Standard Errors Of Regression Coefficients Research Articles

АНАЛИЗ ФАКТОРОВ ОСЛАБЛЕНИЯ ХВОЙНЫХ ДРЕВОСТОЕВ В РЕКРЕАЦИОННЫХ НАСАЖДЕНИЯХ

Исследования проводились с 2015 по 2018 г. на 11 постоянных пробных площадях, заложенных в рекреационных насаждениях сосны Pinus sylvestris и ели Picea abies в Санкт-Петербурге и Выборге и в насаждениях общего пользования г. Нарва-Йыэсуу (Эстония). Основные факторы ослабления насаждений, как сосны, так и ели, – сумма токсичных солей и кислотность почвы. С ними коррелируют уровни ионов натрия, хлора, магния, кальция, гидрокарбоната и сульфат-иона. Наиболее сильна корреляционная связь состояния насаждений ели с концентрацией ионов хлора. Коэффициенты регрессий оценок состояния насаждений сосны и ели на оценки загрязнения почв токсичными солями значимо не различаются, несмотря на различия в организации корневых систем ели. Возможная причина – проникновение токсичных солей в более глубокие слои почвы. Воздействие рекреационных нагрузок, дендропатогенных организмов, вредителей и погодных условий не влияет на состояние насаждений, но при максимальном уровне загрязнения и наихудшем состоянии насаждений отмечена наибольшая активность вредителей и патогенов. Полученные регрессионные уравнения могут быть использованы для прогнозов состояния древостоев сосны и ели в зависимости от загрязнения почв по двум уровням – летальном и предельно допустимом. Найденные различия пороговых значений загрязнения, стандартных ошибок регрессионных коэффициентов, минимальных и максимальных пороговых величин загрязнений почв токсичными солями между анализируемыми породами невелики. Это позволяет использовать средние от пороговых значений в качестве нормативов предельно допустимого и летального загрязнений почв, а также для мониторинга и прогнозирования состояния древостоев.

Calibration and evaluation of Quigley's hybrid housing price model in Microsoft Excel.

Quigley derived his hybrid price model to improve the precision of predicted prices of sold homes by statistically merging data of resold homes in a repeat sales model with that of once-sold homes in a single sales hedonic price model. The literature has few applications of the hybrid model aside from those by Quigley and his collaborators. Two reasons for this underuse may be its computational intensiveness and its marginal empirical improvement in comparison with two other models. This paper first demystifies this computational intensiveness by calibrating models in Microsoft Excel with transferable procedures into other software. It second evaluates the hybrid price model’s empirical improvement as a reason for its underuse by predicting prices of 2,559 sold and resold homes observed in two inner-city neighbourhoods in Windsor, Ontario, during a 30-year period. The results as hypothesized are its lower standard errors of regression coefficients and higher simple R-squared than those of a single sales hedonic price model. Moreover, the hybrid model’s predictions have higher correlations than those of the single sales model with not only in-sample observed prices or changes in prices but also out-of-sample ones. The conclusion speculates in plans for future research about reasons for two models’ similar or dissimilar regression coefficients and standard errors predicting correspondingly similar or dissimilar sale prices of homes through time.

A Simulation Study on the Performances of Classical Var and Sims-Zha Bayesian Var Models in the Presence of Autocorrelated Errors

It is well known that a high degree of positive dependency among the errors generally leads to 1) serious underestimation of standard errors for regression coefficients; 2) prediction intervals that are excessively wide. This paper set out to study the performances of classical VAR and Sims-Zha Bayesian VAR models in the presence of autocorrelated errors. Autocorrelation levels of (-0.99, -0.95, -0.9, -0.85, -0.8, 0.8, 0.85, 0.9, 0.95, 0.99) were considered for short term (T = 8, 16); medium term (T = 32, 64) and long term (T = 128, 256). The results from 10,000 simulation revealed that BVAR model with loose prior is suitable for negative autocorrelations and BVAR model with tight prior is suitable for positive autocorrelations in the short term. While for medium term, the BVAR model with loose prior is suitable for the autocorrelation levels considered except in few cases. Lastly, for long term, the classical VAR is suitable for all the autocorrelation levels considered except in some cases where the BVAR models are preferred. This work therefore concludes that the performance of the classical VAR and Sims-Zha Bayesian VAR varies in terms of the autocorrelation levels and the time series lengths.

