Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -