Inside IES Research

Notes from NCER & NCSER

Going beyond existing menus of statistical procedures: Bayesian multilevel modeling with Stan

For nearly 15 years, NCER has supported the development and improvement of innovative methodological and statistical tools and approaches that will better enable applied education researchers to conduct high-quality, rigorous education research. This blog spotlights the work of Andrew Gelman, a professor of statistics and political science at Columbia University, and Sophia Rabe-Hesketh, a professor of statistics at the School of Education at the University of California, Berkeley. IES has supported their research on hierarchical modeling and Bayesian computation has for many years. In this interview blog, Drs. Gelman and Rabe-Hesketh reflect on how Bayesian modeling applies to educational data and describe the general principles and advantages of Bayesian analysis.

What motivates your research on hierarchical modeling and Bayesian computation?

Education data can be messy. We need to adjust for covariates in experiments and observational studies, and we need to be able to generalize from non-random, non-representative samples to populations of interest.

The general motivation for multilevel modeling is that we are interested in local parameters, such as public opinion by states, small-area disease incidence rates, individual performance in sports, school-district-level learning loss, and other quantities that vary among people, across locations, and over time. In non-Bayesian settings, the local parameters are called random effects, varying intercepts/slopes, or latent variables.

Bayesian and non-Bayesian models differ in how completely the researcher using them must specify the probability distributions of the parameters. In non-Bayesian models, typically only the data model (also called the likelihood function) must be specified. The underlying parameters, such as the variances of random intercepts, are treated as unknown constants. On the other hand, the Bayesian approach requires specifying a full probability model for all parameters.  

A researcher using Bayesian inference encodes additional assumptions about all parameters into prior distributions, then combines information about the parameters from the data model with information from the prior distributions. This results in a posterior distribution for each parameter, which, compared to non-Bayesian model results, provides more information about the appropriateness of the model and supports more complex inferences.

What advantages are there to the Bayesian approach?

Compared to other estimates, Bayesian estimates are based on many more assumptions. One advantage of this is greater stability at small sample sizes. Another advantage is that Bayesian modeling can be used to produce flexible, practice-relevant summaries from a fitted model that other approaches cannot produce. For instance, when modeling school effectiveness, researchers using the Bayesian approach can rely on the full probability model to justifiably obtain the rankings of schools or the probabilities that COVID-related declines in NAEP mean test scores for a district or state have exceeded three points, along with estimates for the variability of these summaries. 

Further, Bayesian inference supports generalizability and replicability by freely allowing uncertainty from multiple sources to be integrated into models. Without allowing for uncertainty, it’s difficult to understand what works for whom and why. A familiar example is predicting student grades in college courses. A regression model can be fit to obtain a forecast with uncertainty based on past data on the students, and then this can be combined with student-specific information. Uncertainties in the forecasts for individual students or groups of students will be dependent and can be captured by a joint probability model, as implemented by posterior simulations. This contrasts with likelihood-based (non-Bayesian) inference where predictions and their uncertainty are typically considered only conditionally on the model parameters, with maximum likelihood estimates plugged in. Ignoring uncertainty leads to standard error estimates that are too small on average (see this introduction to Bayesian multilevel regression for a detailed demonstration and discussion of this phenomenon).

What’s an important disadvantage to the Bayesian approach?

Specifying a Bayesian model requires the user to make more decisions than specifying a non-Bayesian model. Until recently, many of these decisions had to be implemented using custom programming, so the Bayesian approach had a steep learning curve. Users who were not up to the programming and debugging task had to work within some restricted class of models that had already been set up with existing software. 

This disadvantage is especially challenging in education research, where we often need to adapt and expand our models beyond a restricted class to deal with statistical challenges such as imperfect treatment assignments, nonlinear relations, spatial correlations, and mixtures, along with data issues such as missingness, students changing schools, guessing on tests, and predictors measured with error.

How did your IES-funded work address this disadvantage?

In 2011, we developed Stan, our open-source Bayesian software, with funding from a Department of Energy grant on large-scale computing. With additional support from the National Science Foundation and IES, we have developed model types, workflows, and case studies for education researchers and also improved Stan’s computational efficiency.