Standard errors estimation in the presence of high leverage point and heteroscedastic errors in multiple linear regression

In this study, the Robust Heteroscedastic Consistent Covariance Matrix (RHCCM) was proposed in order to estimate standard errors of regression coefficients in the presence of high leverage points and heteroscedastic errors in multiple linear regression. Robust Heteroscedastic Consistent Covariance Matrix (RHCCM) is the combination of a robust method and Heteroscedasticit Consistent Covariance Matrix (HCCM). The robust method is used to eliminate the effect of high leverage points while HCCM is mainly used to eliminate the effect of heteroscedastic errors. The performance of RHCCM was assessed through an empirical study and compared with results obtained when the original Heteroscedastic Consistent Covariance Matrix was used.

Maximum Entropy Bootstrap Simulations for Variance Estimation

We report a simulation study where we want to consider a fairly simple data generating process (DGP) used in Nordman and Lahiri (JASA, 2012) with a single fixed regressor and regression errors produced by simple AR(1) processes. We focus on the estimation of standard errors of regression coefficients, not the coefficients themselves. We compare confidence intervals by three inference procedures: the usual Chi-square distribution (Chi-sq), the moving blocks bootstrap (MBB) and a newer maximum entropy bootstrap (meboot). Since simulations have a known true standard error, we can assess the coverage and consistency of the meboot. The traditional Chi-sq confidence intervals have very poor coverage, suggesting that they should not be used in the presence of auto-correlated errors. We also consider the advisability of symmetrizing transformation of the ME density by repeating the experiments. We find that symmetrizing offers a slight advantage. Since the meboot appears to be generally superior to others, it can be recommended.

Could Sequential Residual Centering Resolve Low Sensitivity in Moderated Regression? Simulations and Cancer Symptom Clusters

Multicollinearity constitutes shared variation among predictors that inflates standard errors of regression coefficients. Several years ago, it was proven that the common practice of mean centering in moderated regression cannot alleviate multicollinearity among variables comprising an interaction, but merely masks it. Residual centering (orthogonalizing) is unacceptable because it biases parameters for predictors from which the interaction derives, thus precluding interpretation of moderator effects. I propose and validate residual centering in sequential re-estimations of a moderated regression—sequential residual centering (SRC)—by revealing unbiased multicollinearity conditioning across the interaction and its related terms. Across simulations, SRC reduces variance inflation factors (VIF) regardless of distribution shape or pattern of regression coefficients across predictors. For any predictor, the reduced VIF is used to derive a lower standard error of its regression coefficient. A cancer sample illustrates SRC, which allows unbiased interpretations of symptom clusters. SRC can be applied efficiently to alleviate multicollinearity after data collection and shows promise for advancing synergistic frontiers of research.

Correction of unexpected distributions of P values from analysis of whole genome arrays by rectifying violation of statistical assumptions

BackgroundStatistical analysis of genome-wide microarrays can result in many thousands of identical statistical tests being performed as each probe is tested for an association with a phenotype of interest. If there were no association between any of the probes and the phenotype, the distribution of P values obtained from statistical tests would resemble a Uniform distribution. If a selection of probes were significantly associated with the phenotype we would expect to observe P values for these probes of less than the designated significance level, alpha, resulting in more P values of less than alpha than expected by chance.ResultsIn data from a whole genome methylation promoter array we unexpectedly observed P value distributions where there were fewer P values less than alpha than would be expected by chance. Our data suggest that a possible reason for this is a violation of the statistical assumptions required for these tests arising from heteroskedasticity. A simple but statistically sound remedy (a heteroskedasticity–consistent covariance matrix estimator to calculate standard errors of regression coefficients that are robust to heteroskedasticity) rectified this violation and resulted in meaningful P value distributions.ConclusionsThe statistical analysis of ‘omics data requires careful handling, especially in the choice of statistical test. To obtain meaningful results it is essential that the assumptions behind these tests are carefully examined and any violations rectified where possible, or a more appropriate statistical test chosen.

