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The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a robust inference for internal validity, that is, the PIV, as a robustness index of causal inference. Formally, the PIV is the probability of rejecting the null hypothesis again based on both the observed sample and the counterfactuals, provided the same null hypothesis has already been rejected based on the observed sample. Under either frequentist or Bayesian framework, one can bound the PIV of an inference based on his bounded belief about the counterfactuals, which is often needed when the unconfoundedness assumption is dubious. The PIV is equivalent to statistical power when the NHST is thought to be based on both the observed sample and the counterfactuals. We summarize the process of evaluating internal validity with the PIV into a six-step procedure and illustrate it with an empirical example.

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component--and in particular for the first principal component--to be error-free. In conjunction with the findings in Raykov et al., it is concluded that in practice no principal component can be perfectly reliable for a set of observed variables that are not all free of measurement error, whether or not their error terms correlate, and hence no principal component can practically be error-free.

The inverse probability of treatment weighting (IPTW) approach is commonly used in propensity score analysis to infer causal effects in regression models. Due to oversized IPTW weights and errors associated with propensity score estimation, the IPTW approach can underestimate the standard error of causal effect. To remediate this, bootstrap standard errors have been recommended to replace the IPTW standard error, but the ordinary bootstrap (OB) procedure might still result in underestimation of the standard error because of its inefficient resampling scheme and untreated oversized weights. In this paper, we develop a generalized bootstrap (GB) procedure for estimating the standard error and confidence intervals of the IPTW approach. Compared with the OB procedure and other three procedures in comparison, the GB procedure has the highest precision and yields conservative standard error estimates. As a result, the GB procedure produces short confidence intervals with highest coverage rates. We demonstrate the effectiveness of the GB procedure via two simulation studies and a dataset from the National Educational Longitudinal Study-1988 (NELS-88). [ABSTRACT FROM AUTHOR]

The measurement error in principal components extracted from a set of fallible measures is discussed and evaluated. It is shown that as long as one or more measures in a given set of observed variables contains error of measurement, so also does any principal component obtained from the set. The error variance in any principal component is shown to be (a) bounded from below by the smallest error variance in a variable from the analyzed set and (b) bounded from above by the largest error variance in a variable from that set. In the case of a unidimensional set of analyzed measures, it is pointed out that the reliability and criterion validity of any principal component are bounded from above by these respective coefficients of the optimal linear combination with maximal reliability and criterion validity (for a criterion unrelated to the error terms in the individual measures). The discussed psychometric features of principal components are illustrated on a numerical data set.

A method for evaluating the validity of multicomponent measurement instruments in heterogeneous populations is discussed. The procedure can be used for point and interval estimation of criterion validity of linear composites in populations representing mixtures of an unknown number of latent classes. The approach permits also the evaluation of between-class validity differences as well as within-class validity coefficients. The method can similarly be used with known class membership when distinct populations are investigated, their number is known beforehand and membership in them is observed for the studied subjects, as well as in settings where only the number of latent classes is known. The discussed procedure is illustrated with numerical data.

The internal validity of a causal inference made based on an observational study is often subject to debate. The potential outcomes framework of causal inference stipulates that causal inference is essentially a missing data problem, and we follow this spirit to define the ideal sample as the combination of the observed data and the missing/counterfactual data for regression models. The robustness of a causal inference can be quantified by the probability of a robust inference for internal validity in regression, i.e., the PIVR, which is the probability of rejecting the null hypothesis again for the ideal sample provided the same null hypothesis has been already rejected for the observed sample. Drawing on the relationship between the PIVR and the mean counterfactual outcomes, we formalize a conceptual framework of quantifying the robustness of a regression-based causal inference based on a joint distribution about the mean counterfactual outcomes, holding the observed sample fixed. Interpretatively, the PIVR is the statistical power of the null hypothesis significance testing that is thought to be built on the ideal sample. We demonstrate the conceptual framework of quantifying the robustness of a regression-based causal inference with an empirical example. [ABSTRACT FROM AUTHOR]

The existing model of sudden acceleration changes, referred to as the traffic jerk effect, is mostly based on theoretical hypotheses, and previous research has mainly focused on traditional traffic flow. To this end, this paper investigates the change in the traffic jerk effect between inactive and active vehicle-to-vehicle (V2V) communications based on field experimental data. Data mining results show that the correlation between the jerk effect and the driving behavior increases by 50.6% on average when V2V messages are received. In light of the data analysis results, a new car-following model is proposed to explore the jerk effect in a connected environment. The model parameters are calibrated, and the results show that the standard deviation between the new model simulation data and the observed data decreases by 38.2% compared to that of the full velocity difference (FVD) model. Linear and nonlinear analyses of the calibrated model are then carried out to evaluate the connected traffic flow stability. Finally, the theoretical analysis is verified by simulation experiments. Both the theoretical and simulation results show that the headway amplitude and velocity fluctuations are reduced when considering the jerk effect in a connected environment, and the traffic flow stability is improved., 1. Introduction As the basis of microscopic traffic flow, the car-following model [1, 2] is used to describe the motion characteristics of a vehicle that follows another vehicle. This situation [...]

Nonignorable technical variation is commonly observed across data from multiple experimental runs, platforms, or studies. These so-called batch effects can lead to difficulty in merging data from multiple sources, as they can severely bias the outcome of the analysis. Many groups have developed approaches for removing batch effects from data, usually by accommodating batch variables into the analysis (one-step correction) or by preprocessing the data prior to the formal or final analysis (two-step correction). One-step correction is often desirable due it its simplicity, but its flexibility is limited and it can be difficult to include batch variables uniformly when an analysis has multiple stages. Two-step correction allows for richer models of batch mean and variance. However, prior investigation has indicated that two-step correction can lead to incorrect statistical inference in downstream analysis. Generally speaking, two-step approaches introduce a correlation structure in the corrected data, which, if ignored, may lead to either exaggerated or diminished significance in downstream applications such as differential expression analysis. Here, we provide more intuitive and more formal evaluations of the impacts of two-step batch correction compared to existing literature. We demonstrate that the undesired impacts of two-step correction (exaggerated or diminished significance) depend on both the nature of the study design and the batch effects. We also provide strategies for overcoming these negative impacts in downstream analyses using the estimated correlation matrix of the corrected data. We compare the results of our proposed workflow with the results from other published one-step and two-step methods and show that our methods lead to more consistent false discovery controls and power of detection across a variety of batch effect scenarios. Software for our method is available through GitHub (https://github.com/jtleek/sva-devel) and will be available in future versions of the |$\texttt{sva}$| R package in the Bioconductor project (https://bioconductor.org/packages/release/bioc/html/sva.html). [ABSTRACT FROM AUTHOR]