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Yes, Another Handbook and Why You Might Want to Read This One
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| Pengarang | : | Cynthia W. Langrall |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 2) |
| Halaman | : | 210-213 |
| Abstrak | : | In today's world, data and statistical information permeate our lives, making it imperative that we educate students to be statistically literate. Statistical literacy is the ability to read and interpret statistical information to make informed decisions about events under conditions of uncertainty. Recently, the National Council of Teachers of Mathematics (NCTM) published a document, Catalyzing Change in High School Mathematics: Initiating Critical Conversations (2018), in which it proposed statistics as one of four essential content domains in secondary school mathematics and acknowledged quantitative literacy—the ability to reason both statistically and numerically—as a crucial life skill for all students. For a number of years, statistics has been an important content strand across grade levels in the school mathematics curricula of many countries. Thus, it is understandable that students and even teachers might perceive statistics simply as another topic in mathematics. |
Pair Copula Constructions for Insurance Experience Rating
| Pengarang | : | Peng Shi |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 122-133 |
| Abstrak | : | In nonlife insurance, insurers use experience rating to adjust premiums to reflect policyholders’ previous claim experience. Performing prospective experience rating can be challenging when the claim distribution is complex. For instance, insurance claims are semicontinuous in that a fraction of zeros is often associated with an otherwise positive continuous outcome from a right-skewed and long-tailed distribution. Practitioners use credibility premium that is a special form of the shrinkage estimator in the longitudinal data framework. However, the linear predictor is not informative especially when the outcome follows a mixed distribution. In this article, we introduce a mixed vine pair copula construction framework for modeling semicontinuous longitudinal claims. In the proposed framework, a two-component mixture regression is employed to accommodate the zero inflation and thick tails in the claim distribution. The temporal dependence among repeated observations is modeled using a sequence of bivariate conditional copulas based on a mixed D-vine. We emphasize that the resulting predictive distribution allows insurers to incorporate past experience into future premiums in a nonlinear fashion and the classic linear predictor can be viewed as a nested case. In the application, we examine a unique claims dataset of government property insurance from the state of Wisconsin. Due to the discrepancies between the claim and premium distributions, we employ an ordered Lorenz curve to evaluate the predictive performance. We show that the proposed approach offers substantial opportunities for separating risks and identifying profitable business when compared with alternative experience rating methods. Supplementary materials for this article are available online. |
Surveying Middle Grades Teachers Reasoning About Fraction Arithmetic in Terms of Measured Quantities
| Pengarang | : | Andrew Izsak, Erik Jacobson, and Laine Bradshaw |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 2) |
| Halaman | : | 156-209 |
| Abstrak | : | We report a novel survey that narrows the gap between information about teachers' knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with measured quantities, not by executing computational algorithms, to solve problems. These components—each of which was grounded in past research—were attention to referent units, partitioning and iterating, appropriateness, and reversibility. A second part of the survey asked about teachers' professional preparation and history. We administered the survey to a national sample of in-service middle-grades mathematics teachers in the United States and received responses from 990 of those teachers. We analyzed responses to items in the first part of the survey using the log-linear diagnostic classification model to estimate each teacher's profile of strengths and weaknesses with respect to the four components of reasoning. We report on the diversity of profiles that we found and on relationships between those profiles and various aspects of teachers' professional preparation and history. Our results provide insight into teachers' knowledge resources for enacting standards-based instruction in fraction arithmetic and an example of new possibilities for mathematics education research afforded by recent advances in psychometric modeling. |
Modeling Heterogeneity in Healthcare Utilization Using Massive Medical Claims Data
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 111-121 |
| Abstrak | : | We introduce a modeling approach for characterizing heterogeneity in healthcare utilization using massive medical claims data. We first translate the medical claims observed for a large study population and across five years into individual-level discrete events of care called utilization sequences. We model the utilization sequences using an exponential proportional hazards mixture model to capture heterogeneous behaviors in patients’ healthcare utilization. The objective is to cluster patients according to their longitudinal utilization behaviors and to determine the main drivers of variation in healthcare utilization while controlling for the demographic, geographic, and health characteristics of the patients. Due to the computational infeasibility of fitting a parametric proportional hazards model for high-dimensional, large-sample size data we use an iterative one-step procedure to estimate the model parameters and impute the cluster membership. The approach is used to draw inferences on utilization behaviors of children in the Medicaid system with persistent asthma across six states. We conclude with policy implications for targeted interventions to improve adherence to recommended care practices for pediatric asthma. Supplementary materials for this article are available online. |
Variable Selection for Skewed Model-Based Clustering: Application to the Identification of Novel Sleep Phenotypes
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 95-110 |
