A SIMULTANEOUS EQUATIONS MODEL OF THE CAUSE-EFFECT RELATIONSHIPS AMONG BIOLOGICAL VARIABLES: AN ANALYSIS USING POSTPARTUM BEEF COWS

1990 ◽  
Vol 70 (1) ◽  
pp. 287-299
Author(s):  
R. C. GREER ◽  
R. E. SHORT ◽  
R. A. BELLOWS
Keyword(s):  
Least Squares ◽  
Body Condition ◽  
Biological System ◽  
Beef Cows ◽  
Ordinary Least Squares ◽  
Biological Data ◽  
Simultaneous Equations ◽  
Parameter Estimates ◽  
System Of Equations ◽  
Biological Variables

A path diagram, as the basic model of a biological system, was used to explore the possible relationships generating observed correlations among physiological and body-trait responses in beef cows. The implications for statistical model specification and estimation were discussed. The model specified was a simultaneous system of equations with the physiological and body-trait responses constituting the set of endogenous variables; length of postpartum anestrous interval (PPI) was chosen as the physiological response of primary interest. The set of predetermined variables representing basic determinants of the biological system included plane of nutrition and obstetrical assistance experiments. From the generalized least-squares parameter estimates it was concluded that basic determinants in common explained much of the correlation among observed values of the physiological and body-trait responses. The cause-effect relationships included a recursive dependency of PPI upon postpartum body condition score and parturition date. In addition, it was concluded from the results that management decisions and events before the experimental period were more important in explaining variation in PPI than were the experimental treatments. Leading to the further conclusion that ignoring or attempting to randomize over such influences in the experimental design may jeopardize experimental results. The system of equations approach to analysis of biological data makes clear the importance of completely thinking through the problem before the experiment, the limitations of ordinary least-squares procedures and should have applications in other biological systems. Key words: Simultaneous equations analysis, anestrus, beef cows, body condition, return interval

scholarly journals A Monograph on Nonlinear Regression Models

2018 ◽  
Vol 7 (4.10) ◽  
pp. 543
Author(s):  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
C. Narayana ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Nonlinear Models ◽  
Nonlinear Least Squares ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Nonlinear Regression Model ◽  
Nonlinear Regression Models

This research article uses Matrix Calculus techniques to study least squares application of nonlinear regression model, sampling distributions of nonlinear least squares estimators of regression parametric vector and error variance and testing of general nonlinear hypothesis on parameters of nonlinear regression model. Arthipova Irina et.al [1], in this paper, discussed some examples of different nonlinear models and the application of OLS (Ordinary Least Squares). MA Tabati et.al (2), proposed a robust alternative technique to OLS nonlinear regression method which provide accurate parameter estimates when outliers and/or influential observations are present. Xu Zheng et.al [3] presented new parametric tests for heteroscedasticity in nonlinear and nonparametric models.  

Parameter Estimation in Marketing Models in the Presence of Influential Response Data: Robust Regression and Applications

1984 ◽  
Vol 21 (3) ◽  
pp. 268-277 ◽  
Author(s):  
Vijay Mahajan ◽  
Subhash Sharma ◽  
Yoram Wind
Keyword(s):  
Parameter Estimation ◽  
Regression Analysis ◽  
Least Squares ◽  
Robust Regression ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Parameter Estimates ◽  
Response Data ◽  
Marketing Models ◽  
Marketing Data

In marketing models, the presence of aberrant response values or outliers in data can distort the parameter estimates or regression coefficients obtained by means of ordinary least squares. The authors demonstrate the potential usefulness of the robust regression analysis in treating influential response values in marketing data.

scholarly journals Voluntary appointment of independent directors: evidence from Taiwan

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mao-Feng Kao ◽  
Lynn Hodgkinson ◽  
Aziz Jaafar
Keyword(s):  
Corporate Governance ◽  
Least Squares ◽  
Research Work ◽  
Ordinary Least Squares ◽  
Independent Directors ◽  
Parameter Estimates ◽  
Two Stage ◽  
Data Set ◽  
Content Type ◽  
Two Stage Least Squares