The Determinants of Chronic Bronchitis in Aboriginal Children and Youth

There is limited knowledge concerning chronic bronchitis (CB) in Canadian Aboriginal peoples. To determine the prevalence (crude and adjusted) of CB and its associated risk factors in Canadian Aboriginal children and youth six to 14 years of age. Data from the cross-sectional Aboriginal Peoples Survey were analyzed in the present study. Logistic regression analysis was used to determine risk factors influencing the prevalence of CB among Aboriginal children and youth. The balanced repeated replication method was used to compute standard errors of regression coefficients to account for clustering inherent in the study design. The outcome of interest was based on the question: "Have you been told by a doctor, nurse or other health professional that you have chronic bronchitis?" Demographics, environment and population characteristics (predisposing and enabling resources) were tested for an association with CB. The prevalence of CB was 3.1% for boys and 2.8% for girls. Other significant risk factors of CB were age (OR 1.38 [95% CI 1.24 to 1.52] for 12 to 14 year olds versus six to eight year olds), income (OR 2.28 [95% CI 2.02 to 2.59] for income category <$25,000/year versus ≥$85,000/year), allergies (OR 1.96 [95% CI 1.78 to 2.16] for having allergies versus no allergies), asthma (OR 7.61 [ 95% CI 6.91 to 8.37] for having asthma versus no asthma) and location of residence (rural/urban and geographical location). A significant two-way interaction between sex and body mass index indicated that the relationship between the prevalence of CB and body mass index was modified by sex. The prevalence of CB was related to well-known risk factors among adults, including older age and lower annual income.

Disruptive selection for sternopleural bristle phenotypes inDrosophila ananassae

Disruptive selection is potentially critical in maintaining variation and initiating speciation and plays an important role in the organization of genetic variability in natural populations. It occurs when extreme phenotypes have a fitness advantage over intermediate phenotypes. Disruptive selection for high and low numbers of sternopleural bristles in Drosophila ananassae was applied for 12 generations to test its effect in induction of behavioural isolation. Pattern of mating between flies of high and low lines was tested in an Elens-Wattiaux mating chamber by using a multiple-choice technique after G(5) and G(12). Data was analyzed by calculating χ(2) under the assumption of random mating to test the difference between homoand heterogamic matings, and sexual isolation was tested by calculating the isolation estimate. The results show that there is no evidence for sexual isolation in G(5) and G(12). The realized heritability, standard error of regression coefficient, and t values suggest that disruptive selection for sternopleural bristle phenotypes was effective, but it does not lead to behavioral isolation in D. ananassae. Rather, it induces differences in mating propensity, which is influenced by sternopleural bristle phenotypes.

A Bootstrap Method for Conducting Statistical Inference with Clustered Data

AbstractU.S. state politics researchers often analyze data with observations grouped into clusters. This structure commonly produces unmodeled correlation within clusters, leading to downward bias in the standard errors of regression coefficients. Estimating robust cluster standard errors (RCSE) is a common approach to correcting this bias. However, despite their frequent use, recent work indicates that RCSE can also be biased downward. Here the author provides evidence of that bias and offers a potential solution. Through Monte Carlo simulation of an ordinary least squares (OLS) regression model, the author compares conventional standard error (OLS-SE) and RCSE performance to that of a bootstrap method that resamples clusters of observations (BCSE). The author shows that both OLS-SEandRCSE are biased downward, with OLS-SE being the most biased. In contrast, BCSE are not biased and consistently outperform the other two methods. The author concludes with three replications from recent work and offers recommendations to researchers.

