scholarly journals Learning Attribute Hierarchies From Data: Two Exploratory Approaches

2020 ◽  
pp. 107699862093109
Author(s):  
Chun Wang ◽  
Jing Lu
Keyword(s):  
Latent Variable ◽  
Latent Class ◽  
Hypothesis Test ◽  
Structural Features ◽  
Classification Model ◽  
Ratio Test ◽  
Test Statistic ◽  
Reference Distribution ◽  
Fine Grained ◽  
Log Linear

In cognitive diagnostic assessment, multiple fine-grained attributes are measured simultaneously. Attribute hierarchies are considered important structural features of cognitive diagnostic models (CDMs) that provide useful information about the nature of attributes. Templin and Bradshaw first introduced a hierarchical diagnostic classification model (HDCM) that directly takes into account attribute hierarchies, and hence, HDCM is nested within more general CDMs. They also formulated an empirically driven hypothesis test to statistically test one hypothesized link (between two attributes) at a time. However, their likelihood ratio test statistic does not have a known reference distribution, so it is cumbersome to perform hypothesis testing at scale. In this article, we studied two exploratory approaches that could learn the attribute hierarchies directly from data, namely, the latent variable selection (LVS) approach and the regularized latent class modeling (RLCM) approach. An identification constraint was proposed for the LVS approach. Simulation results revealed that both approaches could successfully identify different types of attribute hierarchies, when the underlying CDM is either the deterministic input noisy and gate model or the saturated log-linear CDM. The LVS approach outperformed the RLCM approach, especially when the total number of attributes increases.

scholarly journals Improved Differentially Private Analysis of Variance

2019 ◽  
Vol 2019 (3) ◽  
pp. 310-330 ◽  
Author(s):  
Marika Swanberg ◽  
Ira Globus-Harris ◽  
Iris Griffith ◽  
Anna Ritz ◽  
Adam Groce ◽  
...  
Keyword(s):  
Analysis Of Variance ◽  
Statistical Power ◽  
Differential Privacy ◽  
Hypothesis Test ◽  
Test Statistic ◽  
Reference Distribution ◽  
Optimal Test ◽  
The Public ◽  
Order Of Magnitude ◽  
Public Setting

Abstract Hypothesis testing is one of the most common types of data analysis and forms the backbone of scientific research in many disciplines. Analysis of variance (ANOVA) in particular is used to detect dependence between a categorical and a numerical variable. Here we show how one can carry out this hypothesis test under the restrictions of differential privacy. We show that the F -statistic, the optimal test statistic in the public setting, is no longer optimal in the private setting, and we develop a new test statistic F1 with much higher statistical power. We show how to rigorously compute a reference distribution for the F1 statistic and give an algorithm that outputs accurate p-values. We implement our test and experimentally optimize several parameters. We then compare our test to the only previous work on private ANOVA testing, using the same effect size as that work. We see an order of magnitude improvement, with our test requiring only 7% as much data to detect the effect.

Examining the L2 reading comprehension ability of adult ELLs: Developing a diagnostic test within the cognitive diagnostic assessment framework

2020 ◽  
pp. 026553222094147
Author(s):  
Tugba Elif Toprak ◽  
Abdulvahit Cakir
Keyword(s):  
Reading Comprehension ◽  
Cognitive Model ◽  
Diagnostic Assessment ◽  
Classification Model ◽  
L2 Reading ◽  
Fine Grained ◽  
Cognitive Diagnostic Assessment ◽  
Comprehension Ability ◽  
Log Linear ◽  
L2 Reading Comprehension

Cognitive diagnostic assessment (CDA) has been applied to language assessment in a number of studies in which a diagnostic classification model (DCM) was retrofitted to the results of a non-diagnostic assessment. However, the need to apply CDA through utilization of an inductive rather than a retrofitted approach has been a recurrent theme in these studies. Thus, this study aimed to develop a diagnostic L2 reading comprehension test in English to investigate adult examinees’ reading performances in an EFL (English as a Foreign Language) academic setting. The test was based on a cognitive model of L2 reading comprehension and was administered to a sample of 1058 examinees across Turkey. The results were analyzed using log-linear cognitive diagnosis modeling (LCDM), which is one of the general DCM families subsuming other core DCMs. The findings of the study indicated that obtaining fine-grained diagnostic information about examinees’ performances in a given domain would be possible by coupling an adequate understanding of the construct with a CDA framework.

