Bootstrap Standard Errors Research Articles

Multi‐region response to conservation buffers targeted for northern bobwhite

AbstractWe coordinated a large‐scale evaluation of northern bobwhite (Colinus virginianus) population response to establishment of 9‐m to 37‐m linear patches (buffers) of native herbaceous vegetation along row‐crop field margins as part of the Conservation Reserve Program practice Habitat Buffers for Upland Birds (CP33). We compared northern bobwhite covey densities on 1,088 paired row‐crop fields with and without native herbaceous buffers in 13 states during autumn, 2006–2008. We used a 2‐stage random effects modeling approach that incorporates the effective area as an offset in generalized linear mixed models to assess regional relationships among autumn bobwhite covey densities and covariates of field type (i.e., fields with vs. without native herbaceous buffers), ecological region, year, survey week, and contracted vegetative cover (i.e., planting native grasses and forbs vs. establishing through natural regeneration). Covey density was correlated with year and interaction effects of field type and ecological region. The year effect suggested annual variation in covey densities, whereas the field type by ecological region interaction suggested covey response to buffers was dependent on spatial location, likely reflecting differences in buffer establishment, succession, and characteristics of the surrounding landscape among regions. Mean fitted covey density on fields across all survey sites was 0.047 (±0.008 bootstrap standard error [BSE]) and 0.031 coveys/ha (±0.003 BSE) on row‐crop fields with and without herbaceous buffers, respectively. Covey density was greater on fields with buffers relative to matched, comparison fields without buffers in the Mississippi Alluvial Valley (241%;P < 0.001) and both the eastern (123%;P < 0.001) and western (60%;P = 0.01) portions of the Southeastern Coastal Plain region. Covey density was an order of magnitude greater in the central Texas region compared to other regions, but exhibited a small response to native herbaceous buffers, as did density of coveys in the Eastern Tallgrass Prairie and Central Hardwoods regions. Disproportionate response to buffers in the Mississippi Alluvial Valley and Southeastern Coastal Plain suggests native herbaceous habitats might be limiting during autumn in these regions, whereas lack of response in the Eastern Tallgrass Prairie, Central Hardwoods, and central Texas regions suggests that herbaceous habitat either was not limiting or buffers failed to provide adequate requirements for bobwhites during autumn. Selection of other habitats to meet security and thermoregulatory needs might have resulted in lack of response in these regions. Native herbaceous cover provided by buffers can provide critical habitat in row‐crop agricultural systems in some regions, and can contribute to regional population recovery objectives of the Northern Bobwhite Conservation Initiative (NBCI). However, range‐wide NBCI recovery objectives will best be met through multiple conservation practices in row‐crop agricultural systems. © 2013 The Wildlife Society.

Inference using attributable risk for a 2×2 case–control study

Asymptotic variance plays an important role in the inference using interval estimate of attributable risk. This paper compares asymptotic variances of attributable risk estimate using the delta method and the Fisher information matrix for a 2×2 case–control study due to the practicality of applications. The expressions of these two asymptotic variance estimates are shown to be equivalent. Because asymptotic variance usually underestimates the standard error, the bootstrap standard error has also been utilized in constructing the interval estimates of attributable risk and compared with those using asymptotic estimates. A simulation study shows that the bootstrap interval estimate performs well in terms of coverage probability and confidence length. An exact test procedure for testing independence between the risk factor and the disease outcome using attributable risk is proposed and is justified for the use with real-life examples for a small-sample situation where inference using asymptotic variance may not be valid.

Estimation of Arterial Travel Time from Automatic Number Plate Recognition Data

Automatic vehicle identification (AVI) systems are increasingly used for the collection of traffic data in urban and freeway networks. Several methods have been proposed for the estimation of travel times from AVI data, mainly for freeways. The problem of estimation of travel times in urban networks was examined. The main difference between freeway and urban networks is that urban network AVI data are often extremely noisy. A major part of that noise is attributed to vehicles that do not traverse the monitored section directly but stop for various reasons. A mixture model was proposed to capture the underlying states of the measurements of AVI travel times in urban areas. The hypothesis was that travel times are drawn from two (or more) populations, one representing normal movement through the network and one representing vehicles that stop for whatever reason. The method was applied with AVI data (collected through a system for automatic recognition of number plates) from a number of corridors in central Stockholm, Sweden. The model was estimated as a mixture of two lognormal distributions, and bootstrap standard errors were calculated. The results illustrate the robustness of the method and its ability to identify the underlying distribution of the latent populations consistent with the characteristics of each route, while standard methods for outlier removal fail.

