Accounting for Heteroskedasticity Resulting from Between-Group Differences in Multilevel Models

Wald χ2 Test for Differential Item Functioning Detection with Polytomous Items in Multilevel Data

Identifying items with differential item functioning (DIF) in an assessment is a crucial step for achieving equitable measurement. One critical issue that has not been fully addressed with existing studies is how DIF items can be detected when data are multilevel. In the present study, we introduced a Lord's Wald χ 2 test-based procedure for detecting both uniform and non-uniform DIF with polytomous items in the presence of the ubiquitous multilevel data structure. The proposed approach is a multilevel extension of a two-stage procedure, which identifies anchor items in its first stage and formally evaluates candidate items in the second stage. We applied the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm to estimate multilevel polytomous item response theory (IRT) models and to obtain accurate covariance matrices. To evaluate the performance of the proposed approach, we conducted a preliminary simulation study that considered various conditions to mimic real-world scenarios. The simulation results indicated that the proposed approach has great power for identifying DIF items and well controls the Type I error rate. Limitations and future research directions were also discussed.

Evaluating two small-sample corrections for fixed-effects standard errors and inferences in multilevel models with heteroscedastic, unbalanced, clustered data

Multilevel modeling (MLM) is commonly used in psychological research to model clustered data. However, data in applied research usually violate one of the essential assumptions of MLM-homogeneity of variance. While the fixed-effect estimates produced by the maximum likelihood method remain unbiased, the standard errors for the fixed effects are misestimated, resulting in inaccurate inferences and inflated or deflated type I error rates. To correct the bias in fixed effects standard errors and provide valid inferences, small-sample corrections such as the Kenward-Roger (KR) adjustment and the adjusted cluster-robust standard errors (CR-SEs) with the Satterthwaite approximation for t tests have been used. The current study compares KR with random slope (RS) models and the adjusted CR-SEs with ordinary least squares (OLS), random intercept (RI) and RS models to analyze small, heteroscedastic, clustered data using a Monte Carlo simulation. Results show the KR procedure with RS models has large biases and inflated type I error rates for between-cluster effects in the presence of level 2 heteroscedasticity. In contrast, the adjusted CR-SEs generally yield results with acceptable biases and maintain type I error rates close to the nominal level for all examined models. Thus, when the interest is only in within-cluster effect, any model with the adjusted CR-SEs could be used. However, when the interest is to make accurate inferences of the between-cluster effect, researchers should use the adjusted CR-SEs with RS to have higher power and guard against unmodeled heterogeneity. We reanalyzed an example in Snijders & Bosker (2012) to demonstrate the use of the adjusted CR-SEs with different models.

The Impact of Restorative Practices on the Use of Out-of-School Suspensions: Results from a Cluster Randomized Controlled Trial

The overuse of exclusionary discipline practices, such as out-of-school suspensions (OSS), has consistently been documented over several decades. The resulting racial discipline disparities and the negative outcomes related to OSS have led policy makers and educators to consider other approaches to school discipline. One such approach, which has gained increasing use in the USA, is restorative practices (RP). However, despite its popularity, the experimental evidence base of the effects of RP and suspensions is extremely limited. To add to this knowledge base, we present findings from a cluster randomized controlled trial with 18 K-12 schools in an urban district in the US Northeast with 5878 students. Multilevel regression results, after 1 year of the intervention, showed no differences in the likelihood of suspension between students in the intervention and control schools and that the effects of the intervention did not vary by race/ethnicity, gender, or student disability status. However, for students in the intervention group, we show reductions in the likelihood of receiving an OSS for students who had previously been suspended.

Nexus between FinTech, renewable energy resource consumption, and carbon emissions

An increase in energy crises and environmental degradation has pushed countries to adopt more sustainable practices. In this situation, financial technology has played an important role to lower carbon emissions by integrating renewable energy resources that can help increase renewable energy resource consumption (REC) and lower carbon emissions (CE). To better understand this transmission mechanism, this study has collected a panel dataset of 26 Morgan Stanley Capital International (MSCI) developing countries for the 2011-2021 period. Furthermore, a proxy indicator for financial technology (FinTech) was developed by extracting relevant data from CrunchBase. Pooled ordinary least square and robust fixed effects technique was adopted to analyse the influence of FinTech on renewable energy and carbon emissions for robustness. Results of the study show that FinTech development promotes renewable energy resource consumption (REC) and discourages carbon emissions (CE), moreover, economic growth positively impacts, and carbon emissions (CE). This research emphasizes the importance of adopting financial technology as an important deterrent of further environmental damage. Additionally, in line with the results of this study, policymakers should design and implement an industrial policy which promotes sustainable economic growth which can pave the path for a circular economy model in the future.