Comparing methods for analyzing overdispersed count data in aquatic toxicology

Endpoints in aquatic toxicity tests can be measured using a variety of measurement scales including dichotomous (survival), continuous (growth) and count (number of young). A distribution is assumed for an endpoint and analyses proceed accordingly. In certain situations, the assumed distribution may be incorrect and this may lead to incorrect statistical inference. The present study considers the analysis of count effects, here motivated by the Ceriodaphnia dubia reproduction study. While the Poisson probability model is a common starting point, this distribution assumes that the mean and variance are the same. This will not be the case if there is some extraneous source of variability in the system, and in this case, the variability may exceed the mean. A computer simulation study was used to examine the impact of overdispersion or outliers on the analysis of count data. Methods that assumed Poisson or negative binomially distributed outcomes were compared to methods that accommodated this potential overdispersion using quasi-likelihood (QL) or generalized linear mixed models (GLMM). If the data were truly Poisson, the adjusted methods still performed at nominal type I error rates. In the cases of overdispersed counts, the Poisson assumed methods resulted in rejection rates that exceeded nominal levels and standard errors for regression coefficients that were too narrow. The negative binomial methods worked best in the case when the data were, in fact, negative binomial but did not maintain nominal characteristics in other situations. In general, the QL and GLMM methods performed reasonably based on the present study, although all procedures suffered some impact in the presence of potential outliers. In particular, the QL is arguably preferred because it makes fewer assumptions than the GLMM and performed well over the range of conditions considered.

Comments on a Note on Permutation Tests of Significance for Multiple Regression Coefficients by Long, et al.

It is noted that a recent paper in the Journal may give a misleading impression of the robustness of classical regression methods. First, the authors show that p-values based on the randomization distributions of regression coefficients may be quite different from p-values based on t-distributions. However, there is no reason why these two types of p-value should be exactly the same, and p-values based on the randomization distributions of t-statistics are usually similar to p-values obtained from t-distributions. These latter p-values are perfectly valid for the purposes of randomization tests. Second, the authors imply that estimating the standard errors of regression coefficients by randomizing the order of the Y values gives better estimates of standard errors than standard theory. In fact these standard errors based on randomization will tend to be too large unless the regression equation accounts for none of the variation in the Y values.

Power determination for geographically clustered data using generalized estimating equations.

Study designs in public health research often require the estimation of intervention effects that have been applied to a cluster of subjects in a common geographic area, rather than randomly assigned to individual subjects, and where the outcome is dichotomous. Statistical methods that account for the intracluster correlation of measurements must be used or the standard errors of regression coefficients will be under-estimated. Generalized estimating equations (GEE) can be used to account for this correlation, although there are no straightforward methods to determine sample-size requirements for adequate power. A simulation study was performed to calculate power in a GEE model for a proposed study of the effect of an intervention, designed to reduce lower-back injuries among nursing personnel employed in nursing homes. Nursing homes will be randomly assigned to either an intervention or control group and all employees within a nursing home will be treated alike. Historical injury data indicates that the baseline-injury risk for each home can be reasonably modelled using a beta distribution. It is assumed that the risk for any individual nurse within a nursing home follows a Bernoulli probability distribution expressed as a logit function of fixed covariates, which have values of odds ratios determined from previous studies which represent characteristics of the study population, and a random-intercept term which is specific for each home. Results indicate that failure to account for intracluster correlation can lead to overestimates of power as well as inflation of type I error by as much as 20 per cent. Although the GEE method accounted for the intracluster correlation when present, estimates of the intracluster correlation were negatively biased when no intracluster correlation was present. In addition, and possibly related to the negatively biased estimates of intracluster correlation, we also found inflated type I error estimates from the GEE method.

Efficiency of robust standard errors for regression coefficients

The standard errors of least squares regression coefficients can be estimated in such a way as to be robust to heteroscedasticity of errors. The possible inefficiency of these robust standard errors is investigated and illustrated. A compromise standard error calculation, based on local smoothing of squared residuals, is also analyzed.