Purpose Using a data set of Taiwanese listed firms from 2002 to 2015, this paper aims to examine the determinants to voluntarily appoint independent directors. Design/methodology/approach This study uses panel estimation to exploit both the cross-section and time-series nature of the data. Further, this paper uses Tobit regression, generalized linear model (GLM) in the additional analysis and the two-stage least squares to mitigate for a possible endogeneity issue. Findings The main findings show that Taiwanese firms with large board sizes tend to voluntarily appoint independent directors and firms that already have independent supervisors more willingly to accept additional independent directors onto the board. Furthermore, ownership concentration and institutional ownership are positively associated with the voluntary appointment of independent directors. On the contrary, firms controlled by family members are generally reluctant to voluntarily appoint independent directors. Research limitations/implications The findings are important for managers, shareholders, creditors and policymakers. In particular, when considering the determinants of the voluntary appointment of independent directors, the results indicate that independent supervisors, outside shareholders and institutional investors are significant factors in influencing effective internal and external corporate governance mechanisms. This research work focuses on the voluntary appointment of independent directors. It would be interesting to compare the effectiveness of voluntary appointments with a mandatory appointment within Taiwan and with other jurisdictions. Originality/value This study incrementally contributes to the corporate governance literature in several ways. First, this study extends the earlier research by using a more comprehensive data set of non-financial Taiwanese firms and using alternative methodologies to investigate the determinants of voluntary appointment of independent directors. Second, prior studies tend to neglect the possible issue of using a censored and fractional dependent variable, the proportion of independent directors, which might yield biased and inconsistent parameter estimates when using ordinary least squares regression estimation. Finally, this study addresses the relevant econometric issues by using the Tobit, GLM and the two-stage least squares for a possible endogeneity concern.

Linear regression models for biomass table construction, using cluster samples

1989 ◽  
Vol 19 (5) ◽  
pp. 664-673 ◽  
Author(s):  
Andrew J. R. Gillespie ◽  
Tiberius Cunia
Keyword(s):  
Least Squares ◽  
Regression Models ◽  
Predictor Variable ◽  
Ordinary Least Squares ◽  
Cluster Sampling ◽  
Parameter Estimates ◽  
Least Squares Regression ◽  
Linear Regression Models ◽  
Estimation Procedures ◽  
Biased Estimates

Biomass tables are often constructed from cluster samples by means of ordinary least squares regression estimation procedures. These procedures assume that sample observations are uncorrelated, which ignores the intracluster correlation of cluster samples and results in underestimates of the model error. We tested alternative estimation procedures by simulation under a variety of cluster sampling methods, to determine combinations of sampling and estimation procedures that yield accurate parameter estimates and reliable estimates of error. Modified, generalized, and jack-knife least squares procedures gave accurate parameter and error estimates when sample trees were selected with equal probability. Regression models that did not include height as a predictor variable yielded biased parameter estimates when sample trees were selected with probability proportional to tree size. Models that included height did not yield biased estimates. There was no discernible gain in precision associated with sampling with probability proportional to size. Random coefficient regressions generally gave biased point estimates with poor precision, regardless of sampling method.

Causal Models in Educational Research: Nonrecursive Models

1978 ◽  
Vol 15 (1) ◽  
pp. 81-97 ◽  
Author(s):  
James G. Anderson
Keyword(s):  
Least Squares ◽  
Ordinary Least Squares ◽  
Causal Models ◽  
Modelling Technique ◽  
Reduced Form ◽  
Parameter Estimates ◽  
Model Data ◽  
Reciprocal Causation ◽  
Causal Modelling ◽  
Endogenous Variables

This paper extends the causal modelling technique described in an earlier article (Anderson and Evans, 1974) to nonrecursive causal models that involve feedback and/or reciprocal causation. The problem of identification is discussed and a rule provided that can be used to determine whether or not a unique set of parameter estimates can be found for each equation that makes up the model. Three different procedures are described for estimating the parameters of these equations, namely, ordinary least squares, indirect least squares, and two-stage least squares. A formula is provided for the derivation of the reduced form of the model. The reduced form provides information concerning the total effect of exogenous variables on endogenous variables in the model. Data from an empirical study have been used to illustrate the causal modelling technique that is described.

