The cumulative logistic probability plot provides an overview about what the logistic model is fitting.
Like linear regression, a logistic model linearly combines the values of the independent variables to produce a prediction; but the linear predictor is further transformed by the logistic function to give the probability, p, of eve being ON.
A logistic model linearly combines the values of independent variables (in this case, the concentrations, x ki, of regulators 1 to k ) to produce a prediction; the predictor, η i, is then transformed by the logistic function to give the probability, p i, of eve being ON.
We then compared the observed probability of selecting A (PA ) by subjects with the probability predicted by the logistic decision function (Green, Figure 2B).
Overall, 864 of 910 patients (84.0%) were correctly classified by the logistic regression model at a predicted probability cut-off of 0.5; six out of 150 having FN and 758 out of 760 not having FN.
The predicted probabilities generated by the logistic model can be viewed as a continuous indicator to be compared with observed binary response variable.
When considering a new sound of one of these kinds, this processing allows: (i) the identification of the sound category to which it belongs, with regard to the probabilities estimated by the logistic regression model and (ii) its correct placement along several perceptual dimensions.
Group membership probabilities predicted by the logistic regression model with thickness and age regressors were used to construct a ROC curve, and the area under the curve (AUC) and its statistical significance were computed (Wilcoxon rank-sum test with continuity correction).
To determine the threshold value that most closely approached the upper-left corner of the ROC curves, we visually inspected the curves (Fig. 1) and compared them with the probability table generated by the logistic regression analysis inherent in the generation of the ROC curve (table not shown).
This is depicted in Fig. 4 by the logistic function between Z and G, the probabilities, and z and g, the unconstrained parameters.