By combining a state-of-the-art inference engine with an expressive modeling language, Stan allows education researchers to build their own models, starting with basic linear and logistic regressions and then adding components of variation and uncertainty and expanding as needed to capture challenges that arise in applied problems at hand.  We recommend the use of Stan as part of a Bayesian workflow of model building, checking, and expansion, making use of graphs of data and fitted models.

Stan can be accessed using R, Python, Stata, Julia, and other software. We recommend getting started by looking at the Stan case studies. We also have a page on Stan for education research and a YouTube channel.

In terms of dealing with the issues that arise in complex educational data, where do we stand today?

Put all this together, and we are in the business of fitting complex models in an open-ended space that goes beyond any existing menu of statistical procedures. Bayesian inference is a flexible way to fit such models, and Stan is a flexible tool that we have developed, allowing general models to be fit in reasonable time using advanced algorithms for statistical computing.  As always with research, there are many loose ends and there is more work to be done, but we can now routinely fit, check, and display models of much greater generality than was before possible, facilitating the goals of understanding processes in education.


This blog was produced by Charles Laurin (Charles.Laurin@ed.gov), NCER program officer for the Statistical and Research Methodology in Education grant program.

Supporting the Pipeline of Scholars of Color with Research, Training, and Mentorship

In recognition of Black History Month, we interviewed Dr. Tamara Bertrand Jones, an associate professor of higher education in the Department of Educational Leadership and Policy Studies at Florida State University and co-principal investigator of the Partners United for Research Pathways Oriented to Social Justice in Education (PURPOSE) program, funded by the IES Pathways to the Education Sciences Research Training Program. In this blog, Dr. Bertrand Jones discusses her experiences conducting research on the professional experiences of underrepresented populations as well as her work supporting emerging scholars of color.

Tamara Bertrand Jones photoHow has your background and experiences shaped your research on the graduate education and professional experiences of underrepresented populations, particularly Black women, in academia?

My dissertation research centered Black perspectives on cultural competence in evaluation. For the first 10 years of my academic career, I worked as an administrator, primarily in student affairs. When I transitioned from administration to faculty, I extended my research to Black experiences in academia. Microaggressions (such as unsolicited advice) that derailed my productivity and diminished my self-confidence immediately greeted me. For example, I was told that my research would be labeled navel-gazing (excessive self-contemplation) because I was a Black woman studying Black women and that this negative label may present challenges for my career. It took time, lots of positive self-affirmation, and validation from my mentors and close Black women colleagues to silence those voices and walk confidently in my contribution as a scholar and my personal purpose for pursuing an academic career. After these experiences, I doubled down on my commitment to demystify the hidden curriculum in the academy and support emerging scholars by being responsive to their identities, experiences, needs, and aspirations.

What is the PURPOSE training program, and what have you learned from administering PURPOSE?

We created PURPOSE to help develop more underrepresented and minoritized education researchers. To date, we have had seven cohorts of PURPOSE Fellows, totaling more than 80 fellows. The program includes critical discussions about social justice and educational inequities, mentoring, professional development, and service-learning research apprenticeships. During their training, we also encourage fellows to reflect on their own identities in terms of race, gender, and social class among other identities while they develop their individual researcher identities. These experiences culminate in capstone research projects related to social justice in education that fellows develop from inception to dissemination during the fellowship year. Taken together, these experiences foster capacities to conduct meaningful research and provide socialization into the rigors of research and graduate school.

We found that fellows experience socialization into education research in ways that help them 1) develop a researcher-identity, and 2) prepare products that demonstrate strong research potential for graduate school. Our fellows have experienced positive gains in their self-efficacy for carrying out a variety of research skills such as conducting literature reviews and working independently and in teams. We believe our approach to culturally relevant education and research methods and valuing the voices of our diverse fellows and mentors will lead to changes in future teaching and research practices.

Based on your research and experiences, what do you see as the greatest needs to improve the education and professional pathways for Black scholars?

