A robust likelihood approach to inference about the kappa coefficient for correlated binary data

2018 ◽  
Vol 28 (4) ◽  
pp. 1188-1202 ◽  
Author(s):  
Tsung-Shan Tsou
Keyword(s):  
Data Analysis ◽  
Binary Data ◽  
Likelihood Function ◽  
Score Test ◽  
Real Data ◽  
Kappa Coefficient ◽  
Correlated Data ◽  
Ratio Test ◽  
Likelihood Approach ◽  
Robust Likelihood

We construct a legitimate likelihood function for the agreement kappa coefficient for correlated data without specifically modelling all levels of correlation. This makes available the likelihood ratio test, the score test and other tools without the knowledge of the underlying distributions. This parametric robust likelihood approach applies to general clustered data scenarios. We provide simulations and real data analysis to demonstrate the advantage of the robust procedure.

A reproducible robust likelihood approach to inference about marginal characteristics of binary data in paired settings

2019 ◽  
Vol 29 (1) ◽  
pp. 282-292
Author(s):  
Tsung-Shan Tsou
Keyword(s):  
Data Analysis ◽  
Binary Data ◽  
Real Data ◽  
Paired Data ◽  
Real Data Analysis ◽  
Marginal Homogeneity ◽  
New Strategy ◽  
Likelihood Approach ◽  
Robust Likelihood ◽  
Joint Probabilities

We introduce a robust likelihood approach to inference about marginal distributional characteristics for paired data without modeling correlation/joint probabilities. This method is reproducible in that it is applicable to paired settings with various sizes. The virtue of the new strategy is elucidated via testing marginal homogeneity in paired triplet scenario. We use simulations and real data analysis to demonstrate the merit of our robust likelihood methodology.

Common risk difference test and interval estimation of risk difference for stratified bilateral correlated data

2018 ◽  
Vol 28 (8) ◽  
pp. 2418-2438
Author(s):  
Xi Shen ◽  
Chang-Xing Ma ◽  
Kam C Yuen ◽  
Guo-Liang Tian
Keyword(s):  
Data Analysis ◽  
Confidence Interval ◽  
Score Test ◽  
Real Data ◽  
Risk Difference ◽  
Error Rates ◽  
Correlated Data ◽  
Test Statistic ◽  
Data Set ◽  
Intra Class Correlation

Bilateral correlated data are often encountered in medical researches such as ophthalmologic (or otolaryngologic) studies, in which each unit contributes information from paired organs to the data analysis, and the measurements from such paired organs are generally highly correlated. Various statistical methods have been developed to tackle intra-class correlation on bilateral correlated data analysis. In practice, it is very important to adjust the effect of confounder on statistical inferences, since either ignoring the intra-class correlation or confounding effect may lead to biased results. In this article, we propose three approaches for testing common risk difference for stratified bilateral correlated data under the assumption of equal correlation. Five confidence intervals of common difference of two proportions are derived. The performance of the proposed test methods and confidence interval estimations is evaluated by Monte Carlo simulations. The simulation results show that the score test statistic outperforms other statistics in the sense that the former has robust type [Formula: see text] error rates with high powers. The score confidence interval induced from the score test statistic performs satisfactorily in terms of coverage probabilities with reasonable interval widths. A real data set from an otolaryngologic study is used to illustrate the proposed methodologies.

A robust likelihood approach to inference about the difference between two multinomial distributions in paired designs

2017 ◽  
Vol 27 (10) ◽  
pp. 3077-3091 ◽  
Author(s):  
Tsung-Shan Tsou
Keyword(s):  
Binary Data ◽  
Pair Correlation ◽  
Real Data ◽  
Model Specification ◽  
Score Statistic ◽  
Parallel Design ◽  
Probability Structure ◽  
Likelihood Approach ◽  
The Difference ◽  
Robust Likelihood

Pairing serves as a way of lessening heterogeneity but pays the price of introducing more parameters to the model. This complicates the probability structure and makes inference more intricate. We employ the simpler structure of the parallel design to develop a robust score statistic for testing the equality of two multinomial distributions in paired designs. This test incorporates the within-pair correlation in a data-driven manner without a full model specification. In the paired binary data scenario, the robust score statistic turns out to be the McNemar’s test. We provide simulations and real data analysis to demonstrate the advantage of the robust procedure.

scholarly journals Multivariate Hypothesis Testing Methods for Evaluating Significant Individual Change

