Bootstrap methods for inference in the Parks model

Non-spherical errors, namely heteroscedasticity, serial correlation and cross-sectional correlation are commonly present within panel data sets. These can cause significant problems for econometric analyses. The FGLS(Parks) estimator has been demonstrated to produce considerable efficiency gains in these settings. However, it suffers from underestimation of coefficient standard errors, oftentimes severe. Potentially, jackknifing the FGLS(Parks) estimator could allow one to maintain the efficiency advantages of FGLS(Parks) while producing more reliable estimates of coefficient standard errors. Accordingly, this study investigates the performance of the jackknife estimator of FGLS(Parks) using Monte Carlo experimentation. We find that jackknifing can -- in narrowly defined situations -- substantially improve the estimation of coefficient standard errors. However, its overall performance is not sufficient to make it a viable alternative to other panel data estimators.

PurposeIn a recent paper, Yoon and Lee (2019) (YL hereafter) propose a weighted Fama and MacBeth (FMB hereafter) two-step panel regression procedure and provide evidence that their weighted FMB procedure produces more efficient coefficient estimators than the usual unweighted FMB procedure. The purpose of this study is to supplement and improve their weighted FMB procedure, as they provide neither asymptotic results (i.e. consistency and asymptotic distribution) nor evidence on how close their standard error estimator is to the true standard error.Design/methodology/approachFirst, asymptotic results for the weighted FMB coefficient estimator are provided. Second, a finite-sample-adjusted standard error estimator is provided. Finally, the performance of the adjusted standard error estimator compared to the true standard error is assessed.FindingsIt is found that the standard error estimator proposed by Yoon and Lee (2019) is asymptotically consistent, although the finite-sample-adjusted standard error estimator proposed in this study works better and helps to reduce bias. The findings of Yoon and Lee (2019) are confirmed even when the average R2 over time is very small with about 1% or 0.1%.Originality/valueThe findings of this study strongly suggest that the weighted FMB regression procedure, in particular the finite-sample-adjusted procedure proposed here, is a computationally simple but more powerful alternative to the usual unweighted FMB procedure. In addition, to the best of the authors’ knowledge, this is the first study that presents a formal proof of the asymptotic distribution for the FMB coefficient estimator.

When estimating the mean value of a variable, or the total amount of a resource, within a specified region it is desirable to report an estimated standard error for the resulting estimate. If the sample sites are selected according to a probability sampling design, it usually is possible to construct an appropriate design-based standard error estimate. One exception is systematic sampling for which no such standard error estimator exists. However, a slight modification of systematic sampling, termed 2-step tessellation stratified (2TS) sampling, does permit the estimation of design-based standard errors. This paper develops a design-based standard error estimator for 2TS sampling. It is shown that the Taylor series approximation to the variance of the sample mean under 2TS sampling may be expressed in terms of either a deterministic variogram or a deterministic covariance function. Variance estimation then can be approached through the estimation of a variogram or a covariance function. The resulting standard error estimators are compared to some more traditional variance estimators through a simulation study. The simulation results show that estimators based on the new approach may perform better than traditional variance estimators.

The robustness of three multiple‐comparison procedures (multiple t test, Tukey WSD and Scheffé S test) to the violation of the homogeneous population variance assumption was investigated using three different standard error estimates. These estimates were (1) the square root of two mean square within/ n , (2) the standard error of the traditional t test and (3) the standard error of the Behrens‐Fisher t ′ statistic. The procedures were highly robust to variance heterogeneity using the Behrens‐Fisher standard error estimate. The procedures were considerably less robust using MSW. The universal use of the Behrens‐Fisher statistic with the Welch solution for critical values is recommended.

The bootstrap: Some large sample theory and connections with robustness

Background: The target of inference in air pollution cohort studies is the association between exposure and disease outcomes. Exposure is typically predicted from monitoring data; the resulting measurement error affects health effect estimates and their confidence intervals. Since standard Berkson and classical measurement error categories are not directly applicable, we present new characterizations and correction methods. Methods: We decompose the measurement error into Berkson-like and classical-like components. Berkson-like error is introduced by smoothing the exposure surface, while the classical-like error results from uncertainty in estimating exposure model parameters. We discuss their impacts in linear health models with exposure surfaces modeled in 1) a parametric framework (with a correctly specified mean model and spatially correlated residuals) and 2) a semi-parametric framework (where locations are random and the deterministic exposure can have a mis-specified mean model). We propose practical correction methods for each. Results: Both measurement error components change the variability of the health effect estimates. Classical-like error introduces bias, although this is frequently small. In the parametric framework Berkson-like error does not introduce bias, whereas in the semi-parametric framework it may introduce bias, depending on whether additional assumptions are satisfied. In the parametric framework, a parametric bootstrap (or a computationally less intensive alternative) can be used for bias correction and/or standard error estimation. In the semi-parametric framework, there are asymptotic methods for bias correction and a simple non-parametric bootstrap can be used to estimate standard errors. Conclusions: Measurement error in air pollution cohort studies is a complex mixture of Berkson-like and classical-like components. There are important implications for study design and for developing post-hoc correction methods.

