Correlation coefficient, predictive model comparisons

Figure 4.14. Predictions of the multi-variate SR model for Re, = 90 and Sc = (1, 1/8) with collinear mean scalar gradients and no backscatter (cb = 0). For these initial conditions, the scalars are uncorrelated pap(0) = gap(0) = 0. The correlation coefficient for the dissipation range, pD, is included for comparison with pap. 

ASM), contrast (CON), entropy (ENT), homogeneity (HOM), and correlation (COR) a mnltiple-layer feed-forward nenral network model was established to predict the three mechanical parameters. These investigators obtained a correlation coefficient above 0.84 in comparison to a conventional method. Also, heated-oil qnalities (acid value, total polar component, and viscosity) were qnantitatively predicted nsing the VIS-NIR hyperspectral analysis and partial least sqnares calibration models (Kazemi et al., 2005). The values for all the quality parameters were above 0.92, indicating a good prediction. 

Comparison of Immunoassay with GC/MS Analysis. The relation between atrazlne concentration determined by GC/MS analysis and trlazlne concentration determined from immunoassay analysis on 127 samples is shown in figure 3. Samples with immunoassay results larger than 5 ug/L are not plotted. Although the two determinations are highly correlated (rank correlation coefficient is 0.90 p<0.0001) the relation is not linear over the 0.2 ug/L to 5 ug/L range of the immunoassay results. Linear and multiple-linear regression models were fitted to the data to enable prediction of atrazlne concentrations from the immunoassay data. 

In addition to the experimental data, the partitioning behavior of MMA between water and CO2 has been modeled. The Peng-Robinson equation of state combined with various mixing rules as described in Section 14.4.1 has been assessed on the ability to correlate phase equilibrium data from literature of the binary subsystems CO2-H2O, MMA-CO2 and MMA-H2O. Subsequently, the model has been used to predict the phase equilibrium behavior of the ternary system CO2-H2O-MMA. Partition coefficients were calculated at four different temperatures at pressures ranging from 5 to 10 MPa. In order to provide a means for comparison, the experimentally determined partition coefficients obtained in the high-pressure extraction unit were used to evaluate the results of the predictive model for phase equilibrium behavior. 

In this final section, we will consider the comparison of two predictive models. The cheminformatics literature is replete with papers comparing predictive models. When developing a new method, it is always important to examine how the method compares with the current state of the art. However, when making comparisons, one must remember that correlations have an associated error. This error is a function of both the correlation coefficient and the number of data points used to obtain the correlation coefficient. When comparing correlation coefficients, we must not only consider the value of the correlation coefficient, but also the confidence intervals around the correlation coefficient. When we have a larger number of data points or a higher correlation coefficient, we are more confident in the correlation and our confidence interval is relatively narrow. When we have a smaller number of data points or our correlation coefficient is lower, the confidence interval around the correlation is larger. If the confidence intervals of two correlations overlap, we cannot claim that one predictive model is superior to another. 

DRAGON descriptors and the combination MOE/PARASURF show the best correlations between predicted and experimental data. In the second step, the comparison of different machine learning algorithms was performed in combination with descriptors calculated by MOE and PARASURF. It turned out that the predictiv-ity improves by the correction approaches available within Cubist. If the model predictions are corrected based on a kNN approach with five neighbors giving best results, correlation coefficients rise to 0.97 for r (train) and 0.47 for r (test) compared... 

Figure 2. Comparison between experimental and model-predicted conversions for 2.5% Pd catalyst using the modified mass transfer coefficient correlations.

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