2017 ◽  
Vol 42 (3) ◽  
pp. 221-239 ◽  
Author(s):  
Chun Wang ◽  
David J. Weiss
Keyword(s):  
Hypothesis Testing ◽  
Research Question ◽  
Latent Trait ◽  
Score Test ◽  
Real Data ◽  
Ratio Test ◽  
Type I ◽  
Individual Change ◽  
Testing Methods ◽  
Measuring Change

The measurement of individual change has been an important topic in both education and psychology. For instance, teachers are interested in whether students have significantly improved (e.g., learned) from instruction, and counselors are interested in whether particular behaviors have been significantly changed after certain interventions. Although classical test methods have been unable to adequately resolve the problems in measuring change, recent approaches for measuring change have begun to use item response theory (IRT). However, all prior methods mainly focus on testing whether growth is significant at the group level. The present research targets a key research question: Is the “change” in latent trait estimates for each individual significant across occasions? Many researchers have addressed this research question assuming that the latent trait is unidimensional. This research generalizes their earlier work and proposes four hypothesis testing methods to evaluate individual change on multiple latent traits: a multivariate Z-test, a multivariate likelihood ratio test, a multivariate score test, and a Kullback–Leibler test. Simulation results show that these tests hold promise of detecting individual change with low Type I error and high power. A real-data example from an educational assessment illustrates the application of the proposed methods.

A new likelihood approach to inference about predictive values of diagnostic tests in paired designs

2016 ◽  
Vol 27 (2) ◽  
pp. 541-548 ◽  
Author(s):  
Tsung-Shan Tsou
Keyword(s):  
Diagnostic Tests ◽  
Screening Test ◽  
Score Test ◽  
Real Data ◽  
Test Results ◽  
Multinomial Model ◽  
Test Statistic ◽  
Predictive Values ◽  
Minimum Number ◽  
Likelihood Approach

Intuitively, one only needs patients with two positive screening test results for positive predictive values comparison, and those with two negative screening test results for contrasting negative predictive values. Nevertheless, current existing methods rely on the multinomial model that includes superfluous parameters unnecessary for specific comparisons. This practice results in complex statistics formulas. We introduce a novel likelihood approach that fits the intuition by including a minimum number of parameters of interest in paired designs. It is demonstrated that our robust score test statistic is identical to a newly proposed weighted generalized score test statistic. Simulations and real data analysis are used for illustration.

Maximum Likelihood for Genome Phylogeny on Gene Content

2004 ◽  
Vol 3 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Hongmei Zhang ◽  
Xun Gu
Keyword(s):  
Maximum Likelihood ◽  
Phylogenetic Trees ◽  
Likelihood Function ◽  
Probability Model ◽  
Real Data ◽  
Mathematical Structure ◽  
Gene Content ◽  
Entire Genome ◽  
Maximum Likelihood Approach ◽  
Likelihood Approach

With the rapid growth of entire genome data, reconstructing the phylogenetic relationship among different genomes has become a hot topic in comparative genomics. Maximum likelihood approach is one of the various approaches, and has been very successful. However, there is no reported study for any applications in the genome tree-making mainly due to the lack of an analytical form of a probability model and/or the complicated calculation burden. In this paper we studied the mathematical structure of the stochastic model of genome evolution, and then developed a simplified likelihood function for observing a specific phylogenetic pattern under four genome situation using gene content information. We use the maximum likelihood approach to identify phylogenetic trees. Simulation results indicate that the proposed method works well and can identify trees with a high correction rate. Real data application provides satisfied results. The approach developed in this paper can serve as the basis for reconstructing phylogenies of more than four genomes.

scholarly journals A Mathematical Tool for Inference in Logistic Regression with Small-Sized Data Sets: A Practical Application on ISW-Ridge Relationships

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Tsung-Hao Chen ◽  
Chen-Yuan Chen ◽  
Hsien-Chueh Peter Yang ◽  
Cheng-Wu Chen
Keyword(s):  
Logistic Regression ◽  
Binary Data ◽  
Score Test ◽  
Wald Test ◽  
Data Sets ◽  
Ratio Test ◽  
Mathematical Tool ◽  
Lack Of Fit ◽  
Large Sample Approximation ◽  
Sample Approximation

