Estimation of the response-error relationship in immunoassay.

1985 ◽  
Vol 31 (11) ◽  
pp. 1802-1805 ◽  
Author(s):  
W A Sadler ◽  
M H Smith
Keyword(s):  
Least Squares ◽  
Weighting Function ◽  
Likelihood Method ◽  
Least Squares Regression ◽  
Response Error ◽  
Regression Methods ◽  
Response Data ◽  
Least Squares Estimators ◽  
Error Functional ◽  
Functional Forms

Abstract Estimation of the response-error relationship in immunoassay provides a weighting function for the main analysis, and may in general be essential to ensure statistically valid data reduction. In this study we generated 50,000 sets of simulated radioimmunoassay response data with a computer, using five response-error functional forms that are commonly assumed. Parameters were estimated by three least-squares regression methods and three that are modifications of a maximum-likelihood method. Two likelihood estimators that require significantly different computing times were shown to be virtually indistinguishable, statistically more efficient than least-squares estimators, and-in contrast to least-squares estimators-to guarantee positive predicted variances in the range of the data.

scholarly journals An Improvised SIMPLS Estimator Based on MRCD-PCA Weighting Function and Its Application to Real Data

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2211
Author(s):  
Siti Zahariah ◽  
Habshah Midi ◽  
Mohd Shafie Mustafa
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Weighting Function ◽  
Real Data ◽  
Least Squares Regression ◽  
Regression Problem ◽  
Leverage Points ◽  
Explanatory Variables ◽  
Diagnostic Plot ◽  
Data Points

Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where p>>n. The statistically inspired modification of the partial least squares (SIMPLS) is a very popular technique for solving a partial least squares regression problem due to its efficiency, speed, and ease of understanding. The execution of SIMPLS is based on the empirical covariance matrix of explanatory variables and response variables. Nevertheless, SIMPLS is very easily affected by outliers. In order to rectify this problem, a robust iteratively reweighted SIMPLS (RWSIMPLS) is introduced. Nonetheless, it is still not very efficient as the algorithm of RWSIMPLS is based on a weighting function that does not specify any method of identification of high leverage points (HLPs), i.e., outlying observations in the X-direction. HLPs have the most detrimental effect on the computed values of various estimates, which results in misleading conclusions about the fitted regression model. Hence, their effects need to be reduced by assigning smaller weights to them. As a solution to this problem, we propose an improvised SIMPLS based on a new weight function obtained from the MRCD-PCA diagnostic method of the identification of HLPs for HDD and name this method MRCD-PCA-RWSIMPLS. A new MRCD-PCA-RWSIMPLS diagnostic plot is also established for classifying observations into four data points, i.e., regular observations, vertical outliers, and good and bad leverage points. The numerical examples and Monte Carlo simulations signify that MRCD-PCA-RWSIMPLS offers substantial improvements over SIMPLS and RWSIMPLS. The proposed diagnostic plot is able to classify observations into correct groups. On the contrary, SIMPLS and RWSIMPLS plots fail to correctly classify observations into correct groups and show masking and swamping effects.

scholarly journals Variability of Drop Size Distributions: Noise and Noise Filtering in Disdrometric Data

2005 ◽  
Vol 44 (5) ◽  
pp. 634-652 ◽  
Author(s):  
Gyu Won Lee ◽  
Isztar Zawadzki
Keyword(s):  
Least Squares ◽  
Drop Size ◽  
Size Distributions ◽  
Least Squares Regression ◽  
Fractional Difference ◽  
Regression Methods ◽  
Sampling Volume ◽  
Filtering Technique ◽  
Drop Size Distributions ◽  
Result Analysis

Abstract Disdrometric measurements are affected by the spurious variability due to drop sorting, small sampling volume, and instrumental noise. As a result, analysis methods that use least squares regression to derive rainfall rate–radar reflectivity (R–Z) relationships or studies of drop size distributions can lead to erroneous conclusions. This paper explores the importance of this variability and develops a new approach, referred to as the sequential intensity filtering technique (SIFT), that minimizes the effect of the spurious variability on disdrometric data. A simple correction for drop sorting in stratiform rain illustrates that it generates a significant amount of spurious variability and is prominent in small drops. SIFT filters out this spurious variability while maintaining the physical variability, as evidenced by stable R–Z relationships that are independent of averaging size and by a drastic decrease of the scatter in R–Z plots. The presence of scatter causes various regression methods to yield different best-fitted R–Z equations, depending on whether the errors on R or Z are minimized. The weighted total least squares (WTLS) solves this problem by taking into account errors in both R and Z and provides the appropriate coefficient and exponent of Z = aRb. For example, with a simple R versus Z least squares regression, there is an average fractional difference in a and b of Z = aRb of 17% and 14%, respectively, when compared with those derived using WTLS. With Z versus R regression, the average fractional difference in a and b is 19% and 12%, respectively. This uncertainty in the R–Z parameters may explain 40% of the “natural variability” claimed in the literature but becomes negligible after applying SIFT, regardless of the regression methods used.

scholarly journals Penalized least squares regression methods and applications to neuroimaging

NeuroImage ◽  
2011 ◽  
Vol 55 (4) ◽  
pp. 1519-1527 ◽  
Author(s):  
Florentina Bunea ◽  
Yiyuan She ◽  
Hernando Ombao ◽  
Assawin Gongvatana ◽  
Kate Devlin ◽  
...  
Keyword(s):  
Least Squares ◽  
Penalized Least Squares ◽  
Least Squares Regression ◽  
Regression Methods

Determination of carbon fraction and nitrogen concentration in tree foliage by near infrared reflectances: a comparison of statistical methods

1996 ◽  
Vol 26 (4) ◽  
pp. 590-600 ◽  
Author(s):  
Katherine L. Bolster ◽  
Mary E. Martin ◽  
John D. Aber
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Near Infrared ◽  
Data Sets ◽  
Independent Data ◽  
Least Squares Regression ◽  
Near Infrared Reflectance ◽  
Regression Methods

Further evaluation of near infrared reflectance spectroscopy as a method for the determination of nitrogen, lignin, and cellulose concentrations in dry, ground, temperate forest woody foliage is presented. A comparison is made between two regression methods, stepwise multiple linear regression and partial least squares regression. The partial least squares method showed consistently lower standard error of calibration and higher R2 values with first and second difference equations. The first difference partial least squares regression equation resulted in standard errors of calibration of 0.106%, with an R2 of 0.97 for nitrogen, 1.613% with an R2 of 0.88 for lignin, and 2.103% with an R2 of 0.89 for cellulose. The four most highly correlated wavelengths in the near infrared region, and the chemical bonds represented, are shown for each constituent and both regression methods. Generalizability of both methods for prediction of protein, lignin, and cellulose concentrations on independent data sets is discussed. Prediction accuracy for independent data sets and species from other sites was increased using partial least squares regression, but was poor for sample sets containing tissue types or laboratory-measured concentration ranges beyond those of the calibration set.

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