Browsing by Subject "Statistical inference"

Now showing 1 - 6 of 6
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    Developing and validating an instrument to measure college students' inferential reasoning in statistics: an argument-based approach to validation
    (2012-06) Park, Jiyoon
    The purpose of this study was to develop and validate an assessment to measure college students' inferential reasoning in statistics. This proposed assessment aims to help statistics educators guide and monitor students' developing ideas of statistical inference. Within the two-stage cycle, the formative and summative stages, this study first built arguments for the use of assessment and score interpretations, and verified inferences made from those arguments. The five claims were used to examine the plausibility of the validity arguments: 1) The test measures students' level of statistical inferential reasoning in two aspects--informal statistical inference and formal statistical inference; 2) The test measures statistical inferential reasoning in the representative test domains; 3) The test produces scores with sufficient precision to be meaningfully reported; 4) The test is functional for the purposes of formative assessment; and 5) The test provides information about students' level of statistical inferential reasoning in the realms of informal and formal statistical inference. Using a mixed-methods study design, different types of validity evidence were gathered and investigated. Three content experts provided their evaluation of the test blueprint and assessment, based on their qualitative reviews. For the revised assessment resulting from the experts' feedback, cognitive interviews were conducted with nine college students using think-aloud protocols, whereby the students verbalized their reasoning as they reached an answer. A pilot-test administered in a classroom provided preliminary information of the psychometric properties of the assessment. The final version of the assessment was administered to 2,056 students in 39 higher education institutions across the United States. For the data obtained from this large-scale assessment, a unidimensional model in confirmatory factor analysis and the Graded Response Model in item response theory were employed to examine the arguments regarding the internal structure and item properties. The results suggest that the AIRS is unidimensional with appropriate levels of item difficulty and information. The pedagogical implications for the use of the AIRS test are discussed with regard to the areas where students showed difficulties in the domain of statistical inference.
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    Development of Real-Time Traffic Adaptive Crash Reduction Measures for the Westbound I-94/35W Commons Section
    (University of Minnesota Center for Transportation Studies, 2008-12) Hourdos, John; Xin, Wuping; Michalopoulos, Panos
    Much research has been conducted in the development, implementation, and evaluation of innovative ITS technologies aiming to improve traffic operations and driving safety. An earlier project succeeded in supporting the hypothesis that certain traffic conditions are favorable to crashes and in developing real-time algorithms for the estimation of crash probability from detector measurements. Following this accomplishment a natural question is “how can this help prevent crashes?” This project has the ambitious plan of not only answering this question but also providing a multifaceted approach that can offer different types of solutions to an agency aimed at reducing crashes in this and other similar locations. This project has two major objectives; first it aimed at utilizing a cutting edge 3D virtual reality system to design and visualize different driver warning systems specifically for the I-94 westbound high crash location in Minneapolis, MN. Second, in view of the desire of local engineers for a more traditional approach, this project explored the use of existing micro-simulation models in the evaluation of safety improvements for the aforementioned high crash area. This report describes the results of these investigations but more importantly describes the lessons learned in the process of the research. These lessons are important because they highlight gaps of technology and knowledge that hampered this and other research projects with similar objectives.
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    Enhancing Machine Learning Accuracy and Statistical Inference via Deep Generative Models
    (2024-08) Liu, Yifei
    Synthetic data refers to data generated by a mechanism designed to mimic the distribution of the raw data. In the era of generative artificial intelligence, the significance of synthetic data has dramatically increased. It offers numerous advantages in data science and machine learning tasks. For instance, synthetic data can be used to augment original datasets, helping to alleviate data scarcity and potentially enhancing the performance of predictive models. Synthetic data can also be tailored to meet standard privacy criteria, enabling data sharing and collaboration across different parties and platforms. For a systematic evaluation of synthetic data applied to downstream tasks, this thesis studies the "generation effect" --- how errors from generative models affect the accuracy/power of the downstream analysis. We provide practical and valid methods of utilizing synthetic data for both prediction and inference tasks, supported by both theoretical insights as well as numerical experiments.
