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This article introduces researchers in the science concerned with developing and studying research methods, measurement, and evaluation (RMME) to the educational data mining (EDM) community. It assumes that the audience is familiar with traditional priorities of statistical analyses, such as accurately estimating model parameters and inferences from those models. Instead, this article focuses on data mining's adoption of statistics and machine learning to produce cutting-edge methods in educational contexts. It answers three questions: (1) What are the primary interests of EDM and RMME researchers?; (2) What is their discipline-specific vocabulary?; and (3) What are the similarities and differences in how the EDM and RMME communities analyze similar types of data?

We propose a novel model, Wide & Deep Item Response Theory (Wide & Deep IRT), to predict the correctness of students' responses to questions using historical clickstream data. This model combines the strengths of conventional Item Response Theory (IRT) models and Wide & Deep Learning for Recommender Systems. By leveraging clickstream data, Wide & Deep IRT provides precise predictions of answer correctness while enabling the exploration of behavioral patterns among different ability groups. Our experimental results based on a real-world dataset (EDM Cup 2023) demonstrate that Wide & Deep IRT outperforms conventional IRT models and state-of-the-art knowledge tracing models while maintaining the ease of interpretation associated with IRT models. Our model performed very well in the EDM Cup 2023 competition, placing second on the public leaderboard and third on the private leaderboard. Additionally, Wide & Deep IRT identifies distinct behavioral patterns across ability groups. In the EDMCup2023dataset, low-ability students were more likely to directly request an answer to a question before attempting to respond, which can negatively impact their learning outcomes and potentially indicates attempts to game the system. Lastly, the Wide & Deep IRT model consists of significantly fewer parameters compared to traditional IRT models and deep knowledge tracing models, making it easier to deploy in practice. The source code is available via Open Science Framework.

Effect sizes are important because they are an accessible way to indicate the practical importance of observed associations or differences. Standardized mean difference (SMD) effect sizes, such as Cohen's d, are widely used in education and the social sciences -- in part because they are relatively easy to calculate. However, SMD effect sizes assume normally distributed data, whereas most data in these fields are ordinal and/or non-normal. In these situations, SMD effect sizes can be biased, and a non-parametric measure such as Cliff's [delta] is more appropriate. This paper provides a practical guide on how to calculate Cliff's [delta]. First, we present a conceptual overview and a worked example. Then we present two methods of calculating Cliff's [delta]: (1) a web-based Shiny application developed to accompany this paper (https://cliffdelta.shinyapps.io/calculator; suitable for all users), and (2) an R tutorial (suitable for R users). This is intended to provide researchers and practitioners with an appropriate and accessible effect size measure for non-normal data.

Historically, organizational researchers have fully embraced frequentist statistics and null hypothesis significance testing (NHST). Bayesian statistics is an underused alternative paradigm offering numerous benefits for organizational researchers and practitioners: e.g., accumulating direct evidence for the null hypothesis (vs. 'fail to reject the null'), capturing uncertainty across a distribution of population parameters (vs. a 95% confidence interval on a single point estimate) -- and through these benefits, communicating statistical findings more clearly. Although organizational methodologists in the past have promoted Bayesian methods, only now is easy-to-use JASP statistical software available for more widespread implementation. Moreover, the software is free to download and use, is menu-driven, and is supported by an active multidisciplinary user community. Using JASP, our tutorial compares and contrasts frequentist and Bayesian approaches for two analyses: a multiple linear regression analysis and a linear mixed regression analysis.

The procedures of carrying out factorial invariance to validate a construct were well developed to ensure the reliability of the construct that can be used across groups for comparison and analysis, yet mainly restricted to the frequentist approach. This motivates an update to incorporate the growing Bayesian approach for carrying out the Bayesian factorial invariance, as well as the frequentist approach, using the recent add-on R packages to show the procedures systematically for testing measurement equivalence via multigroup confirmatory factor analysis. The practical procedure and guidelines for carrying out factorial invariance under MCFA using a classic empirical example are demonstrated. Comparison between the frequentist and the Bayesian procedures and demonstration using priors are another two nuclei of the paper.