A Multivariate Hidden Markov Model for the Identification of Sea Regimes from Incomplete Skewed and Circular Time Series

The identification of sea regimes from environmental multivariate times series is complicated by the mixed linear–circular support of the data, by the occurrence of missing values, by the skewness of some variables, and by the temporal autocorrelation of the measurements. We address these issues simultaneously by a hidden Markov approach, and segment the data into pairs of toroidal and skew-elliptical clusters by means of the inferred sequence of latent states. Toroidal clusters are defined by a class of bivariate von Mises densities, while skew-elliptical clusters are defined by mixed linear models with positive random effects. The core of the classification procedure is an EM algorithm accounting for missing measurements, unknown cluster membership, and random effects as different sources of incomplete information. Moreover, standard simulation routines allow for the efficient computation of bootstrap standard errors. The proposed procedure is illustrated for a multivariate marine time series, and identifies a number of wintertime regimes in the Adriatic Sea.

Bootstrapping GEE models for fMRI regional connectivity

An Alzheimer's fMRI study has motivated us to evaluate inter-regional correlations during rest between groups. We apply generalized estimating equation (GEE) models to test for differences in regional correlations across groups. Both the GEE marginal model and GEE transition model are evaluated and compared to the standard pooling Fisher-z approach using simulation studies. Standard errors of all methods are estimated both theoretically (model-based) and empirically (bootstrap). Of all the methods, we find that the transition models have the best statistical properties. Overall, the model-based standard errors and bootstrap standard errors perform about the same. We also demonstrate the methods with a functional connectivity study in a healthy cognitively normal population of ApoE4+ participants and ApoE4- participants who are recruited from the Adult Children's Study conducted at the Washington University Knight Alzheimer's Disease Research Center.

Poverty and inequality in European regions

The European Union Statistics on Income and Living Conditions (EU-SILC) is the main source of information about poverty and economic inequality in the member states of the European Union. The sample sizes of its annual national surveys are sufficient for reliable estimation at the national level but not for inferences at the sub-national level, failing to respond to a rising demand from policy-makers and local authorities. We provide a comprehensive map of median income, inequality (Gini coefficient and Lorenz curve) and poverty (poverty rates) based on the equivalised household income in the countries in which the EU-SILC is conducted. We study the distribution of income of households (pro-rated to its members), not merely its median (or mean), because we regard its dispersion and frequency of lower extremes (relative poverty) as important characteristics. The estimation for the regions with small sample sizes is improved by the small-area methods. The uncertainty of complex nonlinear statistics is assessed by bootstrap. Household-level sampling weights are taken into account in both the estimates and the associated bootstrap standard errors.

Structured Partisan Competition: A Vote Shares Model of Party Alignments and Realignments*

Objective. This study develops and tests an aggregate “vote shares” model of party alignments and realignments, building a theoretical framework around “structured political composition” (Rabinowitz, Gurian, and Macdonald, 1984, p. 6). The vote shares model conceptualizes party alignments as latent class constructs, or factors, and changes in these latent class constructs as party realignments. Methods. Confirmatory factor analysis (CFA) model with bias corrected bootstrap estimates and standard errors is used where the cases are counties and the variables are aggregate election outcomes. The data come from Kansas from 1900 to 2010. Results. Comparing the findings of the vote‐shares approach to those of Nardulli (2005) and Sundquist (1983) suggests that the vote shares model provides a greater depth of understanding and a more accurate portrait of the timing of realignments and the partisan bias of new alignments in Kansas. The vote shares model also overcomes the major problem of false positives associated with landslide elections, a problem that plagued most previous aggregate voting models. Conclusion. The vote‐shares model of party alignments and realignments provides a viable alternative for analyzing historic and current election returns where the votes are aggregated by a geographically defined government jurisdiction (parish, county, city, or district).