In the over 14 years I have been a faculty member, I recognize that there are myriad ways to be successful in academia while remaining true to who you are. Through my work on early career professionals in partnership with Sisters of the Academy (SOTA), a community of Black women in higher education, I strive to create an environment where emerging scholars are exposed to scholars who represent diverse ways of being in academia. These models can shape emerging scholars’ vision of their future possible selves and help them develop their own pathways that are congruent with who they are. If institutions lack those models in their faculty, I urge leaders to intentionally connect with groups or organizations like SOTA that have the expertise and access to individuals who can serve in those roles from their emerging scholars.

What advice would you give to emerging scholars from underrepresented, minoritized groups that are pursuing a career in education research?

Often emerging scholars from underrepresented, minoritized groups are not encouraged to engage in work that speaks to their soul or can meaningfully impact the communities they serve. As in my experience, underrepresented emerging scholars are often told that doing research on our identity groups or researching issues that these groups experience is limiting, pigeonholing, and too self-reflective. Emerging Black scholars, in particular, are told they must approach their work in ways that are contradictory to their values or diminish their self-concepts. These messages can stunt growth and hinder the ability to identify innovative solutions to education’s most-pressing problems.

Because of this, I encourage all emerging scholars to consider the following reflective questions, guided by my emerging professional development framework—the 5 I’s, to help align their education research careers with how they see themselves, individually and in community.

  • Identity: How does my identity influence my research?
  • Intention: How can I create synergy between my research and scholarship, courses I teach, service I perform, and who I am as a scholar?
  • Implementation: How does my positionality influence my research design choices?
  • Influence: Who needs to know about my work? How can partnership extend the impact of my work?
  • Impact: How can my work be used to create better educational environments for marginalized or minoritized communities, or change education policy, research, or practice in meaningful ways?

This interview blog is part of a larger IES blog series on diversity, equity, inclusion and accessibility (DEIA) in the education sciences. It was produced by Akilah Nelson (akilah.nelson@ed.gov), a program officer within the National Center for Special Education Research.

Unlocking Opportunities: Understanding Connections Between Noncredit CTE Programs and Workforce Development in Virginia

With rapid technological advances, the U.S. labor market exhibits a growing need for more frequent and ongoing skill development. Community college noncredit career and technical education (CTE) programs that allow students to complete workforce training and earn credentials play an essential role in providing workers with the skills they need to compete for jobs in high-demand fields. Yet, there is a dearth of research on these programs because noncredit students are typically not included in state and national postsecondary datasets. In this guest blog for CTE Month, researchers Di Xu, Benjamin Castleman, and Betsy Tessler discuss their IES-funded exploration study in which they build on a long-standing research partnership with the Virginia Community College System and leverage a variety of data sources to investigate the Commonwealth’s FastForward programs. These programs are noncredit CTE programs designed to lead to an industry-recognized credential in one of several high-demand fields identified by the Virginia Workforce Board.

In response to the increasing demand for skilled workers in the Commonwealth, the Virginia General Assembly passed House Bill 66 in 2016 to establish the New Economy Workforce Credential Grant Program (WCG) with the goal of providing a pay-for-performance model for funding noncredit training. The WCG specifically funds FastForward programs that lead to an industry-recognized credential in a high-demand field in the Commonwealth. Under this model, funding is shared between the state, students, and training institutions based on student performance, with the goal of ensuring workforce training is affordable for Virginia residents. An important implication of WCG is that it led to systematic, statewide collection of student-level data on FastForward program enrollment, program completion, industry credential attainment, and labor market performance. Drawing on these unique data, coupled with interviews with key stakeholders, we generated findings on the characteristics of FastForward programs, as well as the academic and labor market outcomes of students enrolled in these programs. We describe the preliminary descriptive findings below.

FastForward programs enroll a substantially different segment of the population from credit-bearing programs and offer a vital alternative route to skill development and workforce opportunities, especially for demographic groups often underrepresented in traditional higher education. FastForward programs in Virginia enroll a substantially higher share of Black students, male students, and older students than short-duration, credit-bearing programs at community colleges that typically require one year or less to complete. Focus groups conducted with FastForward students at six colleges indicate that the students were a mix of workers sent by their employers to learn specific new skills and students who signed up for a FastForward program on their own. Among the latter group were older career changers and recent high school graduates, many of whom had no prior college experience and were primarily interested in landing their first job in their chosen field. Moreover, 61% of FastForward participants have neither prior nor subsequent enrollment in credit-bearing programs, highlighting the program’s unique role in broadening access to postsecondary education and career pathways.

