Does victim forgiveness relieve perpetrator guilt? Examining null effects with equivalence tests and Bayes factor

2021 ◽  
Author(s):  
Yoshiya Furukawa ◽  
Ken’ichiro Nakashima ◽  
Yasuko Morinaga
Keyword(s):  
Bayes Factor ◽  
Equivalence Tests

scholarly journals Bayesian Hodges-Lehmann tests for statistical equivalence in the two-sample setting: Power analysis, type I error rates and equivalence boundary selection in biomedical research

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Riko Kelter
Keyword(s):  
Biomedical Research ◽  
Bayes Factor ◽  
Type I Error ◽  
Error Rates ◽  
Type I ◽  
Equivalence Testing ◽  
Type I Error Rates ◽  
Equivalence Tests ◽  
Statistical Equivalence ◽  
The Relationship

Abstract Background Null hypothesis significance testing (NHST) is among the most frequently employed methods in the biomedical sciences. However, the problems of NHST and p-values have been discussed widely and various Bayesian alternatives have been proposed. Some proposals focus on equivalence testing, which aims at testing an interval hypothesis instead of a precise hypothesis. An interval hypothesis includes a small range of parameter values instead of a single null value and the idea goes back to Hodges and Lehmann. As researchers can always expect to observe some (although often negligibly small) effect size, interval hypotheses are more realistic for biomedical research. However, the selection of an equivalence region (the interval boundaries) often seems arbitrary and several Bayesian approaches to equivalence testing coexist. Methods A new proposal is made how to determine the equivalence region for Bayesian equivalence tests based on objective criteria like type I error rate and power. Existing approaches to Bayesian equivalence testing in the two-sample setting are discussed with a focus on the Bayes factor and the region of practical equivalence (ROPE). A simulation study derives the necessary results to make use of the new method in the two-sample setting, which is among the most frequently carried out procedures in biomedical research. Results Bayesian Hodges-Lehmann tests for statistical equivalence differ in their sensitivity to the prior modeling, power, and the associated type I error rates. The relationship between type I error rates, power and sample sizes for existing Bayesian equivalence tests is identified in the two-sample setting. Results allow to determine the equivalence region based on the new method by incorporating such objective criteria. Importantly, results show that not only can prior selection influence the type I error rate and power, but the relationship is even reverse for the Bayes factor and ROPE based equivalence tests. Conclusion Based on the results, researchers can select between the existing Bayesian Hodges-Lehmann tests for statistical equivalence and determine the equivalence region based on objective criteria, thus improving the reproducibility of biomedical research.

Assessing the Replication Bayes Factor: The Case of Global Versus Local Priming

2014 ◽  
Author(s):  
Sarahanne Field ◽  
Eric-Jan Wagenmakers ◽  
Ben Newell ◽  
Don Van Ravenzwaaij
Keyword(s):  
Bayes Factor

scholarly journals Equivalence Testing for Regression Discontinuity Designs

2020 ◽  
pp. 1-17
Author(s):  
Erin Hartman
Keyword(s):  
Political Science ◽  
Current Practice ◽  
Regression Discontinuity ◽  
Regression Function ◽  
Superior Performance ◽  
Equivalence Testing ◽  
Simulation Studies ◽  
Equivalence Tests ◽  
Regression Discontinuity Designs ◽  
Testing Approach

Abstract Regression discontinuity (RD) designs are increasingly common in political science. They have many advantages, including a known and observable treatment assignment mechanism. The literature has emphasized the need for “falsification tests” and ways to assess the validity of the design. When implementing RD designs, researchers typically rely on two falsification tests, based on empirically testable implications of the identifying assumptions, to argue the design is credible. These tests, one for continuity in the regression function for a pretreatment covariate, and one for continuity in the density of the forcing variable, use a null of no difference in the parameter of interest at the discontinuity. Common practice can, incorrectly, conflate a failure to reject evidence of a flawed design with evidence that the design is credible. The well-known equivalence testing approach addresses these problems, but how to implement equivalence tests in the RD framework is not straightforward. This paper develops two equivalence tests tailored for RD designs that allow researchers to provide statistical evidence that the design is credible. Simulation studies show the superior performance of equivalence-based tests over tests-of-difference, as used in current practice. The tests are applied to the close elections RD data presented in Eggers et al. (2015b).

scholarly journals Relationship between Sleep Duration Trajectories and Self-Rated Depressive Symptoms in South Koreans with Physical Disabilities

Healthcare ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 361
Author(s):  
Su Jeong Yi ◽  
Yoo Mi Jeong ◽  
Jae-Hyun Kim
Keyword(s):  
Mental Health ◽  
Depressive Symptoms ◽  
Sleep Duration ◽  
Bayes Factor ◽  
Physical Disabilities ◽  
Disabled People ◽  
Physically Disabled ◽  
The Disabled ◽  
Physically Disabled People ◽  
The Relationship