Learning a second language (L2) is dependent upon numerous external and internal factors, among which motivation plays a relevant role. In fact, motivation has been recognized as crucial in the L2 learning process (Ushioda, 2012). Such has been its importance that interest in L2 motivation has led to the development of theories such as the L2 motivational construct, and the L2 motivational self system (Dörnyei, 2005, 2009). Nevertheless, despite the academic focus on L2 learning motivation (Dörnyei & Ushioda, 2013), the impact of additional L2 lessons on students already engaged in formal L2 instruction at an official educational level (e.g., Higher Education) remaines vastly underexplored. Thus, this study aims to bridge this gap by analyzing the differences between 118 undergraduate EFL students who attended extra L2 lessons and those who did not. Considering the complex nature of the motivational construct, a Bayesian network analysis was used, categorizing motivations into two modules based on attendance of additional L2 lessons. This allowed us to observe the different factors of motivation as a whole construct, and not individually. The findings revealed that students who attended extra lessons are internally motivated toward self-improvement, whereas those who do not attend extra L2 lessons are influenced by external pressures and career aspirations.

Multimodal learning analytics (MMLA) research has shown the feasibility of building automated models of collaboration quality using artificial intelligence (AI) techniques (e.g., supervised machine learning (ML)), thus enabling the development of monitoring and guiding tools for computer-supported collaborative learning (CSCL). However, the practical applicability and performance of these automated models in authentic settings remains largely an under-researched area. In such settings, the quality of data features or attributes is often affected by noise, which is referred to as attribute noise. This paper undertakes a systematic exploration of the impact of attribute noise on the performance of different collaboration-quality estimation models. Moreover, we also perform a comparative analysis of different ML algorithms in terms of their capability of dealing with attribute noise. We employ four ML algorithms that have often been used for collaboration-quality estimation tasks due to their high performance: random forest, naive Bayes, decision tree, and AdaBoost. Our results show that random forest and decision tree outperformed other algorithms for collaboration-quality estimation tasks in the presence of attribute noise. The study contributes to the MMLA (and learning analytics (LA) in general) and CSCL fields by illustrating how attribute noise impacts collaboration-quality model performance and which ML algorithms seem to be more robust to noise and thus more likely to perform well in authentic settings. Our research outcomes offer guidance to fellow researchers and developers of (MM)LA systems employing AI techniques with multimodal data to model collaboration-related constructs in authentic classroom settings.

This research aims to compare the ability and item parameter estimations of Item Response Theory according to Maximum likelihood and Bayesian approaches in different Monte Carlo simulation conditions. For this purpose, depending on the changes in the priori distribution type, sample size, test length, and logistics model, the ability and item parameters estimated according to the maximum likelihood and Bayesian method and the differences in the RMSE of these parameters were examined. The priori distribution (normal, left-skewed, right-skewed, leptokurtic, and platykurtic), test length (10, 20, 40), sample size (100, 500, 1000), logistics model (2PL, 3PL). The simulation conditions were performed with 100 replications. Mixed model ANOVA was performed to determine RMSE differentiations. The prior distribution type, test length, and estimation method in the differentiation of ability parameter and RMSE were estimated in 2PL models; the priori distribution type and test length were significant in the differences in the ability parameter and RMSE estimated in the 3PL model. While prior distribution type, sample size, and estimation method created a significant difference in the RMSE of the item discrimination parameter estimated in the 2PL model, none of the conditions created a significant difference in the RMSE of the item difficulty parameter. The priori distribution type, sample size, and estimation method in the item discrimination RMSE were estimated in the 3PL model; the a priori distribution and estimation method created significant differentiation in the RMSE of the lower asymptote parameter. However, none of the conditions significantly changed the RMSE of item difficulty parameters.

