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Research Commentary: Unpacking the Links Between Equitable Teaching Practices and Standards for Mathematical Practice: Equity for Whom and Under What Conditions
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| Pengarang | : | Filiberto Barajas-López and Gregory V. Larnell |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 4) |
| Halaman | : | 349-361 |
| Abstrak | : | In their commentary, “Toward a Framework for Research Linking Equitable Teaching with the Standards for Mathematical Practice,” Bartell et al. (2017) provide a stepping-stone into the challenge of clarifying the interface between equity and standards setting in mathematics education by devising a framework that relates the Common Core State Standards for Mathematics to an explicit articulation of equitable teaching practices. In this commentary, we respond to this proposed framework and aim to clarify some key elements. Furthermore, we draw on our own positionings and scholarly interests to critique and bolster the framework by focusing on the tensions related to co-opting the Common Core for equity-oriented purposes, the framework's relationship to neoliberalism, and the role of racialized rhetoric and nondominant family and community knowledge. |
Multiple Testing of Submatrices of a Precision Matrix With Applications to Identification of Between Pathway Interactions
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 328-339 |
| Abstrak | : | Making accurate inference for gene regulatory networks, including inferring about pathway-by-pathway interactions, is an important and difficult task. Motivated by such genomic applications, we consider multiple testing for conditional dependence between subgroups of variables. Under a Gaussian graphical model framework, the problem is translated into simultaneous testing for a collection of submatrices of a high-dimensional precision matrix with each submatrix summarizing the dependence structure between two subgroups of variables. A novel multiple testing procedure is proposed and both theoretical and numerical properties of the procedure are investigated. Asymptotic null distribution of the test statistic for an individual hypothesis is established and the proposed multiple testing procedure is shown to asymptotically control the false discovery rate (FDR) and false discovery proportion (FDP) at the prespecified level under regularity conditions. Simulations show that the procedure works well in controlling the FDR and has good power in detecting the true interactions. The procedure is applied to a breast cancer gene expression study to identify between pathway interactions. Supplementary materials for this article are available online. |
Error Variance Estimation in Ultrahigh-Dimensional Additive Models
| Pengarang | : | Zhao Chen |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 315-327 |
| Abstrak | : | Error variance estimation plays an important role in statistical inference for high-dimensional regression models. This article concerns with error variance estimation in high-dimensional sparse additive model. We study the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to spurious correlations that are even higher in nonparametric models than linear models. We further propose an accurate estimate for error variance in ultrahigh-dimensional sparse additive model by effectively integrating sure independence screening and refitted cross-validation techniques. The root n consistency and the asymptotic normality of the resulting estimate are established. We conduct Monte Carlo simulation study to examine the finite sample performance of the newly proposed estimate. A real data example is used to illustrate the proposed methodology. Supplementary materials for this article are available online. |
Choosing and Justifying Robust Methods for Educational Research
| Pengarang | : | Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer, and James Hiebert |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 4) |
| Halaman | : | 342-348 |
| Abstrak | : | In our recent editorials (Cai et al., 2019a, 2019b), we discussed the important roles that research questions and theoretical frameworks play in conceptualizing, carrying out, and reporting mathematics education research. In this editorial, we discuss the methodological choices that arise when one has articulated research questions and constructed at least a rudimentary theoretical framework. Just as the researcher must justify the significance of research questions and the appropriateness of the theoretical framework, we argue that the researcher must thoroughly describe and justify the selection of methods. Indeed, the research questions and the theoretical framework should drive the choice of methods (and not the reverse). In other words, a sufficiently well-specified set of research questions and theoretical framework establish the parameters within which the most productive methods will be selected and developed. |
Block-Diagonal Covariance Selection for High-Dimensional Gaussian Graphical Models
| Pengarang | : | Emilie Devijver |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 306-314 |
| Abstrak | : | Gaussian graphical models are widely used to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To reduce the number of parameters to estimate in the model, we propose a nonasymptotic model selection procedure supported by strong theoretical guarantees based on an oracle type inequality and a minimax lower bound. The covariance matrix of the model is approximated by a block-diagonal matrix. The structure of this matrix is detected by thresholding the sample covariance matrix, where the threshold is selected using the slope heuristic. Based on the block-diagonal structure of the covariance matrix, the estimation problem is divided into several independent problems: subsequently, the network of dependencies between variables is inferred using the graphical lasso algorithm in each block. The performance of the procedure is illustrated on simulated data. An application to a real gene expression dataset with a limited sample size is also presented: the dimension reduction allows attention to be objectively focused on interactions among smaller subsets of genes, leading to a more parsimonious and interpretable modular network. Supplementary materials for this article are available online. |
Analysis of Gap Times Based on Panel Count Data With Informative Observation Times and Unknown Start Time
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 294-305 |
