Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

Liu, Wei; Lin, Shui Wai; Piegorsch, Walter W.

doi:10.1111/j.1751-5823.2007.00027.x

Cited by 36 publications

(20 citation statements)

References 53 publications

(90 reference statements)

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“…Analysts often plot T s around the meta‐regression line, which helps to capture the meaning of the meta‐regression and to see how well it explains variability in T s (Borman and Grigg, ; Lau et al ., ). Relatively rare to date are meta‐regression plots including confidence bands around the regression line to highlight at what levels of a moderator estimates exceed the null value or some benchmark criterion of clinical significance (Hayter et al ., ; Liu et al ., ). There also are few tools presently available to display patterns from meta‐regressions with multiple moderator factors.…”

Section: A Bivariate Example Moving the Constantmentioning

confidence: 97%

Depicting estimates using the intercept in meta‐regression models: The moving constant technique

Johnson

Huedo‐Medina

2011

Research Synthesis Methods

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In any scientific discipline, the ability to portray research patterns graphically often aids greatly in interpreting a phenomenon. In part to depict phenomena, the statistics and capabilities of meta-analytic models have grown increasingly sophisticated. Accordingly, this article details how to move the constant in weighted meta-analysis regression models (viz. “meta-regression”) in order to illuminate the patterns in such models across a range of complexities. Although it is commonly ignored in practice, the constant (or intercept) in such models can be indispensible when it is not relegated to its usual static role. The moving constant technique makes possible estimates and confidence intervals at moderator levels of interest as well as continuous confidence bands around the meta-regression line itself. Such estimates, in turn, can be highly informative to interpret the nature of the phenomenon being studied in the meta-analysis, especially when a comparison to an absolute or a practical criterion is the goal. Knowing the point at which effect size estimates reach statistical significance or other practical criteria of effect size magnitude can be quite important. Examples ranging from simple to complex models illustrate these principles. Limitations and extensions of the strategy are discussed.

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Section: A Bivariate Example Moving the Constantmentioning

confidence: 97%

Depicting estimates using the intercept in meta‐regression models: The moving constant technique

Johnson

Huedo‐Medina

2011

Research Synthesis Methods

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“…These pointwise confidence intervals are calculated at a value x using the well-known result . Simultaneous confidence intervals that have 95% probability of simultaneously including all true y values are somewhat wider [17].…”

Section: Consistency Checksmentioning

confidence: 99%

Calibration of Nondestructive Assay Instruments: An Application of Linear Regression and Propagation of Variance

Croft¹,

Burr²

2014

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Several nondestructive assay (NDA) methods to quantify special nuclear materials use calibration curves that are linear in the predictor, either directly or as an intermediate step. The linear response model is also often used to illustrate the fundamentals of calibration, and is the usual detector behavior assumed when evaluating detection limits. It is therefore important for the NDA community to have a common understanding of how to implement a linear calibration according to the common method of least squares and how to assess uncertainty in inferred nuclear quantities during the prediction stage following calibration. Therefore, this paper illustrates regression, residual diagnostics, effect of estimation errors in estimated variances used for weighted least squares, and variance propagation in a form suitable for implementation. Before the calibration can be used, a transformation of axes is required; this step, along with variance propagation is not currently explained in available NDA standard guidelines. The role of systematic and random uncertainty is illustrated and expands on that given previously for the chosen practical NDA example.A listing of open-source software is provided in the Appendix.

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“…Liu, Lin, and Piegorsch (2008) review theory and methodology associated with simultaneous confidence bands for linear regression. Scheffé's (1953Scheffé's ( , 1959 familiar method for comparing all contrasts readily extends to the multiple regression context.…”

Section: Introductionmentioning

confidence: 99%

Functional Data Analysis in Ecosystem Research: The Decline of Oweekeno Lake Sockeye Salmon and Wannock River Flow

Ainsworth

Routledge

Cao

2011

JABES

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Functional regression is a natural tool for exploring the potential impact of the physical environment (continuously monitored) on biological processes (often only assessed annually). This paper explores the potential use of functional regression analysis and the closely related functional principal component analysis for studying the relationship between river flow (continuously monitored) and salmon abundance (measured annually). The specific example involves a depressed sockeye salmon population in Rivers Inlet, BC. Particular attention is given to (i) the role of subject matter expertise and cross-validation techniques in guiding decisions on basis functions and smoothing parameters, and (ii) the importance of restricting the time domain for the continuously monitored variable to a scientifically meaningful period of time. In addition, we derive a joint confidence region for the functional regression coefficient function and discuss its use relative to the more commonly used pointwise confidence intervals. The analysis points to a substantial negative correlation between early spring river flow and marine survival of the sockeye salmon that subsequently migrate down the inlet.

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Construction of Exact Simultaneous Confidence Bands for a Simple Linear Regression Model

Cited by 36 publications

References 53 publications

Depicting estimates using the intercept in meta‐regression models: The moving constant technique

Depicting estimates using the intercept in meta‐regression models: The moving constant technique

Calibration of Nondestructive Assay Instruments: An Application of Linear Regression and Propagation of Variance

Functional Data Analysis in Ecosystem Research: The Decline of Oweekeno Lake Sockeye Salmon and Wannock River Flow

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