This study investigates the impact of Project-Based Learning (PBL) with an emphasis on statistics on 26 Kinesiology students from a prominent Chilean university. A mixed-methodological approach was employed for the qualitative and quantitative analysis of data collected through surveys, supplementary interviews, and performance evaluations of these students. Furthermore, group grades during the project execution were examined. The correlation between academic performance and the perception of learning through this method was explored. The results indicate a generally favorable assessment of PBL, emphasizing its contribution to the development of statistical and scientific skills, as well as improvement in academic performance, with the option to incorporate additional methods to cater to different student needs. It is concluded that PBL is a potential pedagogical strategy that promotes active engagement in learning and the development of practical skills relevant to health sciences students in Chile.

This paper argues that engaging students in informal statistical reasoning from early school years is essential for the development of statistical understanding. We investigated if and how children aged six-seven years old identified variation in a table of data and made predictions through the design of a teaching experiment. The classroom teaching experiment was comprised of four 45 minutes lessons addressing the understanding and interpretation of data sets. In order to describe students' informal predictive reasoning, we used the framework of "data lenses". More specifically, we analyzed the different types of answers the students produced as they engaged in predictive reasoning during an interview given before and after the teaching experiment. The participation of students in (classroom) and out-of-school (family) communities of practice was also taken into consideration. Our results demonstrate that the students benefited from their learning experience and developed data understanding.

Dual Enrollment (DE) or Dual Credit (DC) programs have become increasingly prevalent at both the high school and college settings. These programs enable students to earn both high school and college credit and get a head start on their college education. Additionally, students in these programs must take university core curriculum courses to fulfill their college education requirements. A course that several students take is Introductory to Biology, a STEM (Science, Technology, Engineering, and Mathematics) course. This course is an introductory science course and may present a challenge for students in that there is a large quantity of material discussed. Moreover, students must adapt to new study strategies excel in the course. Moreover, educational administrators or school leaders, administrators or principals must consider student performance and therefore must look at location and student performance to better improve student outcomes. Scant studies look at school leaders' perception on science dual enrollment courses. Moreover, administrators must have systems in place to promote high quality instruction and student success in dual enrollment courses. This study will look at students taking introductory biology courses and their performance at both the high school and non-high school locations (i.e. college environment) in Texas using the Mann-Whitney U statistical test. In addition, this study will provide recommendations to high school leaders such as administrators and principals regarding location and student outcomes for students in dual enrollment biology courses to ensure high quality instruction and student achievement are in place.

The traditional points system and subsequent Grade Point Average (GPA) in education perpetuates an evaluation of academic performance which reflects arbitrary weighting of assignments and/or assessments. As such, GPAs which are calculated using a traditional points system are not unidimensional in their design. The baseball batting and slugging percentage, which serves as established metrics for performance evaluations among baseball players, better reflects unidimensionality. In essence, this paper puts forth an analysis and discussion which posits that baseball batting average and slugging percentage can serve as an example for how unidimensionality can become more prevalent in educational assessments, especially as it relates to the traditional points system and GPA.

The study compared two survey datasets from higher education students in Germany and Ghana regarding access to digital devices; perceived value of digital media, tools, and services used for learning; gap analysis of the actual and desired use of digital teaching and learning formats; and types of media usage profiles among students. The findings underscored commonalities between the two groups, revealing that students in both contexts are equipped with mobile devices, and are highly utilized for their learning. Similarly, both student groups exhibit a preference for utilizing external media, tools and services not owned nor administered by their respective universities. However, a stark contrast emerged in terms of the provision of, and expressed demand for digital teaching and learning formats, attributable to significant disparities in the underlying internet infrastructure and service provision between the two countries. The high intensity in the use of videos, social networks and messaging applications means majority of the students in both contexts were classified as entertainment users of media by means of a latent class analysis. While students in Germany showed differentiation between non-traditional and traditional students in terms of their media usage patterns, there was little differentiation among Ghanaian students. The study concludes by offering suggestions for enhancing support for non-traditional learning and improving digital education in Ghana and similar contexts.

This article presents the results of applying an educational sequence implemented with technological support on an LMS and focused on peer assessment that was designed specifically to address key concepts in statistics with first-year undergraduate students. Individualized information is available for a total of n=232 students to support the empirical conclusions that are drawn. Based on the comparison of the peer assessments and the academic performance obtained in the two previous academic years in which a different methodology was applied, differential effects are found in the quality of the assignments presented. This, together with the perception of the learning by the students, suggests the incorporation of peer assessment processes in future curricular design.

The present paper investigates one aspect of questionable research practices relating to Arabic L1 learners of foreign languages, namely the use of statistics. The objective of the paper is to argue that reproducible research requires adopting wise practices in linguistics and that the excessive focus on quantification does not seem to serve this purpose. Statistical significance tests in quantitative research are routinely used in linguistic inquiry as well as language teaching and learning studies with a view to supporting the relevant explanatory insights in linguistics. In this article, I will expose the misuse of statistics by doctoral students in English departments of Morocco working on Arabic L1 learners' data, by highlighting some practices that are at odds with international good practices in academic research in linguistics. I will take stock of the current questionable practices in this regard to dispel some of the misunderstanding about the use of statistics which is now gaining grounds lest this becomes an orthodoxy. I will argue that research on Arabic L1 learners' data should be focused more on exploration and discovery, as well as the validation of epistemological insights than on mere descriptive quantification geared to hypothesis verification. These areas of focus constitute the crux of academic research in linguistics, but they seem to be lost in statistics in doctoral students' theses. Recommendations and solutions are provided for enhancing transparency and improving reproducibility of doctoral research outcomes to advance theory building and the delivery of new research lines in linguistics as well as to avoid the risk of research waste, in line with the requirements of open science.

Bayesian Knowledge Tracing (BKT) is a popular interpretable computational model in the educational mining community that can infer a student's knowledge state and predict future performance based on practice history, enabling tutoring systems to adaptively select exercises to match the student's competency level. Existing BKT implementations do not scale to large datasets and are difficult to extend and improve in terms of prediction accuracy. On the other hand, uninterpretable neural network (NN) student models, such as Deep Knowledge Tracing, enjoy the speed and modeling flexibility of popular computational frameworks (e.g., PyTorch, Tensorflow, etc.), making them easy to develop and extend. To bridge this gap, we develop a collection of BKT recurrent neural network (RNN) cells that are much faster than brute-force implementations and are within an order of magnitude of a fast, fine-tuned but inflexible C++ implementation. We leverage our implementation's modeling flexibility to create two novel extensions of BKT that significantly boost its performance. The first merges item response theory (IRT) and BKT by modeling multidimensional problem difficulties and student abilities without fitting student-specific parameters, allowing the model to easily generalize to new students in a principled way. The second extension discovers the discrete assignment matrix of problems to knowledge components (KCs) via stochastic neural network techniques and supports further guidance via problem input features and an auxiliary loss objective. Both extensions are learned in an end-to-end fashion; that is, problem difficulties, student abilities, and assignments to knowledge components are jointly learned with BKT parameters. In synthetic experiments, the skill discovery model can partially recover the true generating problem-KC assignment matrix while achieving high accuracy, even in some cases where the true KCs are structured unfavorably (interleaving sequences). On a real dataset where problem content is available, the skill discovery model matches BKT with expert-provided skills, despite using fewer KCs. On seven out of eight real-world datasets, our novel extensions achieve prediction performance that is within 0.04 AUC-ROC points of state-of-the-art models. We conclude by showing visualizations of the parameters and inferences to demonstrate the interpretability of our BKT RNN models on a real-life dataset.

The aim of the present exploratory study was to examine students' situational engagement and motivation in the statistics classroom at Zayed University, in Dubai, United Arab Emirates (UAE). Two instruments were used for this purpose: a) experience sampling method (ESM), and b) the validated Mathematics Motivation Questionnaire (MMQ). This study employed two samples, at undergraduate level (2nd and 4th Semesters). Participants consisted of 100 students enrolled in Statistics I and Statistics II (Probability and Structure of Randomness). The results indicate that, apart from challenge and effort, emotional engagement is not significantly different across different activities. The results also indicate increases in intrinsic value and utility value and decreases in test anxiety. Finally, results indicate higher engagement and effort when social interaction is purposely planned and fostered, such as in small groups. On the contrary, individual class activities seem to generate slightly lower levels of engagement and effort. These findings have significant implications for educators and researchers who seek to enhance students' engagement and motivation in their statistics courses.

