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.

scholarly journals Least Likely Observations in Regression Models for Categorical Outcomes

2002 ◽  
Vol 2 (3) ◽  
pp. 296-300 ◽  
Author(s):  
Jeremy Freese
Keyword(s):  
Logistic Regression ◽  
Regression Models ◽  
Binary Logistic Regression ◽  
Positive Outcome ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Least Squares Regression ◽  
Binary Logistic Regression Model ◽  
Ordered Logistic Regression ◽  
Negative Outcome

This article presents a method and program for identifying poorly fitting observations for maximum-likelihood regression models for categorical dependent variables. After estimating a model, the program leastlikely will list the observations that have the lowest predicted probabilities of observing the value of the outcome category that was actually observed. For example, when run after estimating a binary logistic regression model, leastlikely will list the observations with a positive outcome that had the lowest predicted probabilities of a positive outcome and the observations with a negative outcome that had the lowest predicted probabilities of a negative outcome. These can be considered the observations in which the outcome is most surprising given the values of the independent variables and the parameter estimates and, like observations with large residuals in ordinary least squares regression, may warrant individual inspection. Use of the program is illustrated with examples using binary and ordered logistic regression.

A Calibration Tutorial for Spectral Data. Part 1: Data Pretreatment and Principal Component Regression Using Matlab

1996 ◽  
Vol 4 (1) ◽  
pp. 225-242 ◽  
Author(s):  
Paul Geladi ◽  
Harald Martens
Keyword(s):  
Least Squares ◽  
Spectral Data ◽  
Partial Least Squares ◽  
Regression Models ◽  
Principal Component Regression ◽  
Principal Component ◽  
Ordinary Least Squares ◽  
Least Squares Regression ◽  
Statistical Parameters ◽  
Calibration Samples

Regression and calibration play an important role in analytical chemistry. All analytical instrumentation is dependent on a calibration that uses some regression model for a set of calibration samples. The ordinary least squares (OLS) method of building a multivariate linear regression (MLR) model has strict limitations. Therefore, biased or regularised regression models have been introduced. Some selected ones are ridge regression (RR), principal component regression (PCR) and partial least squares regression (PLS or PLSR). Also, artificial neural networks (ANN) based on back-propagation can be used as regression models. In order to understand regression models more is needed than just a set of statistical parameters. A deeper understanding of the underlying chemistry and physics is always equally important. For spectral data this means that a basic understanding of spectra and their errors is useful and that spectral representation should be included in judging the usefulness of the data treatment. A “constructed” spectrometric example is introduced. It consists of real spectrometric measurements in the range 408–1176 nm for 26 calibration samples and 10 test samples. The main response variable is litmus concentration, but other constituents such as bromocresolgreen and ZnO are added as interferents and also the pH is changed. The example is introduced as a tutorial. All calculations are shown in detail in Matlab. This makes it easy for the reader to follow and understand the calculations. It also makes the calculations completely traceable. The raw data are available as a file. In Part 1, the emphasis is on pretreatment of the data and on visualisation in different stages of the calculations. Part 1 ends with principal component regression calculations. Partial least squares calculations and some ANN results are presented in Part 2.

scholarly journals NIR-chemometric approaches for evaluating carbonization characteristics of hydrothermally carbonized lignin

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sung-Wook Hwang ◽  
Un Taek Hwang ◽  
Kyeyoung Jo ◽  
Taekyeong Lee ◽  
Jinseok Park ◽  
...  
Keyword(s):  
Least Squares ◽  
Infrared Spectra ◽  
Regression Models ◽  
Near Infrared ◽  
Prediction Models ◽  
Hydrothermal Carbonization ◽  
Ordinary Least Squares ◽  
Least Squares Regression ◽  
Near Infrared Spectra ◽  
Mean Square Errors

AbstractThe aim of this study is to establish prediction models for the non-destructive evaluation of the carbonization characteristics of lignin-derived hydrochars as a carbon material in real time. Hydrochars are produced via the hydrothermal carbonization of kraft lignins for 1–5 h in the temperature range of 175–250 °C, and as the reaction severity of hydrothermal carbonization increases, the hydrochar is converted to a more carbon-intensive structure. Principal component analysis using near-infrared spectra suggests that the spectral regions at 2132 and 2267 nm assigned to lignins and 1449 nm assigned to phenolic groups of lignins are informative bands that indicate the carbonization degree. Partial least squares regression models trained with near-infrared spectra accurately predicts the carbon content, oxygen/carbon, and hydrogen/carbon ratios with high coefficients of determination and low root mean square errors. The established models demonstrate better prediction than ordinary least squares regression models.

