Latent scale linear models for multivariate ordinal responses and analysis by the method of weighted least squares

1987 ◽  
Vol 39 (1) ◽  
pp. 191-210 ◽  
Author(s):  
Hiroyuki Uesaka ◽  
Chooichiro Asano
Keyword(s):  
Least Squares ◽  
Linear Models ◽  
Weighted Least Squares ◽  
Latent Scale

Calibration of stormwater quality regression models: a random process?

2010 ◽  
Vol 62 (4) ◽  
pp. 875-882 ◽  
Author(s):  
A. Dembélé ◽  
J.-L. Bertrand-Krajewski ◽  
B. Barillon
Keyword(s):  
Experimental Data ◽  
Least Squares ◽  
Regression Models ◽  
Linear Models ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Data Sets ◽  
Data Set ◽  
Urban Catchments

Regression models are among the most frequently used models to estimate pollutants event mean concentrations (EMC) in wet weather discharges in urban catchments. Two main questions dealing with the calibration of EMC regression models are investigated: i) the sensitivity of models to the size and the content of data sets used for their calibration, ii) the change of modelling results when models are re-calibrated when data sets grow and change with time when new experimental data are collected. Based on an experimental data set of 64 rain events monitored in a densely urbanised catchment, four TSS EMC regression models (two log-linear and two linear models) with two or three explanatory variables have been derived and analysed. Model calibration with the iterative re-weighted least squares method is less sensitive and leads to more robust results than the ordinary least squares method. Three calibration options have been investigated: two options accounting for the chronological order of the observations, one option using random samples of events from the whole available data set. Results obtained with the best performing non linear model clearly indicate that the model is highly sensitive to the size and the content of the data set used for its calibration.

Analysis of Coded Wire Tag Returns from Commercial Catches

1992 ◽  
Vol 49 (9) ◽  
pp. 1816-1825 ◽  
Author(s):  
R. M. Cormack ◽  
J. R. Skalski
Keyword(s):  
Least Squares ◽  
Linear Models ◽  
Coho Salmon ◽  
Weighted Least Squares ◽  
Oncorhynchus Kisutch ◽  
Normal Distributions ◽  
Constant Variance ◽  
Log Linear ◽  
Zero Counts ◽  
Sample Fraction

Three alternative but equivalent approaches to the analysis of coded wire tag (CWT) data using log-linear models are presented. All three use iteratively weighted least squares to estimate treatment effects in hatchery releases under the assumption that the variance of a count is proportional to its expected value. The commonly made assumption of normal distributions with constant variance for recovery rates is inefficient. Analysis of tag recovery at the most disaggregated level (i.e. the level at which the sample fraction f is measured) is found necessary for valid inferences. Failure to include zero counts in analyses of recovery data is also shown to induce or mask interactions among CWT recoveries. Recoveries of CWT from coho salmon (Oncorhynchus kisutch) are used to illustrate the method of analysis. Coordinated CWT releases to facilitate mixing of stocks is recommended in the design of hatchery studies.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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