| Abstrak | : | In biomedical studies, one is often interested in repeat events with longitudinal observations occurring only intermittently, resulting in panel count data. The first stage of labor, measured through unit-increments of cervical dilation in pregnant women, provides such an example. Obstetricians are interested in assessing the gap time distribution of per-unit increments of cervical dilation for better management of labor process. Typically, only intermittent medical examinations for cervical dilation occur after (already dilated) women get admitted to hospital. The observation frequency is very likely correlated to how fast/slow she dilates. Thus, one could view such data as panel count data with informative observation times and unknown start time. Here, we propose semiparametric proportional rate models for the event process and the observation process, with a multiplicative subject-specific frailty variable capturing the correlation between the two processes. Inference procedures for the gap times between consecutive events are proposed when the start times are known as well when unknown, using likelihood-based approach and estimating equations. The methodology is assessed through simulation study and through large sample property. A detailed analysis using the proposed methods is applied to data from two studies: the Collaborative Perinatal Project and the Consortium on Safe Labor. Supplementary materials for this article are available online. |
A General Framework for Estimation and Inference From Clusters of Features
| Pengarang | : | Stephen Reid |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 280-293 |
| Abstrak | : | Applied statistical problems often come with prespecified groupings to predictors. It is natural to test for the presence of simultaneous group-wide signal for groups in isolation, or for multiple groups together. Current tests for the presence of such signals include the classical F-test or a t-test on unsupervised group prototypes (either group centroids or first principal components). In this article, we propose test statistics that aim for power improvements over these classical approaches. In particular, we first create group prototypes, with reference to the response, and then test with likelihood ratio statistics incorporating only these prototypes. We propose a model, called the “prototype model,” which naturally models this two-step procedure. Furthermore, we introduce an inferential schema detailing the unique considerations for different combinations of prototype formation and univariate/multivariate testing models. The prototype model also suggests new applications to estimation and prediction. Prototype formation often relies on variable selection, which invalidates classical Gaussian test theory. We use recent advances in selective inference to account for selection in the prototyping step and retain test validity. Simulation experiments suggest that our testing procedure enjoys more power than do classical approaches. Supplementary materials for this article are available online. |
Classified Mixed Model Prediction
| Pengarang | : | Jiming Jiang |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 269-279 |
| Abstrak | : | Many practical problems are related to prediction, where the main interest is at subject (e.g., personalized medicine) or (small) sub-population (e.g., small community) level. In such cases, it is possible to make substantial gains in prediction accuracy by identifying a class that a new subject belongs to. This way, the new subject is potentially associated with a random effect corresponding to the same class in the training data, so that method of mixed model prediction can be used to make the best prediction. We propose a new method, called classified mixed model prediction (CMMP), to achieve this goal. We develop CMMP for both prediction of mixed effects and prediction of future observations, and consider different scenarios where there may or may not be a “match” of the new subject among the training-data subjects. Theoretical and empirical studies are carried out to study the properties of CMMP, including prediction intervals based on CMMP, and its comparison with existing methods. In particular, we show that, even if the actual match does not exist between the class of the new observations and those of the training data, CMMP still helps in improving prediction accura |
ECA: High-Dimensional Elliptical Component Analysis in Non-Gaussian Distributions
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 252-268 |
| Abstrak | : | We present a robust alternative to principal component analysis (PCA)—called elliptical component analysis (ECA)—for analyzing high-dimensional, elliptically distributed data. ECA estimates the eigenspace of the covariance matrix of the elliptical data. To cope with heavy-tailed elliptical distributions, a multivariate rank statistic is exploited. At the model-level, we consider two settings: either that the leading eigenvectors of the covariance matrix are nonsparse or that they are sparse. Methodologically, we propose ECA procedures for both nonsparse and sparse settings. Theoretically, we provide both nonasymptotic and asymptotic analyses quantifying the theoretical performances of ECA. In the nonsparse setting, we show that ECA’s performance is highly related to the effective rank of the covariance matrix. In the sparse setting, the results are twofold: (i) we show that the sparse ECA estimator based on a combinatoric program attains the optimal rate of convergence; (ii) based on some recent developments in estimating sparse leading eigenvectors, we show that a computationally efficient sparse ECA estimator attains the optimal rate of convergence under a suboptimal scaling. Supplementary materials for this article are available online. |
Mathematical Persistence Among Four African American Male Graduate Students: A Critical Race Analysis of Their Experiences
| Pengarang | : | Christopher C. Jett |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 3) |
| Halaman | : | 311-340 |
| Abstrak | : | The stories of high-achieving African American mathematics students are gaining prominence in the research literature. In this multiple case study, I use a critical race theoretical frame to document and analyze the experiences of 4 mathematically persistent African American male students who earned undergraduate degrees in mathematics and subsequently enrolled in mathematics or mathematics education graduate programs. The findings reveal that these African American men drew from internal factors to influence their mathematical persistence and identified how racial microaggressions manifest themselves in postundergraduate contexts. Recommendations for practice, policy implications, and future research directions that emerged from this study are discussed to better understand African American men's mathematics experiences. |