A Comparison of Bias and Mean Squared Error in Parameter Estimates of Interaction Effects: Moderated Multiple Regression versus Error-in-Variables Regression

1996 ◽  
Vol 31 (1) ◽  
pp. 69-94 ◽  
Author(s):  
Lance E. Anderson ◽  
Eugene F. Stone-Romero ◽  
John Tisak
Keyword(s):  
Multiple Regression ◽  
Mean Squared Error ◽  
Interaction Effects ◽  
Parameter Estimates ◽  
Moderated Multiple Regression ◽  
Error In Variables ◽  
Squared Error

Estimating an Autoregressive Current Effects Model of Sales Response when Observations are Aggregated over Time: Least Squares versus Maximum Likelihood

1988 ◽  
Vol 25 (3) ◽  
pp. 301-307
Author(s):  
Wilfried R. Vanhonacker
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Serial Correlation ◽  
Mean Squared Error ◽  
Generalized Least Squares ◽  
Parameter Estimates ◽  
Squared Error ◽  
Positive Serial Correlation ◽  
Serial Correlation Coefficient ◽  
Over Time

Estimating autoregressive current effects models is not straightforward when observations are aggregated over time. The author evaluates a familiar iterative generalized least squares (IGLS) approach and contrasts it to a maximum likelihood (ML) approach. Analytic and numerical results suggest that (1) IGLS and ML provide good estimates for the response parameters in instances of positive serial correlation, (2) ML provides superior (in mean squared error) estimates for the serial correlation coefficient, and (3) IGLS might have difficulty in deriving parameter estimates in instances of negative serial correlation.

scholarly journals PENERAPAN METODE PENDUGAAN AREA KECIL (SMALL AREA ESTIMATION) PADA PENENTUAN PROPORSI RUMAH TANGGA MISKIN DI KABUPATEN KLUNGKUNG

2013 ◽  
Vol 2 (3) ◽  
pp. 35 ◽  
Author(s):  
PUTU EKA ARIWIJAYANTHI ◽  
I WAYAN SUMARJAYA ◽  
TJOKORDA BAGUS OKA
Keyword(s):  
Small Area ◽  
Empirical Bayes ◽  
Mean Squared Error ◽  
Estimation Method ◽  
Parameter Estimates ◽  
Bayes Methods ◽  
Mean Squared Errors ◽  
Direct Estimation ◽  
Squared Error ◽  
Empirical Bayes Methods

Small area is an area with insufficient sample for direct estimation. Limited survey objects, cause direct estimation can not produce better parameter estimates. Based on this, an indirect estimation method called empirical Bayes is used to obtain a better estimate. This study will compare means squared error by  direct estimation method and empirical Bayes method to find a better method on a small area. Jackknife is used to get the means squared error in the empirical Bayes. The results is, empirical Bayes methods give a better parameters based on mean squared errors. Empirical Bayes can produce a smaller mean squared error more than direct estimation in small area.

Multiple imputation with sequential penalized regression

2018 ◽  
Vol 28 (5) ◽  
pp. 1311-1327 ◽  
Author(s):  
Faisal M Zahid ◽  
Christian Heumann
Keyword(s):  
Missing Data ◽  
Sample Size ◽  
Multiple Imputation ◽  
Missing Values ◽  
Mean Squared Error ◽  
Real Life ◽  
Penalized Regression ◽  
Parameter Estimates ◽  
Squared Error ◽  
Software Packages

Missing data is a common issue that can cause problems in estimation and inference in biomedical, epidemiological and social research. Multiple imputation is an increasingly popular approach for handling missing data. In case of a large number of covariates with missing data, existing multiple imputation software packages may not work properly and often produce errors. We propose a multiple imputation algorithm called mispr based on sequential penalized regression models. Each variable with missing values is assumed to have a different distributional form and is imputed with its own imputation model using the ridge penalty. In the case of a large number of predictors with respect to the sample size, the use of a quadratic penalty guarantees unique estimates for the parameters and leads to better predictions than the usual Maximum Likelihood Estimation (MLE), with a good compromise between bias and variance. As a result, the proposed algorithm performs well and provides imputed values that are better even for a large number of covariates with small samples. The results are compared with the existing software packages mice, VIM and Amelia in simulation studies. The missing at random mechanism was the main assumption in the simulation study. The imputation performance of the proposed algorithm is evaluated with mean squared imputation error and mean absolute imputation error. The mean squared error ([Formula: see text]), parameter estimates with their standard errors and confidence intervals are also computed to compare the performance in the regression context. The proposed algorithm is observed to be a good competitor to the existing algorithms, with smaller mean squared imputation error, mean absolute imputation error and mean squared error. The algorithm’s performance becomes considerably better than that of the existing algorithms with increasing number of covariates, especially when the number of predictors is close to or even greater than the sample size. Two real-life datasets are also used to examine the performance of the proposed algorithm using simulations.