The Long Shadow of Ferguson: Legitimacy, Legal Cynicism, and Public Perceptions of Police Militarization

2018 ◽  
Vol 65 (2) ◽  
pp. 151-182 ◽  
Author(s):  
Richard K. Moule ◽  
Bryanna Hahn Fox ◽  
Megan M. Parry
Keyword(s):  
Least Squares ◽  
Regression Models ◽  
National Sample ◽  
Ordinary Least Squares ◽  
Public Perceptions ◽  
Least Squares Regression ◽  
Legal Socialization ◽  
Legal Cynicism ◽  
Perceptions Of Police ◽  
Influence Perceptions

This study examines public perceptions of police militarization, specifically whether individuals believe police are too militarized, and support for practices associated with militarization. Drawing on concepts found in the legal socialization literature—legitimacy and legal cynicism—this study tests hypotheses regarding whether these constructs influence perceptions of militarization. Using a national sample of 702 American adults, a series of ordinary least squares regression models are used to analyze the relationships between legitimacy, cynicism, and perceptions of police militarization. Results suggested that higher levels of legitimacy reduced beliefs that police are too militarized while also increasing support for practices associated with militarization. Cynicism increased beliefs that the police are too militarized, but had no effect on support for militarization. Perceptions of militarization are thus influenced by legal socialization.

scholarly journals A Comparative Analysis on Some Estimators of Parameters of Linear Regression Models in Presence of Multicollinearity

2018 ◽  
pp. 1-8
Author(s):  
Warha, Abdulhamid Audu ◽  
Yusuf Abbakar Muhammad ◽  
Akeyede, Imam
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Models ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Linear Regression Models ◽  
Independent Variables ◽  
Different Levels

Linear regression is the measure of relationship between two or more variables known as dependent and independent variables. Classical least squares method for estimating regression models consist of minimising the sum of the squared residuals. Among the assumptions of Ordinary least squares method (OLS) is that there is no correlations (multicollinearity) between the independent variables. Violation of this assumptions arises most often in regression analysis and can lead to inefficiency of the least square method. This study, therefore, determined the efficient estimator between Least Absolute Deviation (LAD) and Weighted Least Square (WLS) in multiple linear regression models at different levels of multicollinearity in the explanatory variables. Simulation techniques were conducted using R Statistical software, to investigate the performance of the two estimators under violation of assumptions of lack of multicollinearity. Their performances were compared at different sample sizes. Finite properties of estimators’ criteria namely, mean absolute error, absolute bias and mean squared error were used for comparing the methods. The best estimator was selected based on minimum value of these criteria at a specified level of multicollinearity and sample size. The results showed that, LAD was the best at different levels of multicollinearity and was recommended as alternative to OLS under this condition. The performances of the two estimators decreased when the levels of multicollinearity was increased.

scholarly journals Depression, Masculine Norm Adherence, and Fathering Behavior

2018 ◽  
Vol 40 (1) ◽  
pp. 48-84 ◽  
Author(s):  
Kevin Shafer ◽  
Brandon Fielding ◽  
Erin K. Holmes
Keyword(s):  
Least Squares ◽  
Father Involvement ◽  
Regression Models ◽  
Ordinary Least Squares ◽  
Positive Control ◽  
Harsh Parenting ◽  
Least Squares Regression ◽  
Independent Effects ◽  
The Impact

While, overall, fathers have become more involved as parents, there may be significant variability in how involved fathers are in the lives of their children. This study examines how paternal depression and masculine norm adherence affect father involvement. Using new data from the Survey of Contemporary Fatherhood ( N = 2,181) and ordinary least squares regression models, we focus on the effect of depression on four measures of fathering behavior, with masculine norm adherence as a moderator. Results indicated that depression and masculinity had independent effects on father involvement. Furthermore, masculinity moderated the effect of depression for warmth, engagement, and use of harsh parenting—but not positive control. These results have important implications for how we think about the impact of depression on parenting and the role of socialized response in understanding fathering outcomes.

Effect of cluster sampling in biomass tables construction: linear regression models

1982 ◽  
Vol 12 (2) ◽  
pp. 255-263 ◽  
Author(s):  
E. F. Briggs ◽  
T. Cunia
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Cluster Sampling ◽  
Least Squares Regression ◽  
Linear Regression Models ◽  
Biomass Component ◽  
Regression Techniques ◽  
Classical Linear Regression

To construct tree biomass tables it is customary to select the sample trees by cluster sampling and then to apply the classical least squares regression techniques under the assumption of simple random sampling. A modified linear regression procedure is proposed for which the assumption of simple random sampling is no longer required. The procedure can be used when (i) the regression of a biomass component on tree characteristics other than biomass can be approximated reasonably well by a linear function and (ii) the number of sample clusters is sufficiently large. Applied to two large cluster samples of trees, where the cluster size is approximately equal to five trees, and compared with the classical linear regression approach, the modified procedure results in biomass tables which arc essentially the same. The confidence intervals, however, are quite different. The classical least squares regression method results in intervals which, on the average, are about 60% as large as those calculated by the modified procedure.

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