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Statistical analysis of second harmonic generation experiments: a phenomenological model

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Statistical analysis of second harmonic generation experiments: a phenomenological model. / Welsh, AH; Mansson, RA; Frey, JG; Danos, L.

In: Chemometrics and Intelligent Laboratory Systems, Vol. 75, No. 1, 28.01.2005, p. 45-54.

Research output: Contribution to journalJournal article

Harvard

Welsh, AH, Mansson, RA, Frey, JG & Danos, L 2005, 'Statistical analysis of second harmonic generation experiments: a phenomenological model', Chemometrics and Intelligent Laboratory Systems, vol. 75, no. 1, pp. 45-54. https://doi.org/10.1016/j.chemolab.2004.05.002

APA

Welsh, AH., Mansson, RA., Frey, JG., & Danos, L. (2005). Statistical analysis of second harmonic generation experiments: a phenomenological model. Chemometrics and Intelligent Laboratory Systems, 75(1), 45-54. https://doi.org/10.1016/j.chemolab.2004.05.002

Vancouver

Welsh AH, Mansson RA, Frey JG, Danos L. Statistical analysis of second harmonic generation experiments: a phenomenological model. Chemometrics and Intelligent Laboratory Systems. 2005 Jan 28;75(1):45-54. https://doi.org/10.1016/j.chemolab.2004.05.002

Author

Welsh, AH ; Mansson, RA ; Frey, JG ; Danos, L. / Statistical analysis of second harmonic generation experiments: a phenomenological model. In: Chemometrics and Intelligent Laboratory Systems. 2005 ; Vol. 75, No. 1. pp. 45-54.

Bibtex

@article{d8ebcfef221c479f80c5ac735348b9b7,
title = "Statistical analysis of second harmonic generation experiments: a phenomenological model",
abstract = "We discuss issues arising in fitting theoretically derived nonlinear models with complex coefficients to data from surface Second Harmonic Generation (SHG) experiments conducted at the air/liquid interface. We explore different parametrisations for the complex parameters and show that the Enter (magnitude and phase angle) parametrisation is preferable to the real and imaginary parts parametrisation, both theoretically and empirically. We emphasise the importance and value of diagnostic plots for evaluating the quality of model fit. We derive approximate standard errors for the parameter estimates and discuss issues of making inference about ratios of parameters. We consider approximate confidence intervals (using the approximate standard errors), profile likelihood intervals, Fieller's method and bootstrap intervals. Fieller's method (and the bootstrap intervals) provide useful information on the value of the simpler approximate confidence intervals. We also propose and implement a likelihood ratio test to assess whether a common model can be fitted to several independent data sets. Finally, the methods are applied to data sets obtained from SHG experiments on L-phenylalanine at the air/water interface and toluene. (C) 2004 Elsevier B.V. All rights reserved.",
keywords = "SURFACE, AIR-WATER-INTERFACE, complex coefficients, nonlinear least squares, likelihood ratio test, EQUILIBRIUM, 2ND HARMONIC-GENERATION, ratios of parameters, confidence intervals, NITROPHENOL",
author = "AH Welsh and RA Mansson and JG Frey and L Danos",
year = "2005",
month = jan,
day = "28",
doi = "10.1016/j.chemolab.2004.05.002",
language = "English",
volume = "75",
pages = "45--54",
journal = "Chemometrics and Intelligent Laboratory Systems",
issn = "0169-7439",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Statistical analysis of second harmonic generation experiments: a phenomenological model

AU - Welsh, AH

AU - Mansson, RA

AU - Frey, JG

AU - Danos, L

PY - 2005/1/28

Y1 - 2005/1/28

N2 - We discuss issues arising in fitting theoretically derived nonlinear models with complex coefficients to data from surface Second Harmonic Generation (SHG) experiments conducted at the air/liquid interface. We explore different parametrisations for the complex parameters and show that the Enter (magnitude and phase angle) parametrisation is preferable to the real and imaginary parts parametrisation, both theoretically and empirically. We emphasise the importance and value of diagnostic plots for evaluating the quality of model fit. We derive approximate standard errors for the parameter estimates and discuss issues of making inference about ratios of parameters. We consider approximate confidence intervals (using the approximate standard errors), profile likelihood intervals, Fieller's method and bootstrap intervals. Fieller's method (and the bootstrap intervals) provide useful information on the value of the simpler approximate confidence intervals. We also propose and implement a likelihood ratio test to assess whether a common model can be fitted to several independent data sets. Finally, the methods are applied to data sets obtained from SHG experiments on L-phenylalanine at the air/water interface and toluene. (C) 2004 Elsevier B.V. All rights reserved.

AB - We discuss issues arising in fitting theoretically derived nonlinear models with complex coefficients to data from surface Second Harmonic Generation (SHG) experiments conducted at the air/liquid interface. We explore different parametrisations for the complex parameters and show that the Enter (magnitude and phase angle) parametrisation is preferable to the real and imaginary parts parametrisation, both theoretically and empirically. We emphasise the importance and value of diagnostic plots for evaluating the quality of model fit. We derive approximate standard errors for the parameter estimates and discuss issues of making inference about ratios of parameters. We consider approximate confidence intervals (using the approximate standard errors), profile likelihood intervals, Fieller's method and bootstrap intervals. Fieller's method (and the bootstrap intervals) provide useful information on the value of the simpler approximate confidence intervals. We also propose and implement a likelihood ratio test to assess whether a common model can be fitted to several independent data sets. Finally, the methods are applied to data sets obtained from SHG experiments on L-phenylalanine at the air/water interface and toluene. (C) 2004 Elsevier B.V. All rights reserved.

KW - SURFACE

KW - AIR-WATER-INTERFACE

KW - complex coefficients

KW - nonlinear least squares

KW - likelihood ratio test

KW - EQUILIBRIUM

KW - 2ND HARMONIC-GENERATION

KW - ratios of parameters

KW - confidence intervals

KW - NITROPHENOL

U2 - 10.1016/j.chemolab.2004.05.002

DO - 10.1016/j.chemolab.2004.05.002

M3 - Journal article

VL - 75

SP - 45

EP - 54

JO - Chemometrics and Intelligent Laboratory Systems

JF - Chemometrics and Intelligent Laboratory Systems

SN - 0169-7439

IS - 1

ER -