Tests of Significance in Forward Selection Regression With an<i>F</i>-to-Enter Stopping Rule

Wilkinson, Leland; Dallal, Gerard E.

doi:10.1080/00401706.1981.10487682

Cited by 23 publications

(5 citation statements)

References 11 publications

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“…Using a stepwise regression method [ 21 , 22 ], we identified the relevant predictors for the model. When restricted to a linear model without interactions, we found that the model prediction was not sufficient.…”

Section: Discussionmentioning

confidence: 99%

“…As potential predictors, we considered RC a , RC p , and CCT (for scenario A), PC (for scenario B), ACD, LT, and PIOLP. The stepwise regression algorithm [ 21 , 22 ] was initialized with a constant model and restricted to first- and second-order terms (linear and quadratic quantities) without interactions. Depending on the significance level ( p value), terms were added (if p ≤ 0.01) or removed (if p ≥ 0.1) from the model.…”

Section: Methodsmentioning

confidence: 99%

“…The final model was defined by the regression coefficients and the respective p values. To evaluate the model performance of the final models, we recorded the root-mean-squared prediction error, the adjusted coefficient of determination R 2 , and the F statistics (F and p value) comparing the final model to the initial constant model [ 21 ].…”

Section: Methodsmentioning

confidence: 99%

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Monte-Carlo simulation for calculating phakic supplementary lenses based on a thick and thin lens model using anterior segment OCT data

Langenbucher,

Cayless,

Kormanyos

et al. 2023

Graefes Arch Clin Exp Ophthalmol

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Background Phakic lenses (PIOLs, the most common and only disclosed type being the implantable collamer lens, ICL) are used in patients with large or excessive ametropia in cases where laser refractive surgery is contraindicated. The purpose of this study was to present a strategy based on anterior segment OCT data for calculating the refraction correction (REF) and the change in lateral magnification (ΔM) with ICL implantation. Methods Based on a dataset (N = 3659) containing Casia 2 measurements, we developed a vergence-based calculation scheme to derive the REF and gain or loss in ΔM on implantation of a PIOL having power PIOLP. The calculation concept is based on either a thick or thin lens model for the cornea and the PIOL. In a Monte-Carlo simulation considering, all PIOL steps listed in the US patent 5,913,898, nonlinear regression models for REF and ΔM were defined for each PIOL datapoint. Results The calculation shows that simplifying the PIOL to a thin lens could cause some inaccuracies in REF (up to ½ dpt) and ΔM for PIOLs with high positive power. The full range of listed ICL powers (− 17 to 17 dpt) could correct REF in a range from − 17 to 12 dpt with a change in ΔM from 17 to − 25%. The linear regression considering anterior segment biometric data and the PIOLP was not capable of properly characterizing REF and ΔM, whereas the nonlinear model with a quadratic term for the PIOLP showed a good performance for both REF and ΔM prediction. Conclusion Where PIOL design data are available, the calculation concept should consider the PIOL as thick lens model. For daily use, a nonlinear regression model can properly predict REF and ΔM for the entire range of PIOL steps if a vergence calculation is unavailable.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Monte-Carlo simulation for calculating phakic supplementary lenses based on a thick and thin lens model using anterior segment OCT data

Langenbucher,

Cayless,

Kormanyos

et al. 2023

Graefes Arch Clin Exp Ophthalmol

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show abstract

“…In practice, they solve a least-squares problem by minimizing the sum of squares of the residuals (prediction errors). Second-order polynomial models can be fitted by using several methods [38][39][40][41][42][43]. In this work, the Forward Stepwise Regression method has been used, which successively incorporates one by one those independent variables that contribute to predicting a dependent variable from the most to the least predictive.…”

Section: Polynomial Models and Fitting Methodsmentioning

confidence: 99%

Modelling of the Acetification Stage in the Production of Wine Vinegar by Use of Two Serial Bioreactors

et al. 2020

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In the scope of a broader study about modelling wine acetification, the use of polynomial black-box models seems to be the best choice. Additionally, the use of two serially arranged bioreactors was expected to result in increased overall acetic acid productivity. This paper describes the experiments needed to obtain enough data for modelling the process and the use of second-order polynomials for this task. A fractional experimental design with central points was used with the ethanol concentrations during loading of the bioreactors, their operation temperatures, the ethanol concentrations at unloading time, and the unloaded volume in the first one as factors. Because using two serial reactors imposed some constraints on the operating ranges for the process, an exhaustive combinatorial analysis was used to identify a working combination of such ranges. The obtained models provided highly accurate predictions of the mean overall rate of acetic acid formation, the mean total production of acetic acid of the two-reactor system, and ethanol concentration at the time the second reactor is unloaded. The operational variables associated with the first bioreactor were the more strongly influential to the process, particularly the ethanol concentration at the time the first reactor was unloaded, the unloaded volume, and the ethanol concentration when loading.

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“…The question arises if there are ways of assessing the significance of new resonances. One criterion is given by the F -test [34] which tests for the significance of new fit parameters, like the Breit-Wigner coupling, or bare coupling of an s-channel resonance state in a K-matrix or dynamical coupled-channel approach. This method has two practical drawbacks: On the one hand, data from different experiments tend to have systematic inconsistencies so that the resulting fits are never good in the statistical sense (e.g., passing a χ 2 test).…”

Section: Introductionmentioning

confidence: 99%

Towards the minimal spectrum of excited baryons

et al. 2019

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In the light baryon sector resonances can be broad and overlapping and are in most cases not directly visible in the cross section data. Automatized model selection techniques that introduce penalties for resonances can be used to determine the minimally needed set of resonances to describe the data. Several possible penalization schemes are compared. As an application we perform a blindfold identification of hyperon resonances in theKN → KΞ reaction based on the Least Absolute Shrinkage and Selection Operator (LASSO) in combination with the Bayesian Information Criterion (BIC). We find ten resonances -out of the 21 above-threshold hyperon resonances with spin J ≤ 7/2 listed by the Particle Data Group. In traditional analyses, it is practically impossible to test the relevance of all resonances and their combinations that may potentially contribute to the reaction. By contrast, the present method proves capable of determining the relevant resonances among a large pool of candidates.

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Tests of Significance in Forward Selection Regression With anF-to-Enter Stopping Rule

Cited by 23 publications

References 11 publications

Monte-Carlo simulation for calculating phakic supplementary lenses based on a thick and thin lens model using anterior segment OCT data

Monte-Carlo simulation for calculating phakic supplementary lenses based on a thick and thin lens model using anterior segment OCT data

Modelling of the Acetification Stage in the Production of Wine Vinegar by Use of Two Serial Bioreactors

Towards the minimal spectrum of excited baryons

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