Log model

Manning WG, Mullahy J. Estimating log models to transform or not to transform. J Health Econ 2000 20 461-94. 

The constant variance assumption can be relaxed via either a rescaling of the response or a weighted fit (4). Similarly, if an appropriate model is used, the normality assumption may be relaxed (4). For example, with a dichotomous response, a logit-log model may be appropriate (5). Other response patterns (e.g., Poisson) may be fit via a generalized linear model (6). For quantitative responses, it is often most practical to find a rescaling or transformation of the response scale to achieve nearly constant variance and nearly normal responses. Finally, if samples are grouped, then blocks or other experiment design structures must be included in the model (7-12). 

Figure 7-4 The estimated expected excess response due to Hg exposure as a function of the Hg concentration calculated using the linear, square root, and logarithmic (log) model. Source E. Budtz-Jorgensen, Copenhagen University, N. Keiding, Copenhagen University, and P. Grandjean, University of Southern Denmark, unpublished material. May 5, 2000.

Figure 11.2 The residuals of the linear log-log model developed in figure 11.1 as a function of toluene concentration.

A natinal extension of the classical LOG model, in which the orientational dependence of the barrier to reaction is taken into account and which leads to the concept of a cone-of-acceptance which depends on collision energy, was proposed by Smith [1,5] and independently by Levine and Bernstein [6], although, as later pointed ont by Levine [7], these models are similar to that suggested as long ago as in 1932 by Pelzer and Wigner... 

The rapid expansion of horizontal drilling has accelerated the development of numerical methods to calculate the responses of 3D induction logging models that include anisotropic bedding and deviated boreholes with invasion. Indeed, in deviated well with noncylindrical invasion caused by gravity segregation, it is practically impossible to interpret induction responses without 3D modeling. 

Empirical relations relating the abrasion to the shear rate, particle sizes and polymer concentrations were generated using linear, semi-log, and log-log models. The log-log model appeared to best fit the data obtained. The Empirical equations can be utilized to predict abrasion associated with other mud systems. 

Period 1 [PMIO] Period 2 [PMIO] Equation 16.9 Difference Method Equation 16.10 Log Model ... 

Fig. 15. The dissociation cross section (in A ) plotted against the initial molecular state quantum numbers. All the states have approximately the same internal energy. Three sets of points are plotted filled circles correspond to H + H2, filled triangles to Ar + H25 and open circles are values calculated from a line-of-centers (LOG) model.

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