Physically disabled persons can have sleep problems, which affects their mental health more than those in non-disabled people. However, there are few studies on the relationship between sleep duration and mental health targeting physically disabled people in South Korea, and existing studies on the disabled have mostly used data collected from convenience rather than nationally representative samples, limiting the generalization of the results. This study used data from the second wave of the Panel Survey of Employment for the Disabled (PSED, 2016–2018, 1st–3rd year). Participants included 1851 physically disabled individuals. The Chi-square test and generalized estimating equation (GEE) were used and the Akaike information criterion (AIC) value and the AIC log Bayes factor approximation were used to select sleep trajectories. This is the first study to elucidate multiple sleep trajectories in physically disabled people in Korea, and the relationship between sleep duration trajectories and self-rated depressive symptoms. People with physical disabilities who sleep more than 9 h have the highest risk of depression and need more intensive management as a priority intervention.

Bayesian approach to discriminant problems for count data with application to multilocus short tandem repeat dataset

2020 ◽  
Vol 19 (2) ◽  
Author(s):  
Koji Tsukuda ◽  
Shuhei Mano ◽  
Toshimichi Yamamoto
Keyword(s):  
Sample Size ◽  
Classification Accuracy ◽  
Tandem Repeats ◽  
Bayes Factor ◽  
Characteristic Curve ◽  
Geometric Mean ◽  
Previous Method ◽  
Threshold Adjustment ◽  
Two Populations ◽  
Short Tandem

AbstractShort Tandem Repeats (STRs) are a type of DNA polymorphism. This study considers discriminant analysis to determine the population of test individuals using an STR database containing the lengths of STRs observed at more than one locus. The discriminant method based on the Bayes factor is discussed and an improved method is proposed. The main issues are to develop a method that is relatively robust to sample size imbalance, identify a procedure to select loci, and treat the parameter in the prior distribution. A previous study achieved a classification accuracy of 0.748 for the g-mean (geometric mean of classification accuracies for two populations) and 0.867 for the AUC (area under the receiver operating characteristic curve). We improve the maximum values for the g-mean to 0.830 and the AUC to 0.935. Computer simulations indicate that the previous method is susceptible to sample size imbalance, whereas the proposed method is more robust while achieving almost identical classification accuracy. Furthermore, the results confirm that threshold adjustment is an effective countermeasure to sample size imbalance.

scholarly journals Identification of genetic loci affecting body mass index through interaction with multiple environmental factors using structured linear mixed model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hae-Un Jung ◽  
Won Jun Lee ◽  
Tae-Woong Ha ◽  
Ji-One Kang ◽  
Jihye Kim ◽  
...  
Keyword(s):  
Body Mass Index ◽  
Environmental Factors ◽  
Body Mass ◽  
Bayes Factor ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Interaction Analysis ◽  
Carbohydrate Intake ◽  
Calorie Intake ◽  
Environment Interaction

AbstractMultiple environmental factors could interact with a single genetic factor to affect disease phenotypes. We used Struct-LMM to identify genetic variants that interacted with environmental factors related to body mass index (BMI) using data from the Korea Association Resource. The following factors were investigated: alcohol consumption, education, physical activity metabolic equivalent of task (PAMET), income, total calorie intake, protein intake, carbohydrate intake, and smoking status. Initial analysis identified 7 potential single nucleotide polymorphisms (SNPs) that interacted with the environmental factors (P value < 5.00 × 10−6). Of the 8 environmental factors, PAMET score was excluded for further analysis since it had an average Bayes Factor (BF) value < 1 (BF = 0.88). Interaction analysis using 7 environmental factors identified 11 SNPs (P value < 5.00 × 10−6). Of these, rs2391331 had the most significant interaction (P value = 7.27 × 10−9) and was located within the intron of EFNB2 (Chr 13). In addition, the gene-based genome-wide association study verified EFNB2 gene significantly interacting with 7 environmental factors (P value = 5.03 × 10−10). BF analysis indicated that most environmental factors, except carbohydrate intake, contributed to the interaction of rs2391331 on BMI. Although the replication of the results in other cohorts is warranted, these findings proved the usefulness of Struct-LMM to identify the gene–environment interaction affecting disease.

scholarly journals A Bayesian solution to the Behrens–Fisher problem

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
Fco. Javier Girón ◽  
Carmen del Castillo
Keyword(s):  
Closed Form ◽  
Hierarchical Model ◽  
Bayes Factor ◽  
Bayes Factors ◽  
Simple Solution ◽  
Asymptotic Approximations ◽  
Normal Distributions ◽  
Fisher Distribution ◽  
Leibler Divergence

AbstractA simple solution to the Behrens–Fisher problem based on Bayes factors is presented, and its relation with the Behrens–Fisher distribution is explored. The construction of the Bayes factor is based on a simple hierarchical model, and has a closed form based on the densities of general Behrens–Fisher distributions. Simple asymptotic approximations of the Bayes factor, which are functions of the Kullback–Leibler divergence between normal distributions, are given, and it is also proved to be consistent. Some examples and comparisons are also presented.

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