Imagine that your predictor is age ranged from 0-100. Your coefficient is 2. You want to compare your coefficients with 1 as a classical logistic function. Your classical function is exp(x)/1+exp(x). You correct as exp(x-50)/1+exp(x-50) to align the turning point on the middle of predictor range.
Then you perform -integrate- function on both of the above conditions in R.
> integrate(function(x){exp(x-50)/(1+exp(x-50))}, 0, 100)
50 with absolute error < 5.6e-13
> integrate(function(x){exp(2*x-50)/(1+exp(2*x-50))}, 0, 100)
75 with absolute error < 8.3e-13
Is comparison of 75 with 50 useful? What is its interpretation?
*** Another way is to perform ROC post estimation. I do not mean it!
Por su puesto que la curva logistica S es muy útul para explicar el ritmo de crecimiento del sistema productivo por ejemplo, para replantear la aplicación de nuevas estrategias cuando la curva empieza el declive en la grafica de la vida útil de un proceso industrial. Comprender que el crecimiento de un ser humano desde la concepción no es infinito...se estabiliza a los nueve meses, llega a la vida y la madre pudo parir al recien nacido, pero el ser sigue creciendo hasta la madurez y despues, decrece ligeramente hasta que culmina su ciclo de vida.Estos procesos se explicancon la curva logística S
I don't think it s that useful, vague , (not sure what question you wanted answer to through that approach)... you may be interested in information about the relative sensitivity, the precision, or even where the "worthless test" falls? But , perhabs you may wish to plot the curves and compare for closeness to the y axis. The plots will enable you to visualize and compare the cut-off points, and even models for the optima performing classifier. Perhabs iteration approach too.
{There are softwares that can help you get a test of the differences in area under the ROC curve[STATA, R]., and AUC can also be computed using the trapezoidal rule.}
* The Area Under the ROC curve (AUC) is an aggregated metric that evaluates how well a logistic regression model classifies positive and negative outcomes at all possible cutoff points. A measure of the ability of a classifier to distinguish between classes and is used as a summary of the ROC curve. The acceptable ability to classify can range from 0.7 to 1, and the larger it is the better, 0.8 is excellent. I would love to learn from others' input , following.
Abiodun Christian Ibiloye
" perhabs you may wish to plot the curves and compare for closeness to the y axis " --> Yes! I was looking for an equivalent for ROC curve in logistic regression.
Yes, as you mentioned, there is a post estimation command in Stata for ROC estimation after logistic regression (lroc).
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