This survey paper presents recent relevant research in mathematics education produced in Spain, which allows the identification of different broad lines of research developed by Spanish groups of scholars. First, we present and describe studies whose research objectives are related to student learning of specific curricular contents and process-oriented competencies, namely arithmetic, algebra, geometry, functions and calculus, probability and statistics, and argumentation or proof in geometric contexts. Next, we present characteristics and foci of investigations dealing with different aspects of mathematics teacher education, encompassing a large part of Spanish research in mathematics education. The descriptions of other transversal lines of research complement the previous two big blocks: research on students with special educational needs and the effects of using technology in different curricular contents and educational levels. Finally, we report on the research activities and advances of Spanish research in mathematics education from two main theoretical frameworks created or developed by Spanish researchers. This plurality of research strands also corresponds to a wide range of international collaborations, especially with Latin American colleagues.

Post-instrument covariates are often included as controls in instrumental variable (IV) analyses to address a violation of the exclusion restriction. However, we show that such analyses are subject to biases unless strong assumptions hold. Using linear constant-effects models, we present asymptotic bias formulas for three estimators (with and without measurement error): IV with post-instrument covariates, IV without post-instrument covariates, and ordinary least squares. In large samples and when the model provides a reasonable approximation, these formulas sometimes allow the analyst to bracket the parameter of interest with two estimators and allow the analyst to choose the estimator with the least asymptotic bias. We illustrate these points with a discussion of the settler mortality IV used by Acemoglu, Johnson, and Robinson.

This article uses the interventionist theory of causation, a counterfactual theory taken from philosophy of science, to strengthen causal analysis in process tracing research. Causal claims from process tracing are re-expressed in terms of so-called hypothetical interventions, and concrete evidential tests are proposed which are shown to corroborate process tracing claims. In particular, three steps are prescribed for an interventionist investigation, and each step in turn is shown to make the causal analysis more robust, amongst others by disambiguating causal claims and clarifying or strengthening the existing methodological advice on counterfactual analysis. The article's claims are then illustrated using a concrete example, Haggard and Kaufman's analysis of the Argentinian transition to democracy. It is shown that interventionism could have strengthened the authors' conclusions. The article concludes with a short Bayesian analysis of its key methodological proposals.

In real-world situations, multidimensional data may appear on large-scale tests or psychological surveys. The purpose of this study was to investigate the effects of the quantity and magnitude of cross-loadings and model specification on item parameter recovery in multidimensional Item Response Theory (MIRT) models, especially when the model was misspecified as a simple structure, ignoring the quantity and magnitude of cross-loading. A simulation study that replicated this scenario was designed to manipulate the variables that could potentially influence the precision of item parameter estimation in the MIRT models. Item parameters were estimated using marginal maximum likelihood, utilizing the expectation-maximization algorithms. A compensatory two-parameter logistic-MIRT model with two dimensions and dichotomous item-responses was used to simulate and calibrate the data for each combination of conditions across 500 replications. The results of this study indicated that ignoring the quantity and magnitude of cross-loading and model specification resulted in inaccurate and biased item discrimination parameter estimates. As the quantity and magnitude of cross-loading increased, the root mean square of error and bias estimates of item discrimination worsened.

Identifying the knowledge resources teachers productively and unproductively draw upon can provide a means by which to create support structures to develop a more robust understanding of the content. To provide more informed grade-level support structures in teacher education programs, this study examined the knowledge resources 20 secondary pre-service teachers (PSTs) and 13 elementary PSTs drew upon when solving a comparison proportional reasoning problem. Data from written work and videos of PSTs' explanations were analyzed using the robust understanding of proportional reasoning for teaching framework. Both elementary and secondary PSTs ubiquitously drew upon the same four knowledge resources (comparison of quantities, ratios, proportional situation, and ratio as measure). Elementary PSTs were more apt to counterproductively draw upon the knowledge resource ratios ? fractions, while secondary PSTs more often counterproductively drew upon equivalence. Mathematics educators can leverage the knowledge resources afforded by this task and strategically highlight productive and counterproductive resources to tailor instruction that develops PSTs' robust understanding of proportional reasoning.