The effects of number of samples and random error on the factor analysis/multiple regression (FA/MR) receptor modeling technique

The effects of normally distributed random errors and of sample size on the stability of FA/MR results were examined as applied to a data set from the ATEOS studies. Three levels of normally distributed random errors were added to the original data set to produce five perturbed data sets for FA testing and a total of 10 for testing the MR results. Reductions of sample size from 138 cases to 70 and 35 cases (24-h daily samples) were performed both randomly and systematically. The addition of random errors reduced squared multiple correlation coefficients to the same extent for different sample sizes. The effect of a reduction in sample had a more significant impact on the standard errors of regression coefficients than did added random errors of up to ± 30% of the measured independent variables. Reducing the data sets to 70 and 35 cases resulted in nonsignificant coefficients for a variable whose t-value was relatively small in the data set with 138 cases. This analysis demonstrated the usefulness of the degrees of freedom criteria suggested by Henry (1984, Atmospheric Environment 18, 1507–1515) for minimum sample size in multivariate analysis. The results also showed that data sets with smaller sample sizes tend to give larger R 2 s than the data sets with larger samples sizes, due to their fewer degrees of freedom. It is recommended that the relative significance of parameters that can contribute to the variance of the data set be investigated.

Liquid scintillation counting for 14C uptake of single algal cells isolated from natural samples

Short term rates of 14C uptake for single cells and small numbers of isolated algal cells of five phytoplankton species from natural populations were measured by liquid scintillation counting. Regression analysis of uptake rates per cell for cells isolated from unialgal cultures of seven species of dinoflagellates, ranging in volume from ca. 103 to 107 µm3, gave results identical to uptake rates per cell measured by conventional 14C techniques. Relative standard errors of regression coefficients ranged between 3 and 10%, indicating that for any species there was little variation in photosynthesis per cell.

The Student's t Test in Multiple Regression Under Simple Collinearity

This paper is concerned with the validity of the conventional t tests on regression coefficients when there is serious multicollinearity between the explanatory variables. It is well known that increasing multicollinearity causes the true standard errors of regression coefficients to rise. The crucial question, however, is whether the conventional formulas will in practice reflect this rise. The purpose of this note is to show that the conventional t tests will in practice reflect this rise. But this note also points out the danger involved in mechanically dropping variables from multiple regression equations by t tests because t values of the regression coefficients may not be significantly different from zero when the true (population) values of these coefficients are in fact not zero, if the explanatory variables are highly intercorrelated.

Balanced Repeated Replications for Standard Errors

Abstract Balanced repeated replications (BRR) is a general method for computing standard errors. It is useful when mathematical distribution theory is impractical or lacking, and especially for analytical statistics based on complex samples where clustering destroys the independence of observations. Presented are results of methods used to measure standard errors of regression coefficients for several multivariate techniques. The basic designs of the several samples comprised two primary selections (PS) per stratum. Each replication was a half-sample, created by selecting one PS from each stratum. The variance of the coefficient , estimated from the entire sample, is measured by , where bj is the same estimator based on a half-sample. To increase the precision of the variance estimate, select k repeated replications and obtain the mean of the k computed variances, . Balanced repeated replications reduce the number of repetitions needed; e.g., 48 balanced replications sufficed for 47 strata in our samples. Though proofs are complete only for linear statistics, rationale and results are offered to indicate that BRR provides needed estimates of errors for nonlinear statistics. The ratios, , of actual standard errors to those of simple random sampling, (srs), are investigated for several statistics in five empirical studies. In each study the average values of exceed 1.00 and range from 1.05 for less clustered to 1.46 for more clustered samples.

Balanced Repeated Replications for Standard Errors

Abstract Balanced repeated replications (BRR) is a general method for computing standard errors. It is useful when mathematical distribution theory is impractical or lacking, and especially for analytical statistics based on complex samples where clustering destroys the independence of observations. Presented are results of methods used to measure standard errors of regression coefficients for several multivariate techniques. The basic designs of the several samples comprised two primary selections (PS) per stratum. Each replication was a half-sample, created by selecting one PS from each stratum. The variance of the coefficient , estimated from the entire sample, is measured by , where bj is the same estimator based on a half-sample. To increase the precision of the variance estimate, select k repeated replications and obtain the mean of the k computed variances, . Balanced repeated replications reduce the number of repetitions needed; e.g., 48 balanced replications sufficed for 47 strata in our samples....