An Introduction to Bootstrap Methods

Stine, Robert A.

doi:10.1177/0049124189018002003

Cited by 295 publications

(184 citation statements)

References 35 publications

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“…The null hypothesis of no conditional indirect effect can be rejected if the CI does not contain 0. As MacKinnon et al (2004) show in the context of simple mediator models with no moderation, the application of a bias correction to a percentile CI can improve its accuracy (for computational details, see Efron, 1987;Efron & Tibshirani, 1998;Lunneborg, 2000;Preacher & Hayes, 2006;Stine, 1989). Later we present and discuss an SPSS macro that can be used to obtain bootstrapped confidence intervals (percentile, biascorrected, and bias-corrected and accelerated) for all of the conditional indirect effects discussed in this article.…”

Section: Using Bootstrapping To Assess Moderated Mediationmentioning

confidence: 98%

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Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions

Preacher

Rucker²,

Hayes

2007

Multivariate Behavioral Research

8,234

6,813

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This article provides researchers with a guide to properly construe and conduct analyses of conditional indirect effects, commonly known as moderated mediation effects. We disentangle conflicting definitions of moderated mediation and describe approaches for estimating and testing a variety of hypotheses involving conditional indirect effects. We introduce standard errors for hypothesis testing and construction of confidence intervals in large samples but advocate that researchers use bootstrapping whenever possible. We also describe methods for probing significant conditional indirect effects by employing direct extensions of the simple slopes method and Johnson-Neyman technique for probing significant interactions. Finally, we provide an SPSS macro to facilitate the implementation of the recommended asymptotic and bootstrapping methods. We illustrate the application of these methods with an example drawn from the Michigan Study of Adolescent Life Transitions, showing that the indirect effect of intrinsic student interest on mathematics performance through teacher perceptions of talent is moderated by student math self-concept.

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Section: Using Bootstrapping To Assess Moderated Mediationmentioning

confidence: 98%

“…MacKinnon et al (2004) showed that such corrections can improve CIs and inferences when used in the context of simple mediation models. For the complex computational details of these corrections to percentile CIs, see Efron (1987), Efron and Tibshirani (1998), Lunneborg (2000), Preacher and Hayes (2006), or Stine (1989).…”

Section: Bootstrappingmentioning

confidence: 99%

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions

Preacher

Rucker²,

Hayes

2007

Multivariate Behavioral Research

8,234

6,813

View full text Add to dashboard Cite

show abstract

“…The idea behind bootstrapping (the "bootstrap principle") is that the observed distribution of the 6*'s approximates the true distribution of Ö . Thus, this distribution of the 6°'s can be used to gain insight about the true behavior of the estimate (See Stine (1989) for a brief discussion, including the choice of resampling from residuals or from the actual data). Faraway (1990) uses bootstrapping as a method of choosing the bandwidth in kemel regression.…”

Section: Bootstrappingmentioning

confidence: 99%

Model robust regression: combining parametric, nonparametric, and semiparametric methods

Mays

Birch

Starnes

2001

Journal of Nonparametric Statistics

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In obtaining a regression tit to a set of data, ordinary least squares regression depends directly on the parametric model formulated by the researcher. Ifthis model is incorrect, a least squares analysis may be misleading. Altematively, nonparametric regression (kemel or local polynomial regression, for example) has no dependence on an underlying parametric model, but instead depends entirely on the distances between regressor coordinates and the prediction point of interest. This procedure avoids the necessity of a reliable model, but in using no information from the researcher, may Ht to irregular pattems in the data. The proper combination of these two regression procedures can overcome their respective problems. Considered is the situation where the researcher has an idea of which model should explain the behavior of the data, but this model is not adequate throughout the entire range of the data. An extension of partial linear regression and two methods of model robust regression are developed and compared in this context. These methods involve parametric tits to the data and nonparametric tits to either the data or residuals. The two tits are then combined in the most efficient proportions via a mixing parameter. Performance is based on bias and variance considerations.

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“…Where data on an individual were missing, that person was excluded from analysis of that variable. As there is evidence of geographical clustering of ALL (Cuzick and Hills, 1991), confidence intervals (CIs) in the final model were estimated by bootstrapping (Stine, 1990). As the residual deviance may not be distributed as χ 2 , especially in situations such as the present, where the event data are sparse, the goodness-of-fit of the final model was checked by simulation (Bithell et al, 1995).…”

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confidence: 99%

Quantifying the effect of population mixing on childhood leukaemia risk: the Seascale cluster

Dickinson

Parker

1999

Br J Cancer

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Summary A statistical model was developed based on Poisson regression of incidence of childhood leukaemia and non-Hodgkin's lymphoma (NHL) in relation to population mixing among all 119 539 children born to mothers living in Cumbria, north-west England, (excluding Seascale). This model was used to predict the number of cases in Seascale (the village adjacent to the Sellafield nuclear installation) children, born and diagnosed before 1993. After allowing for age, the incidence of acute lymphoblastic leukaemia (ALL) and NHL was significantly higher among children born in areas with the highest levels of population mixing, relative risk (RR) = 11.7 (95% confidence interval (CI) 3.2-43) and was highest among children of incomers. The model predicted up to 3.0 (95% CI 1.3-6.0) cases of ALL/NHL in children born in Seascale compared to six observed and 2.0 (95% CI 1.0-3.4) cases in children resident, but not born, in Seascale compared to two observed. Population mixing is a significant risk factor for ALL/NHL, especially in young children, accounting for over 50% of cases in Cumbria and most cases in Seascale.Keywords: retrospective cohort study; childhood leukaemia; non-Hodgkin's lymphoma; population mixing; Seascale; epidemiology 144British Journal of Cancer (1999) 81(1), 144-151 © 1999 Cancer Research Campaign Article no. bjoc.1999 Received 16 November 1998 Revised 7 January 1999 Accepted 27 January 1999 National Statistics (ONS) and entered onto a computer database . The motherÕs address was grid-referenced and assigned to one of the 171 electoral wards used in the 1991 census. The fathersÕ and mothersÕ counties of birth (or regions of Scotland) were coded (Mason, 1986). Children were grouped into families using algorithms based on parentsÕ names and measures of population mixing and social class in a ward were based on characteristics of parents. Case ascertainmentCancer registrations for the cohort, recorded throughout the UK, were obtained from ONS, from six regional and national cancer registries and from scrutiny of all relevant death registrations, also obtained from ONS Prior to analysis, it was decided to consider (i) all cases of leukaemia and NHL (leukaemia/NHL); (ii) the following subgroups: common ALL (cALL), other ALL, other leukaemias, NHL; and (iii) solid tumours. Follow-upThere is evidence that many leukaemias diagnosed under the age of 1 year are different at a molecular level from other childhood leukaemias, possibly reflecting a different aetiology (Greaves, 1996(Greaves, , 1997 and so these were excluded. Each child was therefore followed up from age 1 year until he or she reached 15 years, died or emigrated, or until the end of 1992, whichever was the earliest. Hence the person-years at risk were calculated (Table 1). Explanatory variablesAt the individual level, a measure of population mixing was derived from the place of birth of the childÕs parents: each child was categorized as having either both, one or neither parent born outside Cumbria. Additional individual characteristics consi...

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An Introduction to Bootstrap Methods

Cited by 295 publications

References 35 publications

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions

Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions

Model robust regression: combining parametric, nonparametric, and semiparametric methods

Quantifying the effect of population mixing on childhood leukaemia risk: the Seascale cluster

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