. Academic difficulty or lack of academic growth could contribute to students leaving high school or missing assessment days. Alternatively, other student risk factors could affect both academic performance and likelihood of missing assessment days. If academic performance is the outcome of interest amd unobserved academic performance constructs are related to missingness, data are not missing at random.  \nIn this paper, a Bayesian approach is presented for jointly modeling the academic growth and missing data processes in an attempt to account for informative missingness. Using WinBUGS, the model was fit for a sample of schools that test annually in grades 9-11 with a series of vertically-scaled assessments. The results are compared to those from a simpler model that ignores the missing data process, with emphasis on measures of school effects on academic growth.  \nInformative dropout in longitudinal research  \nThis study deals with a common situation where the primary outcome is measured on individuals at multiple time points, and that the research focuses on examining predictors of change in the outcome. Random coefficient models are often used for this purpose. For example, each individual’s vector of outcomes can be described by a person-specific intercept, slope, and possible higher-order terms. The individual effects are not observed and this type of model is also known as a latent growth curve model.  \nA common problem that arises in longitudinal studies is missing data in the primary outcome. Using maximum likelihood estimation on the observed data set results in unbiased estimation when the missingness process only depe","cbCaicZNwdAY1x3y","https://ap.wps.com/l/cbCaicZNwdAY1x3y","pdf",238856,33,"English","# Introduction\n## Informative dropout in longitudinal research\n## Methods overview","[{\"question\":\"What problem does the paper address in longitudinal academic assessments?\",\"answer\":\"It addresses missing primary-outcome data in longitudinal assessments, where missingness may depend on unobserved academic achievement rather than only observed responses and covariates.\"},{\"question\":\"How does the proposed model treat missed assessments?\",\"answer\":\"It jointly models academic growth and the missing-data process under a hierarchical selection framework, explicitly linking missingness to latent growth information via logistic regression.\"},{\"question\":\"How are the results evaluated?\",\"answer\":\"The selection model’s estimates of school effects on academic growth are compared with a simpler model that ignores the missing-data process.\"}]","A Bayesian Hierarchical Selection Model for Academic Growth with Missing Data | PDF",1791520852,83]