Testing Negative Error Variances

Heywood cases, or negative variance estimates, are a common occurrence in factor analysis and latent variable structural equation models. Though they have several potential causes, structural misspecification is among the most important. This article explains how structural misspecification can lead to a Heywood case in the population, and provides several ways to test whether a negative error variance is a symptom of structural misspecification. The authors consider z-tests based on a variety of standard errors, confidence intervals, bootstrap resampling, and likelihood-ratio-type tests. In their discussion of z-tests, the authors demonstrate which of the standard errors are consistent under different kinds of misspecification. They also introduce new tests based on the scaled chi-square difference: the test on the boundary and the signed root of the scaled chi-square difference. A simulation study assesses the performance of these tests. The authors find that signed root tests and z-tests based on the empirical sandwich and the empirical bootstrap standard errors perform best in detecting negative error variances. They outperform z-tests based on the information matrix or distribution-robust standard errors.

Interpreting a Multivariate Analysis of Functional Neuroimaging Data

Interpreting a Multivariate Analysis of Functional Neuroimaging Data

Reward expectations lead to smoking uptake among depressed adolescents

Aims While the comorbidity between adolescent depression and smoking has been well documented, less is known about why smoking is disproportionately higher among depressed adolescents. Emerging research suggests that reward-related mechanisms may be important to consider. This study sought to determine whether adolescents with higher depression symptoms have greater smoking reward expectations, which in turn, influence smoking progression. Participants The sample was composed of 1393 adolescents participating in a longitudinal survey study of adolescent health behaviors. Design and Measurements In this prospective cohort study, variables were measured via self-report every six months from age 14 to age 17 resulting in six waves of data. Findings Parallel processes latent growth curve modeling indicated that higher depression symptoms across mid to late adolescence predicted a 17% increase in smoking reward expectations ( β = 3.50, z = 2.85, p = 0.004), which in turn predicted a 23% increase in the odds of smoking progression ( β = 0.206, z = 3.29, p = 0.001). The indirect effect was significant with delta method ( β indirect = 0.72, z = 3.09, p = 0.002; 95% CI = 0.26, 1.18) and bootstrap ( β indirect = 0.72, z = 2.10, p = 0.03; 95% CI = 0.05, 1.39) standard errors. Conclusions The study provides novel evidence that expectations of smoking reward facilitate smoking uptake among depressed adolescents. Smoking reward expectations may identify depressed adolescents at risk of smoking. Addressing alternative ways to meet the reward expectations rather than smoking may be an important component to consider in the preventing smoking and promoting smoking cessation among adolescents with elevated depression symptoms.

The Markov Process Model of Labor Force Activity: Extended Tables of Central Tendency, Shape, Percentile Points, and Bootstrap Standard Errors

Abstract This paper updates the Skoog-Ciecka (2001) worklife tables, which used 1997–1998 data, and the Krueger (2005) worklife tables, which used 1998–2004 data. The present paper uses data generated by the methodology Krueger devised in his 2003 PhD dissertation. We have pooled the data beginning January 2005 and continuing through December 2009, a period of five years, using observations matched a year apart. Thus, we have roughly four times the data in the first of the previous studies, and about that of the second. We chose this period for a variety of reasons, including recency, business cycle and trend considerations. The result is the most current and disaggregated set of worklife tables, along with extended probability calculations and statistical measures available to forensic economists.

The Markov Process Model of Labor Force Activity: Extended Tables of Central Tendency, Shape, Percentile Points, and Bootstrap Standard Errors

This paper updates the Skoog-Ciecka (2001) worklife tables, which used 1997–1998 data, and the Krueger (2005) worklife tables, which used 1998–2004 data. The present paper uses data generated by the methodology Krueger devised in his 2003 PhD dissertation. We have pooled the data beginning January 2005 and continuing through December 2009, a period of five years, using observations matched a year apart. Thus, we have roughly four times the data in the first of the previous studies, and about that of the second. We chose this period for a variety of reasons, including recency, business cycle and trend considerations. The result is the most current and disaggregated set of worklife tables, along with extended probability calculations and statistical measures available to forensic economists.