In this qualitative study, we examined how prospective mathematics teachers' instructional visions align with their instructional practices through an approximation of practice opportunity. Namely, we employed scripting tasks to understand how prospective teachers complete a scripting task and respond to students' misconceptions, and we compared their instructional visions with their responding practices. The 81 prospective mathematics teachers who were taking the "Misconceptions in Mathematics Teaching" course at two different state universities comprised the participants. Data was obtained from the instructional vision questionnaire and two scripting tasks in fractions. We analyzed the data using the content analysis technique. Our findings indicate that the majority of the participants' instructional visions were aligned with ambitious instruction, while their responding practices were mostly inconsistent with their visions. Our findings suggest that while their instructional visions were highly reform based, prospective mathematics teachers still need to be oriented in an ambitious instructional direction in their practices.

Studies of non-linguistic statistical learning (SL) have often linked performance in SL tasks with differences in language outcomes. Most of these studies have focused on Western and high-income educational contexts, but children worldwide learn in radically different educational systems and communities, and often in a second language. In the west African nation of Côte d'Ivoire, children enter fifth grade (CM-1) with widely varying ages and literacy skills. Across three iteratively-developed experiments, 157 children, age 8-15 years, in rural communities in the greater-Adzópe region of Côte d'Ivoire watched sequences of cartoon images with embedded triplet patterns on touchscreen tablets, while performing a target-detection task. We assessed these tablet-based adaptations of non-linguistic visual SL and asked whether the children's individual differences in performance on the SL tasks were related to their first and second language and literacy skills. We found group-level evidence that children used the statistical regularities in the image sequence to gradually decrease their response times, but their responses on post-test discrimination did not reflect this learning. When evaluating the correlation between SL and language skills, individual differences related to other task demands predicted oral language skills shared by first and second languages, while SL better predicted second language print skills. These findings suggest that non-linguistic SL paradigms can measure similar skills in Ivorian children as previous samples, but they also echo recent calls for further cross-cultural validation, greater internal reliability, and tests for confounding variables (such as processing speed) in studies of individual differences in statistical learning.

Linear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both "Y" and "X" and therefore can provide symmetric estimates of these relationships. The most well-established OR model, the errors-in-variables (EIV) model, assumes that the observed scatter around the line is due entirely to errors of measurement in "Y" and "X" and that the ratio of the error variances is known. If most of the variance around the line is known to be due to the errors of measurement in "Y" and "X," the EIV model can provide an unbiased maximum likelihood estimate for a functional relationship. However, if a substantial part of the variability around the line is due to natural variability, which is not attributable to errors of measurement in "Y" or "X," the ratio of the measurement error variances is not well defined and the EIV model is not directly applicable. The main contribution of this report is the development of a hybrid model that provides plausible estimates for linear functional relationships in cases with substantial natural variability and substantial errors of measurement. An analysis of female and male differential test functioning between an essay test and an objective test used as parts of a licensure examination provides an illustration of the use of the hybrid model.

Teachers routinely observe and interpret student behavior to make judgements about whether and how to support their students' learning. Simulated cases can help pre-service teachers to gain this skill of diagnostic reasoning. With 118 pre-service teachers, we tested whether participants rate simulated cases presented in a serial-cue case format as more authentic and become more involved with the materials compared to cases presented in a whole case format. We further investigated whether participants with varying prior conceptual knowledge (what are symptoms of ADHD and dyslexia) gain more strategic knowledge (how to detect ADHD and dyslexia) with a serial-cue versus whole case format. We found that the case format did not impact authenticity ratings but that learners reported higher involvement in the serial-cue case format condition. Bayes factors provide moderate evidence for the absence of a case format effect on strategic knowledge and strong evidence for the absence of an interaction of case format and prior knowledge. We recommend using serial-cue case formats in simulations as they are a more authentic representation of the diagnostic reasoning process and cognitively involve learners. We call for replications to gather more evidence for the impact of case format on knowledge acquisition. We suggest a further inquiry into the relationship of case format, involvement, and authenticity but think that a productive way forward for designing authentic simulations is attention to aspects that make serial-cue cases effective for diverse learners. For example, adaptive feedback or targeted practice of specific parts of diagnostic reasoning such as weighing evidence.