FastForward programs offer an alternative path for students who are unsuccessful in credit-bearing programs. The vast majority of students (78%) enrolled in only one FastForward program, with the average enrollment duration of 1.5 quarters, which is notably shorter than most traditional credit-bearing programs. While 36% have prior credit-bearing enrollment, fewer than 20% of these students earned a degree or certificate from it, and less than 12% of FastForward enrollees transitioned to credit-bearing training afterward. Interviews with administrators and staff indicated that while some colleges facilitate noncredit-to-credit pathways by granting credit for prior learning, others prioritize employment-focused training and support over stackable academic pathways due to students’ primary interest in seeking employment post-training.

FastForward programs have a remarkable completion rate and are related to high industry credential attainment rates. Over 90% of students complete their program, with two-thirds of students obtaining industry credentials. Student focus groups echoed this success. They praised the FastForward program and colleges for addressing both their tuition and non-tuition needs. Many students noted that they had not envisioned themselves as college students and credited program staff, financial aid, and institutional support with helping them to be successful.

Earning an industry credential through FastForward on average increases quarterly earnings by approximately $1,000. In addition, industry credentials also increase the probability of being employed by 2.4 percentage points on average. We find substantial heterogeneity in economic return across different fields of study, where the fields of transportation (for example, commercial driver’s license) and precision production (for example, gas metal arc welding) seem to be associated with particularly pronounced earnings premiums. Within programs, we do not observe significant heterogeneity in economic returns across student subgroups.

What’s Next?

In view of the strong economic returns associated with earning an industry credential and the noticeable variation in credential attainment between training institutions and programs, our future exploration intends to unpack the sources of variation in program-institution credential attainment rates and to identify specific program-level factors that are within the control of an institution and which are associated with higher credential rates and lower equity gaps. Specifically, we will collect additional survey data from the top 10 most highly-enrolled programs at the Virginia Community College System (VCCS) that will provide more nuanced program-level information and identify which malleable program factors are predictive of higher credential attainment rates, better labor market outcomes, and smaller equity gaps associated with these outcomes.


Di Xu is an associate professor in the School of Education at UC, Irvine, and the faculty director of UCI’s Postsecondary Education Research & Implementation Institute.

Ben Castleman is the Newton and Rita Meyers Associate Professor in the Economics of Education at the University of Virginia.

Betsy Tessler is a senior associate at MDRC in the Economic Mobility, Housing, and Communities policy area.

Note: A team of researchers, including Kelli Bird, Sabrina Solanki, and Michael Cooper contributed jointly to the quantitative analyses of this project. The MDRC team, including Hannah Power, Kelsey Brown, and Mark van Dok, contributed to qualitative data collection and analysis. The research team is grateful to the Virginia Community College System (VCCS) for providing access to their high-quality data. Special thanks are extended to Catherine Finnegan and her team for their valuable guidance and support throughout our partnership.

This project was funded under the Postsecondary and Adult Education research topic; questions about it should be directed to program officer James Benson (James.Benson@ed.gov).

This blog was produced by Corinne Alfeld (Corinne.Alfeld@ed.gov), NCER program officer for the CTE research topic.

It All Adds Up: Why and How to Measure the Cost of Career & Technical Education

Cost analysis is a critical part of education research because it communicates what resources are needed for a particular program or intervention. Just telling education leaders how promising a program or practice can be does not tell the whole story; they need to know how much it will cost so that they can prioritize limited resources. Since 2015, cost analysis has been required for IES-funded Efficacy/Impact studies (and for Development Innovation studies as of 2019) and is included in the IES Standards for Excellence in Education Research.

In this guest blog for CTE Month, two members of the CTE Research Network’s cost analysis working group, David Stern, an advisor to the network, and Eric Brunner, a co-PI of one of the research teams, discuss how costs associated with CTE programs may differ from those of standard education and how to measure those costs.