| Abstrak | : | In sleep research, applying finite mixture models to sleep characteristics captured through multiple data types, including self-reported sleep diary, a wrist monitor capturing movement (actigraphy), and brain waves (polysomnography), may suggest new phenotypes that reflect underlying disease mechanisms. However, a direct mixture model application is challenging because there are many sleep variables from which to choose, and sleep variables are often highly skewed even in homogenous samples. Moreover, previous sleep research findings indicate that some of the most clinically interesting solutions will be those that incorporate all three data types. Thus, we present two novel skewed variable selection algorithms based on the multivariate skew normal (MSN) distribution: one that selects the best set of variables ignoring data type and another that embraces the exploratory nature of clustering and suggests multiple statistically plausible sets of variables that each incorporate all data types. Through a simulation study, we empirically compare our approach with other asymmetric and normal dimension reduction strategies for clustering. Finally, we demonstrate our methods using a sample of older adults with and without insomnia. The proposed MSN-based variable selection algorithm appears to be suitable for both MSN and multivariate normal cluster distributions, especially with moderate to large-sample sizes. Supplementary materials for this article are available online. |
BNP-Seq: Bayesian Nonparametric Differential Expression Analysis of Sequencing Count Data
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 81-94 |
| Abstrak | : | We perform differential expression analysis of high-throughput sequencing count data under a Bayesian nonparametric framework, removing sophisticated ad hoc pre-processing steps commonly required in existing algorithms. We propose to use the gamma (beta) negative binomial process, which takes into account different sequencing depths using sample-specific negative binomial probability (dispersion) parameters, to detect differentially expressed genes by comparing the posterior distributions of gene-specific negative binomial dispersion (probability) parameters. These model parameters are inferred by borrowing statistical strength across both the genes and samples. Extensive experiments on both simulated and real-world RNA sequencing count data show that the proposed differential expression analysis algorithms clearly outperform previously proposed ones in terms of the areas under both the receiver operating characteristic and precision-recall curves. Supplementary materials for this article are available online. |
Modeling for Dynamic Ordinal Regression Relationships: An Application to Estimating Maturity of Rockfish in California
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 68-80 |
| Abstrak | : | We develop a Bayesian nonparametric framework for modeling ordinal regression relationships, which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age, length, and maturity, the latter recorded on an ordinal scale. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models that arise from estimation of cut-off points relating the latent continuous and ordinal responses. A novel-dependent Dirichlet process prior for time-dependent mixing distributions extends the model to the dynamic setting. The methodology is used for a detailed study of relationships between maturity, age, and length for Chilipepper rockfish, using data collected over 15 years along the coast of California. Supplementary materials for this article are available online. |
Compression and Conditional Emulation of Climate Model Output
| Pengarang | : | Joseph Guinness |
| Nama Majalah/Jurnal | : | Journal of the American Statistical Association |
| Volume / Edisi | : | 113 (No. 521) |
| Halaman | : | 56-67 |
| Abstrak | : | Numerical climate model simulations run at high spatial and temporal resolutions generate massive quantities of data. As our computing capabilities continue to increase, storing all of the data is not sustainable, and thus it is important to develop methods for representing the full datasets by smaller compressed versions. We propose a statistical compression and decompression algorithm based on storing a set of summary statistics as well as a statistical model describing the conditional distribution of the full dataset given the summary statistics. We decompress the data by computing conditional expectations and conditional simulations from the model given the summary statistics. Conditional expectations represent our best estimate of the original data but are subject to oversmoothing in space and time. Conditional simulations introduce realistic small-scale noise so that the decompressed fields are neither too smooth nor too rough compared with the original data. Considerable attention is paid to accurately modeling the original dataset—1 year of daily mean temperature data—particularly with regard to the inherent spatial nonstationarity in global fields, and to determining the statistics to be stored, so that the variation in the original data can be closely captured, while allowing for fast decompression and conditional emulation on modest computers. Supplementary materials for this article are available online. |
Linguistic Conventions of Mathematical Proof Writing at the Undergraduate Level: Mathematicians' and Students Perspectives
| Pengarang | : | Kristen Lew and Juan Pablo Mejía-Ramos |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 2) |
| Halaman | : | 121-155 |
| Abstrak | : | This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First, mathematicians believed that mathematical language should obey the conventions of academic language, whereas students were either unaware of these conventions or unaware that these conventions applied to proof writing. Second, students did not fully understand the nuances involved in how mathematicians introduce objects in proofs. Third, mathematicians focused on the context of the proof to decide how formal a proof should be, whereas students did not seem to be aware of the importance of this factor. |
Characteristics of Precalculus Through Calculus 2 Programs: Insights From a National Census Survey
| Pengarang | : | Chris Rasmussen, Naneh Apkarian, Jessica Ellis Hagman, Estrella Johnson, Sean Larsen, David Bressoud |
| Nama Majalah/Jurnal | : | Journal for Research in Mathematics Education |
| Volume / Edisi | : | 50 (No. 1) |
| Halaman | : | 98-111 |
| Abstrak | : | We present findings from a recently completed census survey of all mathematics departments in the United States that offer a graduate degree in mathematics. The census survey is part of a larger project investigating institutional features that influence student success in the introductory mathematics courses that are required of most STEM majors in the United States. We report the viewpoints of departments about characteristics shown to support students' success as well as the extent to which these characteristics are being implemented in programs across the country. We conclude with a discussion of areas where we see the potential for growth and further improvement. |