Against the background of expanding parental choices and declining global birth rates, schools are experiencing rising competition regarding student enrolment. Schools have responded by strategically presenting information about their students' academic achievement and whole-person development orientation in the hope of attracting parents' interest. However, few studies have investigated the impact of these factors on student enrollment, particularly in the context of diverse school types and educational orientations. Accordingly, this study utilized data from 327 secondary schools in Hong Kong to examine the effects of academic achievement orientation and whole-person development orientation on student intake. Using hierarchical regression analysis, we found a positive association between high whole-person development orientation and student intake in aided schools with a strong academic development orientation. The result implies parents are increasingly concerned about their children's academic achievement and whole-person development at school. The study contributes to a broader understanding of the factors influencing parental choice in high-performing education systems, providing valuable insights for policymakers and educators seeking to improve educational offerings, enhance school transparency, and be better aligned with parental expectations.

This analysis employs a Bayesian framework to estimate the impact of a Cognitive-Behavioral Therapy (CBT) intervention on the recidivism of high-risk people under community supervision. The study relies on the reanalysis of experimental datal using a Bayesian logistic regression model. In doing so, new estimates of programmatic impact were produced using weakly informative Cauchy priors and the Hamiltonian Monte Carlo method. The Bayesian analysis indicated that CBT reduced the prevalence of new charges for total, non-violent, property, and drug crimes. However, the effectiveness of the CBT program varied meaningfully depending on the participant's age. The probability of the successful reduction of drug offenses was high only for younger individuals (<26 years old), while there was an impact on property offenses only for older individuals (>26 years old). In general, the probability of the successful reduction of new charges was higher for the older group of people on probation. Generally, this study demonstrates that Bayesian analysis can complement the more commonplace Null Hypothesis Significance Test (NHST) analysis in experimental research by providing practically useful probability information. Additionally, the specific findings of the reestimation support the principles of risk-needs responsivity and risk-stratified community supervision and align with related findings, though important differences emerge. In this case, the Bayesian estimations suggest that the effect of the intervention may vary for different types of crime depending on the age of the participants. This is informative for the development of evidence-based correctional policy and effective community supervision programming.

In relational event networks, the tendency for actors to interact with each other depends greatly on the past interactions between the actors in a social network. Both the volume of past interactions and the time that has elapsed since the past interactions affect the actors' decision-making to interact with other actors in the network. Recently occurred events may have a stronger influence on current interaction behavior than past events that occurred a long time ago--a phenomenon known as "memory decay". Previous studies either predefined a short-run and long-run memory or fixed a parametric exponential memory decay using a predefined half-life period. In real-life relational event networks, however, it is generally unknown how the influence of past events fades as time goes by. For this reason, it is not recommendable to fix memory decay in an ad-hoc manner, but instead we should learn the shape of memory decay from the observed data. In this paper, a novel semi-parametric approach based on Bayesian Model Averaging is proposed for learning the shape of the memory decay without requiring any parametric assumptions. The method is applied to relational event history data among socio-political actors in India and a comparison with other relational event models based on predefined memory decays is provided.