scholarly journals Field Significance of Regression Patterns

2011 ◽  
Vol 24 (19) ◽  
pp. 5094-5107 ◽  
Author(s):  
Timothy DelSole ◽  
Xiaosong Yang
Keyword(s):  
Confidence Interval ◽  
Hypothesis Test ◽  
Significance Test ◽  
Spatial Filter ◽  
Climate Index ◽  
Boreal Winter ◽  
Ratio Test ◽  
Test Statistic ◽  
Canonical Correlations ◽  
The Cross

Regression patterns often are used to diagnose the relation between a field and a climate index, but a significance test for the pattern “as a whole” that accounts for the multiplicity and interdependence of the tests has not been widely available. This paper argues that field significance can be framed as a test of the hypothesis that all regression coefficients vanish in a suitable multivariate regression model. A test for this hypothesis can be derived from the generalized likelihood ratio test. The resulting statistic depends on relevant covariance matrices and accounts for the multiplicity and interdependence of the tests. It also depends only on the canonical correlations between the predictors and predictands, thereby revealing a fundamental connection to canonical correlation analysis. Remarkably, the test statistic is invariant to a reversal of the predictors and predictands, allowing the field significance test to be reduced to a standard univariate hypothesis test. In practice, the test cannot be applied when the number of coefficients exceeds the sample size, reflecting the fact that testing more hypotheses than data is ill conceived. To formulate a proper significance test, the data are represented by a small number of principal components, with the number chosen based on cross-validation experiments. However, instead of selecting the model that minimizes the cross-validated mean square error, a confidence interval for the cross-validated error is estimated and the most parsimonious model whose error is within the confidence interval of the minimum error is chosen. This procedure avoids selecting complex models whose error is close to much simpler models. The procedure is applied to diagnose long-term trends in annual average sea surface temperature and boreal winter 300-hPa zonal wind. In both cases a statistically significant 50-yr trend pattern is extracted. The resulting spatial filter can be used to monitor the evolution of the regression pattern without temporal filtering.

scholarly journals A Hypothesis Test for the Goodness-of-Fit of the Marginal Distribution of a Time Series with Application to Stablecoin Data

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Mark Levene
Keyword(s):  
Time Series ◽  
Goodness Of Fit ◽  
Marginal Distribution ◽  
Hypothesis Test ◽  
Data Sets ◽  
Test Statistic ◽  
Sample Test ◽  
Kolmogorov Smirnov ◽  
Heavy Tailed ◽  
Jensen Shannon Divergence

A bootstrap-based hypothesis test of the goodness-of-fit for the marginal distribution of a time series is presented. Two metrics, the empirical survival Jensen–Shannon divergence (ESJS) and the Kolmogorov–Smirnov two-sample test statistic (KS2), are compared on four data sets—three stablecoin time series and a Bitcoin time series. We demonstrate that, after applying first-order differencing, all the data sets fit heavy-tailed α-stable distributions with 1<α<2 at the 95% confidence level. Moreover, ESJS is more powerful than KS2 on these data sets, since the widths of the derived confidence intervals for KS2 are, proportionately, much larger than those of ESJS.

scholarly journals AutoSense Model for Word Sense Induction

2019 ◽  
Vol 33 ◽  
pp. 6212-6219 ◽  
Author(s):  
Reinald Kim Amplayo ◽  
Seung-won Hwang ◽  
Min Song
Keyword(s):  
Latent Variable ◽  
Word Sense ◽  
Name Disambiguation ◽  
Variable Model ◽  
Fine Grained ◽  
Word Sense Induction ◽  
Author Name Disambiguation ◽  
Competing Models ◽  
Word Senses ◽  
Better Than

Word sense induction (WSI), or the task of automatically discovering multiple senses or meanings of a word, has three main challenges: domain adaptability, novel sense detection, and sense granularity flexibility. While current latent variable models are known to solve the first two challenges, they are not flexible to different word sense granularities, which differ very much among words, from aardvark with one sense, to play with over 50 senses. Current models either require hyperparameter tuning or nonparametric induction of the number of senses, which we find both to be ineffective. Thus, we aim to eliminate these requirements and solve the sense granularity problem by proposing AutoSense, a latent variable model based on two observations: (1) senses are represented as a distribution over topics, and (2) senses generate pairings between the target word and its neighboring word. These observations alleviate the problem by (a) throwing garbage senses and (b) additionally inducing fine-grained word senses. Results show great improvements over the stateof-the-art models on popular WSI datasets. We also show that AutoSense is able to learn the appropriate sense granularity of a word. Finally, we apply AutoSense to the unsupervised author name disambiguation task where the sense granularity problem is more evident and show that AutoSense is evidently better than competing models. We share our data and code here: https://github.com/rktamplayo/AutoSense.