Photo of David SternWhy is cost analysis different in Career & Technical Education (CTE) research?

Due to additional, non-standard components needed in some types of career training, CTE can cost much more than the education resources needed in regular classrooms. For instance, CTE classes often use specialized equipment—for example, hydraulic lifts in automotive mechanics, stoves and refrigerators in culinary arts, or medical equipment in health sciences—which costs significantly more than equipment in the standard classroom. Having specialized equipment for student use can also constrain class size to be smaller, resulting in higher cost-per-pupil.  High schools and community colleges may also build labs within existing buildings or construct separate buildings to house CTE programs with specialized equipment. These required facility expenses will need to be recognized in cost calculations.

CTE programs can also provide co-curricular experiences for students alongside classes in career-related subjects, such as work-based learning, career exploration activities, or integrated academic coursework. Schools are usually required to provide transportation for students to workplaces, college campuses for field trips, or regional career centers, which is another expense. Finally, the budget lines for recruiting and retaining teachers from some higher paying career areas and industries (such as nursing or business) may exceed those for average teacher salaries. All of these costs add up. To provide useful guidance for the field, CTE researchers should measure and report the cost of these features separately.

Photo of Eric BrunnerHow is resource cost different from reported spending? 

There are also some hidden costs to account for in research on CTE. For example, suppose a school does not have a work-based learning (WBL) coordinator, so a CTE teacher is allowed one of their 5 periods each day to organize and oversee WBL, which may include field trips to companies, job shadowing experiences, internships, or a school-based enterprise. The expenditure report would show 20% of the teacher’s salary has been allocated for that purpose. In reality, however, a teacher may devote much more than 20% of their time to this. They may in fact be donating to the program by spending unpaid time or resources (such as transportation in their own vehicle to visit employer sites to coordinate learning plans) outside the workday. It is also possible that the teacher would spend less than 20% of their time on this. To obtain an accurate estimate of the amount of this resource cost at a particular school, a researcher would have to measure how much time the teacher actually spends on WBL.  This could be done as part of an interview or questionnaire.

Similarly, high school CTE programs are increasingly being developed as pathways that allow students to move smoothly to postsecondary education, such as via dual enrollment programs or directly to the labor market. Building and sustaining these pathways takes active collaboration between secondary and postsecondary educators and employers. However, the costs of these collaborations in terms of time and resources are unlikely to be found in a school expenditure report. Thus, an incremental cost analysis for CTE pathway programs must go beyond budgets and expenditure reports to interview or survey program administrators and staff about the resources or “ingredients” that programs require to operate. A recent example of a cost study of a CTE program can be found here.

Are there any resources for calculating CTE Costs?

In this blog, we have presented some examples of how the costs associated with CTE programs may differ from those of a standard education. To help CTE researchers conduct cost analysis, the CTE Research Network has developed a guide to measuring Incremental Costs in Career and Technical Education, which explains how to account for the particular kinds of resources used in CTE. The guide was developed by the working group on cost analysis supported by the CTE Research Network.


The Career and Technical Education (CTE) Research Network has supported several cross-network working groups comprised of members of network research teams and advisors working on issues of broad interest to CTE research. Another CTE Network working group developed an equity framework for CTE researchers, which was described in a blog for CTE month in February, 2023.

This blog was produced by Corinne Alfeld, NCER program officer for the CTE research topic and the CTE Research Network. Contact: Corinne.Alfeld@ed.gov.

IES Makes Three New Awards to Accelerate Breakthroughs in the Education Field

Through the Transformative Research in the Education Sciences Grants program (ALN 84.305T), IES  invests in innovative research that has the potential to make dramatic advances towards solving seemingly intractable problems and challenges in the education field, as well as to accelerate the pace of conducting education research to facilitate major breakthroughs. In the most recent FY 2024 competition for this program, IES invited applications from partnerships between researchers, product developers, and education agencies to propose transformative solutions to major education problems that leverage advances in technology combined with research insights from the learning sciences.

