Errors-in-Variables and Reverse Regression

In his previous work, Roberts (1979,1980) emphasized problems of measurement and possible bias involved in using direct regression, where reward is the dependent variable, and the independent variables consist of a vector of qualifications. He also suggested that these problems could, to a large extent, be solved by using reverse regression, where reward is the independent variable, and the dependent variable consists of a measure of qualifications. The debate on these issues is continuing. (See Blattenberger and Michelson 1980, Finkelstein 1980, Madden 1982, and Blau and Kahn 1983.) In Reverse Regression, Fairness, and Employment Discrimination, however, Conway and Roberts (1983) put primary emphasis on the fact that there are two distinct concepts of fairness associated with direct and reverse regression and that these different perspectives are basic to understanding discrimination. They also point out, quite correctly, that these two concepts will only occasionally be in agreement. Up to this point, their exposition of these issues is clear and helpful. It is when they go on to claim that both concepts are needed to evaluate fairness, and that contradictions between the two pose serious problems for lawyers, statisticians, and judges alike that their conclusions need to be challenged.

Forward versus reverse regression and cointegration

Expansion and collapse are two key features of a financial asset bubble. Bubble expansion may be modeled using a mildly explosive process. Bubble implosion may take several different forms depending on the nature of the collapse and therefore requires some flexibility in modeling. This paper first strengthens the theoretical foundation of the real time bubble monitoring strategy proposed in Phillips, Shi and Yu (2015a,b, PSY) by developing analytics and studying the performance characteristics of the testing algorithm under alternative forms of bubble implosion which capture various return paths to market normalcy. Second, we propose a new reverse sample use of the PSY procedure for detecting crises and estimating the date of market recovery. Consistency of the dating estimators is established and the limit theory addresses new complications arising from the alternative forms of bubble implosion and the endogeneity effects present in the reverse regression. A real-time version of the strategy is provided that is suited for practical implementation. Simulations explore the finite sample performance of the strategy for dating market recovery. The use of the PSY strategy for bubble monitoring and the new procedure for crisis detection are illustrated with an application to the Nasdaq stock market.

The purpose of this study was to determine how consumers’ decisions in using the RedDoorz application, and to find out how the effectiveness of e-service quality in the RedDoorz application as well as customer feedback on the RedDoorz application. This research uses descriptive and associative methods and uses a nonprobability sampling technique that's is purposive sampling. By distributing questionnaires to 130 respondents with a survey on the city of Sukabumi, data collection was done by collecting primary and secondary data, researchers conducted questionnaires testing using validity and reliability tests, also using the classic assumption test that is the Kolmogorov Smirnov normality test to determine residual values normal or reverse regression. The data analysis technique used is a simple correlation coefficient, multiple correlation coefficient, simple linear regression, multiple linear regression, and hypothesis testing using a partial test ( T-test) and simultaneous test ( F test). From the results of the questionnaire, analysis can be declared valid and reliable, as well as the results in testing the normality test of the total population expressed normal distribution. The results of the analysis conducted by researchers are the influence of e-service quality on decision using the RedDoorz application, also the influence of customer feedback on decision using the RedDoorz application, decision using the application can be explained by e-service quality can also be explained by customer feedback, including in the simultaneous test of e-service quality and customer feedback both influence the decision to use the RedDoorz application.

Reverse Regression and Employment Discrimination

This note reviews basic techniques of linear path analysis and demonstrates, using simple examples, how causal phenomena of non-trivial character can be understood, exemplified and analyzed using diagrams and a few algebraic steps.The techniques allow for swift assessment of how various features of the model impact the phenomenon under investigation.This includes: Simpson's paradox, case-control bias, selection bias, missing data, collider bias, reverse regression, bias amplification, near instruments, and measurement errors.

This dissertation includes three papers with each distributed in one chapter. In chapter 1, we proposed an Adaptive Weighting Reverse Regression (AWRR) method to test association between multiple traits and rare variants in a genomic region. AWRR is robust to the directions of effects of causal variants and is also robust to the directions of association of traits. Using extensive simulation studies, we compared the performance of AWRR with canonical correlation analysis (CCA), Single-TOW, and the Weighted Sum Reverse Regression (WSRR). Our results showed that, in all of the simulation scenarios, AWRR is consistently more powerful than CCA. In most scenarios, AWRR is more powerful than Single-TOW and WSRR. In chapter 2, we proposed an “optimal” maximum heritability test (MHT-O) to test the association between multiple traits and a single variant. MHT-O includes a procedure of deleting traits that have weak or no association with the variant. Using extensive simulation studies, we compared the performance of MHT-O with MHT, Trait-based Association Test uses Extended Simes procedure (TATES), SUM_SCORE and MANOVA. Our results showed that, in all of the simulation scenarios, MHT-O is either the most powerful test or comparable to the most powerful test among the five tests we compared. In chapter 3, we developed a statistical method by testing an optimally weighted combination of variants with multiple traits (TOWmuT) to test the association between multiple traits and a weighted combination of variants (rare and/or common) in a genomic region. TOWmuT is robust to the directions of effects of causal variants and is applicable to different types of traits. Using extensive simulation studies, we compared the performance of TOWmuT with the following five existing methods: gene association with multiple traits (GAMuT), multiple sequence kernel association test (MSKAT), adaptive weighting reverse regression (AWRR), single-TOW, and MANOVA. Our results showed that, in all of the simulation scenarios, TOWmuT has correct type I error rates and is consistently more powerful than the other five tests. We also illustrated the usefulness of TOWmuT by analyzing a whole-genome genotyping data from a lung function study.