scholarly journals Co-occurrence subgroups of child sexual abuse, health risk behaviors and their associations among secondary school students in China

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Yan Zhang ◽  
Xiayun Zuo ◽  
Yanyan Mao ◽  
Qiguo Lian ◽  
Shan Luo ◽  
...  
Keyword(s):  
Sexual Abuse ◽  
Child Sexual Abuse ◽  
Secondary School ◽  
Health Risk ◽  
Risk Behaviors ◽  
Latent Variable ◽  
Secondary School Students ◽  
Latent Class ◽  
Computer Assisted ◽  
School Students

Abstract Background Little is known on the co-occurrence and heterogeneity of child sexual abuse (CSA) or health risk behavior (HRB) prevalence nor the associations among the victims. Objectives To detect the prevalence and subgroups of adolescents reporting CSAs or HRBs, and to examine the association between the subgroups. Methods Participants were secondary school students in a national survey in China (N = 8746). Self-reported CSA and HRB experiences were collected through a computer assisted questionnaire. Prevalence and confidence intervals were calculated. Multigroup latent class analysis (LCA) was used to examine latent subgroups of CSA and HRB. Dual latent class regression analysis was used to examine the association between CSA and HRB classes. Results A total of 8746 students participated in our study. The prevalence of having ever experienced any of the reported seven CSA items was 12.9%. The preferred LCA model consisted of a three-class CSA latent variable, i.e. “Low CSAs”(95.7% of the total respondents), “Verbal or exhibitionism CSAs”(3.3%), and “high multiple CSAs” (1.1%); and a three-class HRB latent variable, i.e. “Low HRBs”(70.5%), “externalizing HRBs” (20.7%), and “internalizing HRBs” (8.7%). Students in the “Verbal or exhibitionism CSAs” or “high multiple CSAs” classes had higher probabilities of being in “externalizing HRBs” or “internalizing HRBs” classes. The probabilities were higher in “high multiple CSAs” class(male externalizing OR 4.05, 95%CI 1.71–9.57; internalizing OR 11.77, 95%CI 4.76–29.13; female externalizing OR 4.97, 95%CI 1.99–12.44; internalizing OR 9.87, 95%CI 3.71–26.25) than those in “Verbal or exhibitionism CSA”(male externalizing OR 2.51, 95%CI 1.50–4.20; internalizing OR 3.08, 95%CI 1.48–6.40; female externalizing OR 2.53, 95%CI 1.63–3.95; internalizing OR 6.05, 95%CI 3.73–9.80). Conclusions Prevalence of CSA items varies. Non-contact CSAs are the most common forms of child sexual abuse among Chinese school students. There are different latent class co-occurrence patterns of CSA items or HRB items among the respondents. CSA experiences are in association with HRB experiences and the associations between latent classes are dose-responded. Multi-victimization has more significantly negative effects. The results could help identify high-risk subgroups and promote more nuanced interventions addressing adverse experiences and risk behaviors among at-risk adolescents.

scholarly journals Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 936
Author(s):  
Dan Wang
Keyword(s):  
Kernel Method ◽  
Alternative Hypothesis ◽  
Null Distribution ◽  
Real Data ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Approximation ◽  
Heavy Tailed ◽  
Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

Cause-specific quantile residual life regression

2015 ◽  
Vol 26 (4) ◽  
pp. 1912-1924 ◽  
Author(s):  
Jeong Youn Lim ◽  
Jong-Hyeon Jeong
Keyword(s):  
Residual Life ◽  
Fixed Time ◽  
Estimating Equation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Test Statistic ◽  
Life Distribution ◽  
Finite Sample Properties ◽  
Quantile Residual Life ◽  
Log Linear

We propose a cause-specific quantile residual life regression where the cause-specific quantile residual life, defined as the inverse of the cumulative incidence function of the residual life distribution of a specific type of events of interest conditional on a fixed time point, is log-linear in observable covariates. The proposed test statistic for the effects of prognostic factors does not involve estimation of the improper probability density function of the cause-specific residual life distribution under competing risks. The asymptotic distribution of the test statistic is derived. Simulation studies are performed to assess the finite sample properties of the proposed estimating equation and the test statistic. The proposed method is illustrated with a real dataset from a clinical trial on breast cancer.

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