IES is thrilled to announce that three grants have been awarded in the FY 2024 competition. Building on 20 years of IES research funding to lay the groundwork for advances, these three projects focus on exploring potentially transformative uses of generative artificial intelligence (AI) to deliver solutions that can scale in the education marketplace if they demonstrate positive impacts on education outcomes. The three grants are:

Active Learning at Scale (Active L@S): Transforming Teaching and Learning via Large-Scale Learning Science and Generative AI

Awardee: Arizona State University (ASU; PI: Danielle McNamara)

The project team aims to solve the challenge that postsecondary learners need access to course materials and high-quality just-in-time generative learning activities flexibly and on-the-go.  The solution will be a mobile technology that uses interactive, research-informed, and engaging learning activities created on the fly, customized to any course content with large language models (LLMs). The project team will leverage two digital learning platforms from the SEERNet networkTerracotta and ASU Learning@Scale – to conduct research and will include over 100,000 diverse students at ASU, with replication studies taking place at Indiana University (IU). IES funding has supported a large portion of the research used to identify the generative learning activities the team will integrate into the system—note-taking, self-explanation, summarization, and question answering (also known as retrieval practice). The ASU team includes in-house technology developers and researchers, and they are partnering with researchers at IU and developers at INFLO and Clevent AI Technology LLC. The ASU and IU teams will have the educator perspective represented on their teams, as these universities provide postsecondary education to large and diverse student populations.

Talking Math: Improving Math Performance and Engagement Through AI-Enabled Conversational Tutoring

Awardee: Worcester Polytechnic Institute (PI: Neil Heffernan)

The project team aims to provide a comprehensive strategy to address persistent achievement gaps in math by supporting students during their out-of-school time. The team will combine an evidence-based learning system with advances in generative AI to develop a conversational AI tutor (CAIT– pronounced as “Kate”) to support independent math practice for middle school students who struggle with math, and otherwise, may not have access to after-school tutoring. CAIT will be integrated into ASSISTments, a freely available, evidence-based online math platform with widely used homework assignments from open education resources (OER). This solution aims to dramatically improve engagement and math learning during independent math problem-solving time. The team will conduct research throughout the product development process to ensure that CAIT is effective in supporting math problem solving and is engaging and supportive for all students. ASSISTments has been used by over 1 million students and 30,000 teachers, and IES has supported its development and efficacy since 2003. The project team includes researchers and developers at Worcester Polytechnic Institute and the ASSISTments Foundation, researchers from WestEd, educator representation from Greater Commonwealth Virtual School, and a teacher design team.

Scenario-Based Assessment in the age of generative AI: Making space in the education market for alternative assessment paradigm

Awardee: University of Memphis (PI: John Sabatini)

Educators face many challenges building high-quality assessments aligned to course content, and traditional assessment practices often lack applicability to real world scenarios. To transform postsecondary education, there needs to be a shift in how knowledge and skills are assessed to better emphasize critical thinking, complex reasoning, and problem solving in practical contexts. Supported in large part by numerous IES-funded projects, including as part of the Reading for Understanding Initiative, the project team has developed a framework for scenario-based assessments (SBAs). SBAs place knowledge and skills into a practical context and provide students with the opportunity to apply their content knowledge and critical thinking skills. The project team will leverage generative AI along with their framework for SBAs to create a system for postsecondary educators to design and administer discipline-specific SBAs with personalized feedback to students, high levels of adaptivity, and rich diagnostic information with little additional instructor effort. The project team includes researchers, developers, and educators at University of Memphis and Georgia State University, researchers and developers at Educational Testing Service (ETS), and developers from multiple small businesses including Capti/Charmtech, MindTrust, Caimber/AMI, and Workbay who will participate as part of a technical advisory group.

We are excited by the transformative potential of these projects and look forward to seeing what these interdisciplinary teams can accomplish together. While we are hopeful the solutions they create will make a big impact on learners across the nation, we will also share lessons learned with the field about how to build interdisciplinary partnerships to conduct transformative research and development.


For questions or to learn more about the Transformative Research in the Education Sciences grant program, please contact Erin Higgins (Erin.Higgins@ed.gov), Program Lead for the Accelerate, Transform, Scale Initiative.