Logit method

Prentice, R.L. (1976). A generalization of the probit and logit methods for dose response curves. Biometrics 32 761-768. 

Another transformation of the data is used in the Logit method. A logit is calculated by taking the logarithm of the proportion of organisms affected (p) at a concentration divided by 1 — p. A logit transformation of the data can be used, and the curve fitted by a maximum likelihood method. As with some of the other methods, a dearth of partial kill concentrations requires assumptions by the investigator to calculate an EC or LC value. 

Another widely used curve-fitting algorithm is the four-parameter logistic (4PL), which is a different version of the log-logit method (195,205). 

The concentration of the unknown is then read off the standard curve opposite its B/Bq value. This sigmoid shaped standard curve, because of its linear portion, simplifies data handling. A mathematical transform of the B/Bq vs log dose is shown in Figure 2. This logit of B/Bq vs log dose is a widely used method of standard curve presentation (5,6,7). Logit B/B is defined as follows ... 

The empirical models are based on mathematical functions that mimic the distribution of the standards measured in the assay. They can be based on point to point (interpolation) methods or regression methods. The most widely used empirical models that have been applied to MIP-ILAs include the log-logit model and the four-parameter logistic model. 

During methods evaluation, standard curves should be plotted in several ways, since different plots reveal different reaction characteristics. For example, the bound/free versus concentration plot is very steep at the low concentration end, and may be used to calculate the detection limit of the assay. The sigmoidal plots of bound/total against log concentration clearly show regions of insensitivity (low and high concentration ends) that might not be clearly apparent in the logit-log curve. 

This relationship is established by measurement of samples with known amounts of analyte (calibrators). One may distinguish between solutions of pure chemical standards and samples with known amounts of analyte present in the typical matrix that is to be measured (e.g., human serum). The first situation applies typically to a reference measurement procedure, which is not influenced by matrix effects, and the second case corresponds typically to a field method that often is influenced by matrix components and so preferably is calibrated using the relevant matrix. Calibration functions may be linear or curved, and in the case of immunoassays often of a special form (e.g., modeled by the four-parameter logistic curve) This model (logistic in log x) has been used for both radioimmunoassay and enzyme immunoassay techniques and can be written in several forms as shown (Table 14-1). Nonlinear regression analysis is applied to estimate the relationship, or a logit transforma-... 

The absorbances observed in example from Fig. 1S.8 were fitted by different methods, such as log transformation (Fig. IS.8), logit transformation (Fig. IS.IO) or polynomials (Fig. 15.11). The absorbances expected for the same dilutions were then recalculated by the regression curves given in those figures. 

ESTM NOABORT PRINT=5 MAXEVAL=9999 METHOD=l LAPLACE LIKELIHOOD TABLE ID DV TLLM LLM TLM LM TPOIS POIS LOGIT PPHI PHI PO PN DV EYI VYI EYP VYP DVY ETAl ETA2 ONEHEADER NOPRINT FILE=002.TAB... 

Other statistical methods include the probit, normit, and logit procedures. However, these are not data-collecting but analytical procedures for the estimation of the distribution. They may be used with data collected by the up-and-down or the run-down methods [25]. 

One of several kinds of mathematical relationships can be used to relate dose and effect in order to translate these data to risk estimates at low doses, e.g., linear, quadratic, logit, Weibull, one-hit, multi-hit. Each model is based on certain biochemical and physiological assumptions and has advantages and disadvantages. No one method has been shown to be better than the others. Often they all show a good fit to the experimental data available for different chemicals at higher doses. 

Another way of estimating mean (and median) WT P is to use some parametric method. This involves an assumption that the distribution of yes answers follows a specific probability model. The most commonly employed model in CVM studies is the logit model. The results of the estimation of a simple logit model are found in Table 6.7. Individual data were used for the estimation, and the dummy variable BI DYES takes the value of unity in the case of acceptance of a bid, and zero otherwise. The explanatory variable BID LIRE is simply the bids in thousands of ITL. The estimation was done by the LOGIT command of Limdep 6.0, which implied the use ofthe maximum likelihood (ML) method (see Greene, 1991, p. 484). It is evident from the table that the coefficient of BIDLIRE is... 

In the analysis of the responses, we employed a random utility paradigm implemented via mixed logit and aseertain that the sample displays joint taste intensity distribution for environment friendly produetion methods sueh as organie, integrated erop management and quality eertifieation. The estimated eorrelation strueture was then employed to estimate taste-based market share and mean WTP for eaeh desirable attribute in eaeh share. 

Finally, metallic allotropes with higher coordination numbers have been studied [39,51] and found to be well removed in enthalphy from four-fold coordinated structures below a pressure of 10 Mbar. Here, we report on the geometric optimization and doping properties of the recently proposed purely sp bonded carbon phases [15] and a propotype zeolite structure (sp bonded) called melanoph-logite using the density-functional based tight-binding method (DF-TB) [52,53]. 

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