Depression and body composition among older adults

Objectives: Recent investigations have reported an association between depression and geriatric syndromes associated with low body mass, including frailty and osteoporosis. The objective of this study was to explore the relationship between depression and body composition among older adults. Methods: Data were from a case-cohort study (n = 98) of adults aged 60 and older nested within the Baltimore Epidemiologic Catchment Area (ECA) Study. Lifetime depression syndrome was assessed using the Diagnostic Interview Schedule (DIS). Body composition (total and central lean and fat mass) was assessed by dual-energy x-ray absorptiometry (DEXA). The association between depression and body composition was evaluated using linear regression with bootstrap standard errors. Results: Overall, there was no association between depression and total fat or total lean body mass. Among women, depression was associated with reduced central fat (B = −3.6 kg, p < 0.06) and lean (B = −3.3 kg, p < 0.04) mass adjusting for age, race, smoking status, and physical activity. Depression was unrelated to total or central fat or lean mass among men. Conclusions: Depression is associated with significantly lower central fat and lean mass among older women. These findings are consistent with the hypothesis that depression and frailty are interrelated in later life, particularly among women.

Work stressors and impaired sleep: rumination as a mediator.

An association between stress at work and impaired sleep is theoretically plausible and supported by empirical evidence. The current study's main aim was to investigate how the influence of stressors is carried over into the evening and the night. We assume that this relationship is mediated by perseverative cognitions. We tested this assumption in two cross-sectional samples with structural equation modeling, using bootstrapped standard errors to test for significance. Effort–reward imbalance and time pressure were used as stressors, and rumination as a measure for perseverative cognitions. Results show that the stressors are related to perseverative cognitions, and these are related to impaired sleep in both samples. Indirect effects are significant in both samples. With rumination controlled, direct effects of stressors on sleep are only significant in one out of four cases. Thus, there is full mediation in three out of four cases, and partial mediation in the fourth one. Our results underscore the notion that perseverative cognitions are crucial for transferring negative effects of work stressors into private life, including sleep, thus hindering individuals to successfully recover.

Problematic standard errors and confidence intervals for skewness and kurtosis

Many statistics packages print skewness and kurtosis statistics with estimates of their standard errors. The function most often used for the standard errors (e.g., in SPSS) assumes that the data are drawn from a normal distribution, an unlikely situation. Some textbooks suggest that if the statistic is more than about 2 standard errors from the hypothesized value (i.e., an approximate value for the critical value from the t distribution for moderate or large sample sizes when α = 5%), the hypothesized value can be rejected. This is an inappropriate practice unless the standard error estimate is accurate and the sampling distribution is approximately normal. We show distributions where the traditional standard errors provided by the function underestimate the actual values, often being 5 times too small, and distributions where the function overestimates the true values. Bootstrap standard errors and confidence intervals are more accurate than the traditional approach, although still imperfect. The reasons for this are discussed. We recommend that if you are using skewness and kurtosis statistics based on the 3rd and 4th moments, bootstrapping should be used to calculate standard errors and confidence intervals, rather than using the traditional standard. Software in the freeware R for this article provides these estimates.

A semiparametric estimator of the bivariate distribution function for censored gap times

Let (T(1), T(2)) be gap times corresponding to two consecutive events, which are observed subject to random right-censoring. In this paper, a semiparametric estimator of the bivariate distribution function of (T(1), T(2)) and, more generally, of a functional E [φ(T(1),T(2))] is proposed. We assume that the probability of censoring for T(2) given the (possibly censored) gap times belongs to a parametric family of binary regression curves. We investigate the conditions under which the introduced estimator is consistent. We explore the finite sample behavior of the estimator and of its bootstrap standard error through simulations. The main conclusion of this paper is that the semiparametric estimator may be much more efficient than purely nonparametric methods. Real data illustration is included.

