Power of Simulation Extrapolation in Correction of Covariates Measured with Errors
Joseph Njuguna Karomo,
Samuel Musili Mwalili,
Anthony Wanjoya
Issue:
Volume 5, Issue 2, April 2019
Pages:
13-17
Received:
18 April 2019
Accepted:
21 May 2019
Published:
5 June 2019
Abstract: Statistics is one of the most vibrant disciplines where research is inevitable. Most researches in statistics are concerned with the measurement of values of variables in order to make valid conclusions for decision making. Often, researchers do not use the exact values of the variables since it’s difficult to establish the exact value of variables during data collection. This study aimed at using simulation studies to ascertain the power of Simulation Extrapolation (SIMEX) in correcting the bias of coefficients of a logistic regression model with one covariate measured with error. The corrected coefficient values of the model can then be used to predict the exact values of the explanatory variable. The Mean Square Error and the coverage probability were used to test the adequacy of the different model's estimates. The study showed that the use of SIMEX with the quadratic fitting method would give significantly good estimates of the model’s predictors’ coefficients. For further studies, the researcher recommends the study to be done using other models and with multiple covariates measured with errors.
Abstract: Statistics is one of the most vibrant disciplines where research is inevitable. Most researches in statistics are concerned with the measurement of values of variables in order to make valid conclusions for decision making. Often, researchers do not use the exact values of the variables since it’s difficult to establish the exact value of variables...
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Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model
Issue:
Volume 5, Issue 2, April 2019
Pages:
18-26
Received:
1 January 2019
Accepted:
3 June 2019
Published:
12 June 2019
Abstract: Principal component Analysis (PCA) is one of the popular methods used to solve the multicollinearity problem. Researchers in 2014 proposed an estimator to solve this problem in the linear model when there were stochastic linear restrictions on the regression coefficients. This estimator was called the stochastic restricted principal components (SRPC) regression estimator. The estimator was constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator. It ignores the number of components (orthogonal matrix Tr) that the researchers choose to solve the multicollinearity problem in the data matrix (X). This paper proposed four different methods (Lagrange function, the same technique, the constrained principal component model, and substitute in model) to modify the (SRPC) estimator to be used in case of multicollinearity. Finally, a numerical example, an application, and simulation study have been introduced to illustrate the performance of the proposed estimator.
Abstract: Principal component Analysis (PCA) is one of the popular methods used to solve the multicollinearity problem. Researchers in 2014 proposed an estimator to solve this problem in the linear model when there were stochastic linear restrictions on the regression coefficients. This estimator was called the stochastic restricted principal components (SRP...
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