This study examined the preliminary feasibility, acceptability, and efficacy of an autism-adapted cognitive behavioral therapy for depression in autistic youth, CBT-DAY. Twenty-four autistic youth (11-17 years old) participated in the pilot non-randomized trial including 5 cisgender females, 14 cisgender males, and 5 non-binary youth. Youth participated in 12 weeks of, CBT-DAY and youth depressive symptoms (i.e., primary clinical outcome) and emotional reactivity and self-esteem (i.e., intervention mechanisms) were assessed through self-report and caregiver report at four timepoints: baseline (week 0), midpoint (week 6), post-treatment (week 12), and follow-up (week 24). Results suggested that CBT-DAY may be feasible (16.67% attrition) in an outpatient setting and acceptable to adolescents and their caregivers. Bayesian linear mixed-effects models showed that CBT-DAY may be efficacious in targeting emotional reactivity [[beta][subscript T1-T3] = -2.53, CrI[subscript 95%] (-4.62, -0.58), P[subscript d] = 0.995, d = -0.35] and self-esteem [[beta][subscript T1-T3] = -3.57, CrI[subscript 95%] (-5.17, -2.00), P[subscript d] > 0.999, d = -0.47], as well as youth depressive symptom severity [[beta] = -2.72, CrI[subscript 95%] (-3.85, -1.63), P[subscript d] > 0.999]. Treatment gains were maintained at follow-up. A cognitive behavioral group therapy designed for and with autistic people demonstrates promise in targeting emotional reactivity and self-esteem to improve depressive symptom severity in youth. Findings can be leveraged to implement larger, more controlled trials of CBT-DAY. The trial was registered at Clinicaltrials.gov (Identifier: NCT05430022; https://beta.clinicaltrials.gov/study/NCT05430022).

The sample mean in statistics is a concept of great importance, with its properties being extensively utilized in other areas, such as computer science. This research centers on the concept of the sample mean and its characteristics in a cohort of computer engineering students undertaking a required course in statistics at a university in the Netherlands. The objective of this study was to analyze students' comprehension of the fundamental structure, properties, and applications of the sample mean. A digital mini-course on sample mean was developed and employed with 97 students, who had the option to apply the concepts at their own pace. The action-process-object-schema (APOS) theoretical framework was utilized to analyze the interview responses of seven participants. The majority of participants were able to demonstrate an understanding of the Process conception of the sample mean, with only a minority demonstrating an understanding of the Object conception. The lack of comprehension of the sample mean hindered students' capacity to effectively utilize the associated applications and properties. These findings imply that educators should strive to ensure that students have a sound comprehension of the sample mean so that they are better equipped to work with related applications. Suggestions of this study and further research ideas are indicated.

We conducted a descriptive analysis and meta-analysis of single-case research design (SCRD) studies investigating the effectiveness of the graduated guidance procedure. Once we identified studies through electronic databases and reference lists, we used What Works Clearinghouse (WWC) Standards to evaluate each study. Then, we described studies in terms of various descriptive variables, calculated effect sizes through three non-parametric effect size methods, and analyzed results across studies. Results showed 11 of the 27 studies met WWC Standards or met standards with reservation. Of the 11, seven studies resulted in a large effect. We found the graduated guidance procedure to be an evidence-based practice when evaluating the findings against contemporary evidence standards. However, this review also showed that the majority of the reviewed studies (n = 20) had no effects and only one third of the studies had moderate or strong effects. Implications for researchers and practitioners are discussed.

Marginal maximum likelihood, a common estimation method for item response theory models, is not inherently a Bayesian procedure. However, due to estimation difficulties, Bayesian priors are often applied to the likelihood when estimating 3PL models, especially with small samples. Little focus has been placed on choosing the priors for marginal maximum estimation. In this study, using sample sizes of 1,000 or smaller, not using priors often led to extreme, implausible parameter estimates. Applying prior distributions to the c-parameters alleviated the estimation problems with samples of 500 or more; for the samples of 100, priors on both the a-parameters and c-parameters were needed. Estimates were biased when the mode of the prior did not match the true parameter value, but the degree of the bias did not depend on the strength of the prior unless it was extremely informative. The root mean squared error (RMSE) of the a-parameters and b-parameters did not depend greatly on either the mode or the strength of the prior unless it was extremely informative. The RMSE of the c-parameters, like the bias, depended on the mode of the prior for c.