Pleiotropy is a widespread phenomenon in complex human diseases. Jointly analyzing multiple phenotypes can improve power performance of detecting genetic variants and uncover the underlying genetic mechanism. This study aims to detect the association between genetic variants in a genomic region and multiple phenotypes. We develop the aggregated Cauchy association test to detect the association between rare variants in a genomic region and multiple phenotypes (abbreviated as "Multi-ACAT"). Multi-ACAT first detects the association between each rare variant and multiple phenotypes based on reverse regression and obtains variant-level p-values, then takes linear combination of transformed p-values as the test statistic which approximately follows Cauchy distribution under the null hypothesis. Extensive simulation studies show that when the proportion of causal variants in a genomic region is extremely small, Multi-ACAT is more powerful than the other several methods and is robust to bi-directional effects of causal variants. Finally, we illustrate our proposed method by analyzing two phenotypes [systolic blood pressure (SBP) and diastolic blood pressure (DBP)] from Genetic Analysis Workshop 19 (GAW19). The Multi-ACAT computes extremely fast, does not consider complex distributions of multiple correlated phenotypes, and can be applied to the case with noise phenotypes.

A common problem in randomized clinical trials is nonignorable missingness, namely that the clinical outcome(s) of interest can be missing in a way that is not fully explained by the observed quantities. This happens when the continued participation of patients depends on the current outcome after adjusting for the observed history. Standard methods for handling nonignorable missingness typically require specification of the response mechanism, which can be difficult in practice. This article proposes a reverse regression approach that does not require a model for the response mechanism. Instead, the proposed approach relies on the assumption that missingness is independent of treatment assignment upon conditioning on the relevant outcome(s). This conditional independence assumption is motivated by the observation that, when patients are effectively masked to the assigned treatment, their decision to either stay in the trial or drop out cannot depend on the assigned treatment directly. Under this assumption, one can estimate parameters in the reverse regression model, test for the presence of a treatment effect, and in some cases estimate the outcome distributions. The methodology can be extended to longitudinal outcomes under natural conditions. The proposed approach is illustrated with real data from a cardiovascular study.

Financial Bubble Implosion

BackgroundPrivate and Public security and law enforcement (SLE) sectors perform multiple overlapping job duties.MethodsWorkers’ compensation (WC) SLE first reports of injury (FROI) data (2005–2015) were analyzed to describe injuries, identify differences in awarded WC benefits, and compare the probability of a FROI resulting in awarded benefits between Public and Private SLE. A Pearson’s chi-square test was utilized and reverse selection logistic regression was performed to estimate the odds ratio that a FROI would result in an awarded benefit for Private vs. Public SLE, while adjusting for relevant covariates.ResultsPrivate SLE had higher FROI percentages for younger and for older workers, fall injuries, and back injuries, compared to Public SLE. The adjusted odds that a FROI resulted in an awarded benefit was 1.4 times higher for Private SLE compared to Public SLE; (95% confidence interval [CI] = 1.09,1.69). Middle-aged SLE employee adjusted odds of awarded benefits was 3.3 times (95% CI [1.96, 5.39]) higher compared to younger employees. Adjusted odds of awarded benefits was 3.8 times (95% CI [1.34, 10.61]) higher for gunshots and 1.7 times (95% CI [1.22, 2.39]) higher for fractures/dislocations compared to other nature of injuries. Motor vehicle injury, fall/slip, and strain related FROIs had elevated adjusted odds of awarded benefits compared to other injury causes.ConclusionsResults highlight the importance of injury prevention education and worker safety training for Private and Public SLE sector workers on fall prevention (especially in Private SLE) and strain prevention (especially in Public SLE), as well as motor vehicle safety.

In recent years, the rapid development of logistics has become the driving force of the construction of Logistics Information Platforms, nevertheless, most of which are still underdeveloped, especially the charging and pricing mechanism of the platform is inadequate. Based on the bargain method of the game theory, this essay will build a pricing model and conduct a three-round bargaining reverse regression calculation towards logistics software customized services, resulting in its optimal pricing strategy. Taking National Transport Logistics Public Information Platform as the analyzing example, this essay provides theoretical support for the optimal pricing strategy of logistics software customized services.

Mid-frequency MTF compensation for optical synthetic aperture based on baseline transform scanning via deep learning

Multivariate phenotypes underlie complex traits. Thus, instead of using the end-point trait, it may be statistically more powerful to use a multivariate phenotype correlated to the end-point trait for detecting linkage. In this study, we develop a reverse regression method to analyze linkage of Kofendrerd Personality Disorder affection status in the New York population of the Genetic Analysis Workshop 14 (GAW14) simulated dataset. When we used the multivariate phenotype, we obtained significant evidence of linkage near four of the six putative loci in at least 25% of the replicates. On the other hand, the linkage analysis based on Kofendrerd Personality Disorder status as a phenotype produced significant findings only near two of the loci and in a smaller proportion of replicates.

Yitchak Haberfeld, Barry Gerhart, Re-Examining "Employment Discrimination: An Empirical Test of Forward Versus Reverse Regression", The Journal of Human Resources, Vol. 23, No. 1 (Winter, 1988), pp. 138-144