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    Mediation analysis in longitudinal studies in the presence of measurement error and missing data
    (2018-05) Ssenkusu, John Mbaziira
    Mediation analysis hypothesizes that an exposure causes a mediator and in turn the mediator causes the outcome, so mediation is inherently longitudinal. Unfortunately, potential mediators may be measured with error and regression estimators obtained by ignoring measurement error can be severely biased. This can induce bias in the estimation of causal direct and indirect effects. In Chapter 2, using regression calibration, we show how to adjust for measurement error in longitudinal studies with repeated measurements of the mediator, and evaluate the effect of ignoring measurement error on direct and indirect effects. Rather than assuming normality for the random effects in the linear mixed effects calibration model, we correct for measurement error in the mediator allowing flexibility in the distribution of subject-specific random effects. On the other hand, longitudinal studies face challenges of missing data resulting from loss to follow-up, death, or withdrawal. In mediation analysis, multiple imputation has been shown to perform well for data missing completely at random (MCAR) and missing at random (MAR) in cross-sectional studies, but it is unclear how it performs in longitudinal studies under misspecification of the imputation model, specifically, where the misspecification ignores clustering by subject. In Chapter 3, we examine the impact of ignoring clustering on mediated effect estimates under MCAR and MAR mechanisms with varying degrees of missingness. In Chapter 4, using data from a randomized controlled trial, we examine the mediation effects on child neurodevelopment of intermittent preventive malaria treatment in pregnant women. Chapter 5 concludes and discusses future work.
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    Statistical Methods For High-Dimensional Genetic And Genomic Data
    (2018-06) Wu, Chong
    Modern genetics research constantly creates new types of high-dimensional genetic and genomic data and imposes new challenges in analyzing these data. This thesis deals with several important problems in analyzing high-dimensional genetic and genomic data, ranging from DNA methylation data to human microbiome data. First, we introduce a site selection and multiple imputation method to impute missing data in covariates in epigenome-wide analysis of DNA methylation data, which can help us adjust potential confounders, such as cell type composition. Second, to overcome low power issue of human microbiome association studies, we propose a powerful data-driven approach by weighting the variables (taxa) in a manner determined by the data itself. The increased power of the new test not only decreases the sample size required for a human microbiome association study but also allows for new discoveries with existing datasets. Third, we propose an adaptive test on a high-dimensional parameter of a generalized linear model (in the presence of a low-dimensional nuisance parameter). Benefiting from its adaptivity, the proposed test maintains high statistical power under various high-dimensional scenarios. We further establish its asymptotic null distribution. Finally, we propose a novel pathway-based association test by integrating gene expression, gene functional annotations, and a main genome-wide association study dataset. We applied it to a schizophrenia GWAS summary association dataset and identified 15 novel pathways associated with schizophrenia, such as GABA receptor complex (GO:1902710), which could not be uncovered by the standard single SNP-based analysis or gene-based TWAS.
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    Weigh-in-Motion Sensor and Controller Operation and Performance Comparison
    (Minnesota Department of Transportation, 2018-01) Gupta, Diwakar; Tang, Xiaoxu; Yuan, Lu
    This research project utilized statistical inference and comparison techniques to compare the performance of different Weigh-in-Motion (WIM) sensors. First, we analyzed test-vehicle data to perform an accuracy check of the results reported by the sensor-vendor Intercomp. The results reported by Intercomp mostly matched with our own analysis, but the data were found to be insufficient to reach any conclusions about the accuracy of the sensor under different temperature and speed conditions. Second, based on the limited data from the Intercomp and IRD sensor systems, we performed tests of self-consistency and comparisons of measurements to inform the selection of a superior system. Intercomp sensor data were found to be not self-consistent but IRD data were. Given the different measurements provided by the two sensors, without additional data, we were not able to reach a conclusion regarding the relative accuracy or the duration of consistent observations before needing recalibration. Initial comparisons indicated potential problems with the Intercomp sensor. We then suggested alternate approaches that MNDOT could use to determine whether recalibration was required. Finally, we analyzed ten-month data from the IRD WIM system and four-month data from the Kistler WIM system to evaluate relative sensor accuracy. While both systems were found to be self-consistent within the data time frame, the Kistler system generated more errors than the IRD system. Conclusions regarding relative accuracy could not be reached without additional data. We identified the sorts of measurements that would need to be monitored for recalibration and the methodology needed for estimating future recalibration time.