scholarly journals Methods for fitting equations with two or more non-linear parameters

1976 ◽  
Vol 157 (2) ◽  
pp. 489-492 ◽  
Author(s):  
I A Nimmo ◽  
G L Atkins
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Linear Equations ◽  
Simultaneous Equations ◽  
The Other ◽  
Parameter Estimates ◽  
Non Linear ◽  
Non Linear Equations

1. Descriptions are given of two ways for fitting non-linear equations by least-squares criteria to experimental data. One depends on solving a set of non-linear simultaneous equations, and the other on Taylor's theorem. 2. It is shown that better parameter estimates result when an equation with two or more non-linear parameters is fitted to all the sets of data simultaneously than when it is fitted to each set in turn.

An analysis and comparison of estimation methods for self-referencing equations

2007 ◽  
Vol 37 (8) ◽  
pp. 1472-1484 ◽  
Author(s):  
Chengcai Ni ◽  
Lianjun Zhang
Keyword(s):  
Least Squares ◽  
Mean Squared Error ◽  
Ordinary Least Squares ◽  
Growth And Yield ◽  
Alternative Methods ◽  
Estimation Methods ◽  
Parameter Estimates ◽  
Random Errors ◽  
Mixed Effect ◽  
Individual Tree

Self-referencing equations (SREs) play an important role in modeling stand and individual-tree growth and yield. Over the decades, forest modelers have applied ordinary least-squares (OLS) or generalized least-squares to fit SREs (namely, the SRE method). In this article, we discuss the statistical properties of the SRE method via theoretical and empirical analyses. The SRE method has its disadvantages: (i) the parameter estimates are not the OLS estimates; (ii) the standard errors of the parameters are underestimated; (iii) the model mean squared error is overestimated; and (iv) the model random errors are always correlated and have heterogeneous variances. Thus, statistical inferences based on these model statistics may not be valid. In addition, there is no simple way to overcome these problems, because they arise from the data structures used for model fitting. This study demonstrates that the disadvantages of the SRE method can be circumvented by fitting the corresponding base model, rather than the transformed model, using two alternative methods: dummy variable regression (DVR method) and mixed effect models (MIX method). The DVR and MIX methods can efficiently account for serial autocorrelation and variance heterogeneity and, thus, produce valid model statistics for hypothesis testing and confidence intervals.

scholarly journals A New Approach in Regression Analysis for Modeling Adsorption Isotherms

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Dana D. Marković ◽  
Branislava M. Lekić ◽  
Vladana N. Rajaković-Ognjanović ◽  
Antonije E. Onjia ◽  
Ljubinka V. Rajaković
Keyword(s):  
Least Squares ◽  
Error Function ◽  
Weighted Least Squares ◽  
Equilibrium Concentration ◽  
Ordinary Least Squares ◽  
Parameters Estimation ◽  
Percentage Error ◽  
Parameter Estimates ◽  
Simple Method ◽  
Orthogonal Distance Regression

Numerous regression approaches to isotherm parameters estimation appear in the literature. The real insight into the proper modeling pattern can be achieved only by testing methods on a very big number of cases. Experimentally, it cannot be done in a reasonable time, so the Monte Carlo simulation method was applied. The objective of this paper is to introduce and compare numerical approaches that involve different levels of knowledge about the noise structure of the analytical method used for initial and equilibrium concentration determination. Six levels of homoscedastic noise and five types of heteroscedastic noise precision models were considered. Performance of the methods was statistically evaluated based on median percentage error and mean absolute relative error in parameter estimates. The present study showed a clear distinction between two cases. When equilibrium experiments are performed only once, for the homoscedastic case, the winning error function is ordinary least squares, while for the case of heteroscedastic noise the use of orthogonal distance regression or Margart’s percent standard deviation is suggested. It was found that in case when experiments are repeated three times the simple method of weighted least squares performed as well as more complicated orthogonal distance regression method.

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