The objective of the present study was to assess the comparable applicability of orthogonal projections to latent structures (OPLS) statistical model vs traditional linear regression in order to investigate the role of trans cranial doppler (TCD) sonography in predicting ischemic stroke prognosis. The study was conducted on 116 ischemic stroke patients admitted to a specialty neurology ward. The Unified Neurological Stroke Scale was used once for clinical evaluation on the first week of admission and again six months later. All data was primarily analyzed using simple linear regression and later considered for multivariate analysis using PLS/OPLS models through the SIMCA P+12 statistical software package. The linear regression analysis results used for the identification of TCD predictors of stroke prognosis were confirmed through the OPLS modeling technique. Moreover, in comparison to linear regression, the OPLS model appeared to have higher sensitivity in detecting the predictors of ischemic stroke prognosis and detected several more predictors. Applying the OPLS model made it possible to use both single TCD measures/indicators and arbitrarily dichotomized measures of TCD single vessel involvement as well as the overall TCD result. In conclusion, the authors recommend PLS/OPLS methods as complementary rather than alternative to the available classical regression models such as linear regression.
In the prediction of total stock index, we are faced with some parameters as they are uncertain in future and they can undergo changes, and this uncertainty has a few risks, and for a true analysis, the calculations should be performed under risk conditions. One of the evaluation methods under risk and uncertainty conditions is using geometric Brownian motion random differential equation and simulation by Monte Carlo and quasi-Monte Carlo methods as applied in this study. In Monte Carlo method, pseudo-random sequences are used to generate pseudorandom numbers, but in quasi-Monte Carlo method, quasirandom sequences are used with better uniformity and more rapid convergence compared with pseudo-random sequences. The predictions of total stock index and value at risk by this method are better and more exact than Monte Carlo method. This study at first evaluates random differential equation of geometric Brownian motion and its simulation by quasi-Monte Carlo method, and then its application in the predictions of total stock market index and value at risk can be evaluated.
In multiple regression model, regression variables are usually assumed to be independent from each other. When this assumption is not established, the model would be inappropriate and therefore the results might be incorrect. So, biased regression methods are applied. Ridge regression and principal components regression are two methods of biased regression methods. In this paper, Monte Carlo simulation tests were used for estimating coefficients of ridge and principal components regression. These two methods were compared using minimum squared error (MSE).
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