Estimation of the impact of diabetes-related complications on health utilities for patients with type 2 diabetes in Ontario, Canada

The goal of this study was to analyze health-related quality of life (HRQL) data from a Canadian population with type 2 diabetes in order to estimate the disutility associated with experiencing a diabetes-related complication. The EQ-5D, a standardized instrument for use as a measure of health outcome, was administered to 1,147 patients in Hamilton, Ontario, with type 2 diabetes. After controlling for age, gender, and duration of diabetes, changes in utility values were estimated by regressing the EQ-5D scores onto binary indicators for the presence of an event. The primary method of analysis was Ordinary Least Squares (OLS) and due to concerns over non-Normality, bootstrap standard errors (SE) were calculated. The analysis included 1,143 participants. Based on the OLS model, reductions in HRQL were associated with duration of diabetes (-0.0015, SE=0.0006), experiencing a myocardial infarction (MI) (-0.059, SE=0.017), amputation (-0.063, SE=0.059), stroke (-0.046, SE=0.023), and kidney failure (-0.102, SE=0.047). This study estimated the reductions in HRQL associated with several important complications commonly experienced in patients with diabetes. The greatest impacts on HRQL were associated with kidney failure and MI. The utility values calculated here can be used to assess the outcome of interventions that reduce these diabetes-related complications and will have a useful impact on future economic evaluations of diabetes management strategies in Canada.

Scaling Roll Call Votes withwnominateinR

This paper presents a software package designed to estimate Poole and Rosenthal W-NOMINATE scores in R. The package uses a logistic regression model to analyze political choice data, usually (though not exclusively) from a legislative setting. In contrast to other scaling methods, W-NOMINATE explicitly assumes probabilistic voting based on a spatial utility function, where the parameters of the utility function and the spatial coordinates of the legislators and the votes can all be estimated on the basis of observed voting behavior. Building on software written by Poole in Fortran, the new <b>wnominate</b> package in R facilitates easier data input and manipulation, generates bootstrapped standard errors, and includes a new suite of graphics functions to display the results. We demonstrate the functionality of this package by conducting a natural experiment using roll calls -- an experiment which is greatly simplified by the data manipulation capabilities of the <b>wnominate</b> package in R.

Bootstrap standard error and confidence intervals for the correlations corrected for indirect range restriction

The standard Pearson correlation coefficient, r, is a biased estimator of the population correlation coefficient, ρ(XY) , when predictor X and criterion Y are indirectly range-restricted by a third variable Z (or S). Two correction algorithms, Thorndike's (1949) Case III, and Schmidt, Oh, and Le's (2006) Case IV, have been proposed to correct for the bias. However, to our knowledge, the two algorithms did not provide a procedure to estimate the associated standard error and confidence intervals. This paper suggests using the bootstrap procedure as an alternative. Two Monte Carlo simulations were conducted to systematically evaluate the empirical performance of the proposed bootstrap procedure. The results indicated that the bootstrap standard error and confidence intervals were generally accurate across simulation conditions (e.g., selection ratio, sample size). The proposed bootstrap procedure can provide a useful alternative for the estimation of the standard error and confidence intervals for the correlation corrected for indirect range restriction.

A new non-randomized multi-category response model for surveys with a single sensitive question: Design and analysis

In this article, we develop a non-randomized multi-category response model for a single sensitive survey question with multiple outcomes. Unlike existing randomized response models, our proposed model does not require any randomizing device and the respondents are merely asked to answer a non-sensitive question. It thus reduces cost, ensures reproducibility of respondents’ answer (i.e., the same respondent gives the same answer if the survey is re-conducted under the non-randomized multi-category model), enhances respondents’ trust on the privacy policy, and motivates respondents’ cooperation. We show maximum likelihood estimates (MLEs) of cell probabilities can be obtained in closed-form. Bootstrap standard errors and confidence intervals (CIs) of the cell probabilities or their functions are then given. Bayesian estimation via the data augmentation algorithm is developed when prior information on the parameters of interest is available. Simulation studies are conducted to evaluate the performance of the MLEs and CI estimates. A real data set from a questionnaire on sexual activities in Korean adolescents is used to illustrate the proposed design and analysis methods.