Applying single-level statistical models to multilevel data typically produces underestimated standard errors, which may result in misleading conclusions. This study examined the impact of ignoring multilevel data structure on the estimation of item parameters and their standard errors of the Rasch, two-, and three- parameter logistic models in item response theory (IRT) to demonstrate the degree of such underestimation in IRT. Also, the Lord’s chi-square test using the underestimated standard errors was used to test differential item functioning (DIF) to show the impact of such underestimation on the practical applications of IRT. The results of simulation studies showed that, in the most severe case of multilevel data, the standard error estimate from the standard single-level IRT models was about half of the minimal asymptotic standard error, and the type I error rate of the Lord’s chi-square test was inflated up to .35. The results of this study suggest that standard single-level IRT models may seriously mislead our conclusions in the presence of multilevel data, and therefore multilevel IRT models need to be considered as alternatives.

Hypothesis tests

In social science researches, there may be cases where a category of the dependent variable is seen hundred times less (more) than the other category. Events like wars, mass migrations or coups in social sciences; an event of interest in binary variable(s) may have very low prevalence, resulting in low or even zero cell counts in one or two cells in the 2X2 tables of two factors. In this case, independent variable predict the dependent variable perfectly or almost perfectly, and this leads to an issue called complete or quasi-complete separation problem in statistical modelling. This study aims to compare three methods suggested in the literature for the quasi-complete separation in a real small dataset; penalized maximum likelihood (Firth-type), exact logistic regression and bayesian logistic regression. Methods were compared via odds ratios, odds’ standard error estimates, confidence intervals and statistical significance. Parameter estimates were obtained under three different models with binary and continuous variables. Results show that all methods can provide convergence in the presence of quasi-complete separation. In conclusion, bayesian logistic regression estimates tend to be superior than the other methods in terms of estimation of standard errors.

Purpose: This study aims to explain the use of Importance and Importance Analysis (IPA) with a diagonal regression approach and standard error of estimation (SEE) in the case of lecturers in intellectual capital universities in Indonesia. Theoretical framework: The Lecturer Study of Intellectual Capital University is closely related to the excellence of Human Resources, individually and collectively as a key factor for higher education excellence. Science analysis can produce strategic considerations to improve the overall performance of higher education institutions. Method/design/approach: The research design uses a quantitative approach; the population is all university lecturers in Indonesia. Scale data is in the form of semantic differential, questionnaires are made in Google forms which are shared using social media: email, WhatsApp’s and telegrams. There were 225 answers worthy of analysis, coming from 65 universities spread across 14 provinces in Indonesia. Furthermore, the data were analyzed using Importance and Importance Analysis with a diagonal regression approach and standard error of estimation. Results and conclusion: The study results show that a high difference in the mean importance and importance does not necessarily indicate irrelevant performance, because the spread of the data must be checked from the estimated standard error according to the considered level of accuracy. It is concluded that lecturers at intellectual capital universities in Indonesia currently need improvement in the fields of academic position, learning skills, and relationships between lecturers. Besides that, the indicators that need improvement are innovation, relativity, and lecturer involvement in method-making. Research implications: University lecturers are one of the key factors in the development of universities today. With the presence of lecturers, the university can carry out its business processes as a higher education institution. It seems that this research has not been responded well by all lecturers in Indonesia, it is evident that only 225 respondents want to be involved in this research, even though the benefits are considered very strategic for fostering the role of lecturers in improving the quality of universities as a whole, then the use of semantic differential scales is very suitable for analysis IPA because the data can be implemented directly in the analysis, there is no need for data transformation. Originality/value: Science studies in the field of Intellectual Capital are still new, as well as the use of semantic differential scales and diagonal regression approaches with standard error estimation that have not been found in previous literature.

