Probability logistic regression

Yilmaz, I. 2010. Comparison of landslide susceptibility mapping methodologies for Koyulhisar, Turkey conditional probability, logistic regression, artificial neural networks, and support vector machine. Environmental Earth Sciences 61(4) 821—836. 

Another classification technique is logistic regression [76], which is based on the assumption that a sigmoidal dependency exists between the probability of group membership and one or more predictor variables. It has been used [72] to model eye irritation data. 

This classification of bonds allowed the application of logistic regression analysis (LoRA), which proved of particular benefit for arriving at a function quantifying chemical reactivity. In this method, the binary classification (breakable or non-breakable, represented by 1/0, respectively) is taken as an initial probability P0, which is modelled by the following functional dependence (Eqs. 7 and 8) where f is a linear function, and x. are the parameters considered to be relevant to the problem. The coefficients c. are determined to maximize the fit of the calculated probability of breaking (P) as closely as possible to the initial classification (P0). 

An important feature of the logistic regression method is that although the input modelling data (P0) are binary, the calculated probability (P) is a continuous function. 

One method that we have found particularly useful for our purposes is logistic regression analysis (LoRA). In this method, a binary classification is taken as a probability, Pq (given the value 0 or 1) and modelled by the two coupled equations 5 and 6. 

Notably, in logistic regression-like other multivariate analyses-the effects of causal variables can be shown to influence probabilities of outcomes in response variables independently of one another. The likelihood of using a lawn care company is significantly higher for women than men, for example, no matter the income or education of individuals. 

Fig. 15. Relationship between the alfentanil plasma concentrations and the probability of needing naloxone to restore adequate spontaneous ventilation. The diagram at the upper part shows the alfentanil plasma concentrations of the patients who required naloxone (upward deflection) or did not require naloxone (downward deflection). The plasma concentration-effect curve for this clinical endpoint (lower part) was defined from the quantal data shown in the upper diagram using logistic regression. Bars indicate SE of C5o%. (From Ausems ME, Hug CC, Stanski DR, Burm AGE. Plasma concentrations of alfentanil required to supplement nitrous oxide anaesthesia for general surgery. Anaesthesiology 1986 65 362-73, reproduced by permission.)...

Multiple regression as presented so far is for continuous outcome variables y. For binary, categorical and ordinal outcomes the corresponding technique is called logistic regression. Suppose that in our earlier example we defined success to be disease-free for five years then we might be interested identifying those variables/factors at baseline that were predictive of the probability of success. 

Multiple logistic regression analysis A statistical model used to predict the probability of the occurrence of an event using several predictor variables. 

Logistic regression can be defined as the probability p that an event occurs given d explanatory variables x1,x2,...,xd, as follows ... 

Logistic regression modeling is used for predicting the probability of occurrence of an event by fitting data to a logistic curve.28 It describes the relationship between the categorical response variable and one or more continuous variables.29 Such a model can be described in Equation 3 ... 

Logistic regression (LR) [45] is based on the assumption that there is a logistic relationship between the probability of data class membership and one or more descriptors. The probability can be calculated by using... 

In this example, a number of subjects receiving this particular compound in Phase 1 trials experienced rash. To further evaluate the potential relationship between exposure to the new drug and the probability of experiencing rash, a PK/PD logistic regression model is developed to explore and estimate this relationship. The simulated data are described in Table 24.1 and further explained in Section 24.3.2.2. 

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