The general approach to modeling binary data for the purpose of estimating the propagation of an internal solitary wave (ISW) is based on the maximum likelihood estimate (MLE) method. In cases where the number of observations in the data is small, any inferences made based on the asymptotic distribution of changes in the deviance may be unreliable for binary data (the model's lack of fit is described in terms of a quantity known as the deviance). The deviance for the binary data is given by D. Collett (2003). may be unreliable for binary data. Logistic regression shows that theP-values for the likelihood ratio test and the score test are both<0.05. However, the null hypothesis is not rejected in the Wald test. The seeming discrepancies inP-values obtained between the Wald test and the other two tests are a sign that the large-sample approximation is not stable. We find that the parameters and the odds ratio estimates obtained via conditional exact logistic regression are different from those obtained via unconditional asymptotic logistic regression. Using exact results is a good idea when the sample size is small and the approximateP-values are<0.10. Thus in this study exact analysis is more appropriate.

scholarly journals A Likelihood Approach to Populations Samples of Microsatellite Alleles

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 711-716 ◽  
Author(s):  
Rasmus Nielsen
Keyword(s):  
Likelihood Function ◽  
Ratio Test ◽  
Recursion Method ◽  
Test Models ◽  
Step Model ◽  
Microsatellite Evolution ◽  
One Step ◽  
Likelihood Approach ◽  
The Mean ◽  
Microsatellite Alleles

This paper presents a likelihood approach to population samples of microsatellite alleles. A Markov chain recursion method previously published by Griffiths and Tavaré applied to estimate the likelihood function under different models of microsatellite evolution. The method presented can be applied to estimate a fundamental population genetics parameter θ as well as parameters of the mutational model. The new likelihood estimator provides a better estimator of θ in terms of the mean square error than previous approaches. Furthermore, it is demonstrated how the method may easily be applied to test models of microsatellite evolution. In particular it is shown how to compare a one-step model of microsatellite evolution to a multi-step model by a likelihood ratio test.

Justifying the data analytical choice in single case research in relation to the expected data pattern

2019 ◽  
Author(s):  
Rumen Manolov
Keyword(s):  
Data Analysis ◽  
Visual Analysis ◽  
Multilevel Models ◽  
Single Case ◽  
Analytical Techniques ◽  
Real Data ◽  
Small Scale ◽  
Data User ◽  
Single Case Research ◽  
User Friendly

The lack of consensus regarding the most appropriate analytical techniques for single-case experimental designs data requires justifying the choice of any specific analytical option. The current text mentions some of the arguments, provided by methodologists and statisticians, in favor of several analytical techniques. Additionally, a small-scale literature review is performed in order to explore if and how applied researchers justify the analytical choices that they make. The review suggests that certain practices are not sufficiently explained. In order to improve the reporting regarding the data analytical decisions, it is proposed to choose and justify the data analytical approach prior to gathering the data. As a possible justification for data analysis plan, we propose using as a basis the expected the data pattern (specifically, the expectation about an improving baseline trend and about the immediate or progressive nature of the intervention effect). Although there are multiple alternatives for single-case data analysis, the current text focuses on visual analysis and multilevel models and illustrates an application of these analytical options with real data. User-friendly software is also developed.

Accuracy and sensitivity of different Bayesian methods for genomic prediction using simulation and real data

2020 ◽  
Vol 19 (3) ◽  
Author(s):  
Saheb Foroutaifar
Keyword(s):  
Data Analysis ◽  
Bayesian Methods ◽  
Milk Fat ◽  
Prediction Accuracy ◽  
Real Data ◽  
Fat Percentage ◽  
Real Data Analysis ◽  
Wide Range ◽  
High Heritability ◽  
Qtl Effects

AbstractThe main objectives of this study were to compare the prediction accuracy of different Bayesian methods for traits with a wide range of genetic architecture using simulation and real data and to assess the sensitivity of these methods to the violation of their assumptions. For the simulation study, different scenarios were implemented based on two traits with low or high heritability and different numbers of QTL and the distribution of their effects. For real data analysis, a German Holstein dataset for milk fat percentage, milk yield, and somatic cell score was used. The simulation results showed that, with the exception of the Bayes R, the other methods were sensitive to changes in the number of QTLs and distribution of QTL effects. Having a distribution of QTL effects, similar to what different Bayesian methods assume for estimating marker effects, did not improve their prediction accuracy. The Bayes B method gave higher or equal accuracy rather than the rest. The real data analysis showed that similar to scenarios with a large number of QTLs in the simulation, there was no difference between the accuracies of the different methods for any of the traits.

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