scholarly journals Performance evaluation of listwise deletion for impaired datasets in multiple regression-based prediction

2019 ◽  
Vol 15 (2) ◽  
pp. 1009
Author(s):  
Chanintorn Jittawiriyanukoon
Keyword(s):  
Multiple Regression ◽  
Performance Metrics ◽  
Mean Squared Error ◽  
Absolute Error ◽  
Average Error ◽  
Listwise Deletion ◽  
Squared Error ◽  
Analysis Technique ◽  
The Future ◽  
History Of

<span>Multiple Regression-Based Prediction (MRBP) is an emerging calculation to or analysis technique cope with the future by compiling the history of data. The MRBP characteristic will include an approximation for the associations between physical observations and predictions. MRBP is a predictive model, which will be an important source of knowledge in terms of an interesting trend to be followed in the future. However, there is impairment in the MRBP dataset, wherein each form of missing and noisy data has caused an error and is unavailable further analysis. To overcome this unavailability, so that the data analytics can be moved on, two treatment approaches are introduced. First, the given dataset is denoised; next, listwise deletion (LD) is proposed to handle the missing data. The performance of the proposed technique will be investigated by dealing with datasets that cannot be executed. Employing the Massive Online Analysis (MOA) software, the proposed model is investigated, and the results are summarized. Performance metrics, such as mean squared error (MSE), correlation coefficient (COEF), mean absolute error (MAE), root mean squared error (RMSE), and the average error percentage, are used to validate the proposed mechanism. The proposed LD projection is confirmed through actual values. The proposed LD outperforms other treatments as it only requires less state space, which reflects low computation cost, and proves its capability to overcome the limitation of analysis.</span>

Use of reflectance spectroscopy to estimate the organic carbon and CaCO3 contents of soils

2012 ◽  
Vol 61 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Ádám Csorba ◽  
Vince Láng ◽  
László Fenyvesi ◽  
Erika Michéli
Keyword(s):  
Organic Carbon ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Mean Squared Error ◽  
Reflectance Spectroscopy ◽  
Least Squares Regression ◽  
Root Mean Squared Error ◽  
Squared Error

Napjainkban egyre nagyobb igény mutatkozik olyan technológiák és módszerek kidolgozására és alkalmazására, melyek lehetővé teszik a gyors, költséghatékony és környezetbarát talajadat-felvételezést és kiértékelést. Ezeknek az igényeknek felel meg a reflektancia spektroszkópia, mely az elektromágneses spektrum látható (VIS) és közeli infravörös (NIR) tartományában (350–2500 nm) végzett reflektancia-mérésekre épül. Figyelembe véve, hogy a talajokról felvett reflektancia spektrum információban nagyon gazdag, és a vizsgált tartományban számos talajalkotó rendelkezik karakterisztikus spektrális „ujjlenyomattal”, egyetlen görbéből lehetővé válik nagyszámú, kulcsfontosságú talajparaméter egyidejű meghatározása. Dolgozatunkban, a reflektancia spektroszkópia alapjaira helyezett, a talajok ösz-szetételének meghatározását célzó módszertani fejlesztés első lépéseit mutatjuk be. Munkánk során talajok szervesszén- és CaCO3-tartalmának megbecslését lehetővé tévő többváltozós matematikai-statisztikai módszerekre (részleges legkisebb négyzetek módszere, partial least squares regression – PLSR) épülő prediktív modellek létrehozását és tesztelését végeztük el. A létrehozott modellek tesztelése során megállapítottuk, hogy az eljárás mindkét talajparaméter esetében magas R2értéket [R2(szerves szén) = 0,815; R2(CaCO3) = 0,907] adott. A becslés pontosságát jelző közepes négyzetes eltérés (root mean squared error – RMSE) érték mindkét paraméter esetében közepesnek mondható [RMSE (szerves szén) = 0,467; RMSE (CaCO3) = 3,508], mely a reflektancia mérési előírások standardizálásával jelentősen javítható. Vizsgálataink alapján arra a következtetésre jutottunk, hogy a reflektancia spektroszkópia és a többváltozós kemometriai eljárások együttes alkalmazásával, gyors és költséghatékony adatfelvételezési és -értékelési módszerhez juthatunk.

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