Multiple imputation (MI) is a method for repairing and analyzing data with missing values. MI replaces missing values with a sample of random values drawn from an imputation model. The most popular form of MI, which we call posterior draw multiple imputation (PDMI), draws the parameters of the imputation model from a Bayesian posterior distribution. An alternative, which we call maximum likelihood multiple imputation (MLMI), estimates the parameters of the imputation model using maximum likelihood (or equivalent). Compared to PDMI, MLMI is less computationally intensive, faster, and yields slightly more efficient point estimates. A past barrier to using MLMI was the difficulty of estimating the standard errors of MLMI point estimates. We derive, implement, and evaluate three consistent standard error formulas: (1) one combines variances within and between the imputed datasets, (2) one uses the score function, and (3) one uses the bootstrap to estimate variance components due to sampling and imputation. Formula (1) modifies for MLMI a formula that has long been used under PDMI, while formulas (2) and (3) can be used without modification under either PDMI or MLMI. We have implemented MLMI and the standard error estimators in the mlmi and bootImpute packages for R.

Diastolic fractional flow reserve (dFFR) has been shown to be highly sensitive for detection of inducible myocardial ischemia. However, its reliance on measurement of left-ventricular pressure for zero-flow pressure correction, as well as manual extraction of the diastolic interval, has been its major limitation. Given previous reports of minimal zero-flow pressure at end-diastole, we compared instantaneous ECG-gated end-diastolic FFR with conventional full-cardiac cycle FFR and other diastolic indices in the porcine model. Measurements of FFR in the left anterior descending and left circumflex arteries were performed in an open-chest swine model with an external occluder device on the coronary artery used to produce varying degrees of epicardial stenosis. An ultrasound flow-probe that was placed proximal to the occluder measured absolute blood flow in ml/min, and it was used as a gold standard for FFR measurement. A total of 17 measurements at maximal hyperemia were acquired in 5 animals. Correlation coefficient between conventional mean hyperemic FFR with pressure-wire and directly measured FFR with flow-probe was 0.876 (standard error estimate=0.069; P<0.0001). The hyperemic end-diastolic FFR with pressure-wire correlated better with FFR measured directly with flow-probe (r=0.941, standard error estimate=0.050; P<0.0001). Instantaneous hyperemic ECG-gated FFR acquired at end-diastole, as compared with conventional full-cardiac cycle FFR, has an improved correlation with FFR measured directly with ultrasound flow-probe.

A RE-ANALYSIS OF THE TEMPORAL DEPENDENCE OF TOTAL MORTALITY ON PM10 USING PENALIZED SPLINE AS AN APPROACH TO MODELING POTENTIALLY NONLINEARITY

This study investigates item parameter recovery, standard error estimates, and fit statistics yielded by the WINSTEPS program under the Rasch model and the rating scale model through Monte Carlo simulations. The independent variables were item response model, test length, and sample size. WINSTEPS yielded practically unbiased estimates for the difficulty parameters under the Rasch model and the overall difficulty parameters under the rating scale model. However, the estimates for the intersection parameters under the rating scale model were substantially biased, especially for short tests. The standard errors of the overall difficulties and intersection parameters were slightly underestimated. The cube root-transformed weighted and unweighted item fit statistics did not follow the standard normal distribution in that their empirical sampling variances were much smaller than the expected value of unity. Correction procedures were proposed to make them follow approximately the standard normal distribution so that the usual critical ranges at the α nominal level could be used to screen the misfitting items.

In a simulation study of the estimation of population pharmacokinetic parameters, including fixed and random effects, the estimates and confidence intervals produced by NONMEM were evaluated. Data were simulated according to a monoexponential model with a wide range of design and statistical parameters, under both steady state (SS) and non-SS conditions. Within the range of values for population parameters commonly encountered in research and clinical settings, NONMEM produced parameter estimates for CL, V, sigma CL, and sigma epsilon which exhibit relatively small biases. As the range of variability increases, these biases became larger and more variable. An important exception was bias in the estimate for sigma V which was large even when the underlying variability was small. NONMEM standard error estimates are appropriate as estimates of standard deviation when the underlying variability is small. Except in the case of CL, standard error estimates tend to deteriorate as underlying variability increases. An examination of confidence interval coverage indicates that caution should be exercised when the usual 95% confidence intervals are used for hypothesis testing. Finally, simulation-based corrections of point and interval estimates are possible but corrections must be performed on a case-by-case basis.