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Carl
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The GD and ED$_{n\geq2}$ are not respectively nested because one cannot reduce either model to be equal to the other by choosing particular values for their parameters. Now, let us cut to the chase. The gamma distribution has a shape parameter, and SET formulas do not. As a consequence, SET formulas do not fit the derivative of blood plasma concentration, because they lack shape parameters, and gamma distributions, or their convolutions, do in fact fit the derivatives. In the case of drug persistence in the body, without proper derivative fitting, there is no hope of predicting future plasma concentration of drugs using SET heuristics, whereas fitting of derivatives may permit more exact extrapolation. When one plots SET derivatives from actual data fits, the result is a wiggly curve, with one bump for each exponential term, which is pathognomonic for overfitting. For another example of a non-nested models exhibiting problematic AIC values, in that case for $n$ of small to moderate size, see this answer.

The GD and ED$_{n\geq2}$ are not respectively nested because one cannot reduce either model to be equal to the other by choosing particular values for their parameters. Now, let us cut to the chase. The gamma distribution has a shape parameter, and SET formulas do not. As a consequence, SET formulas do not fit the derivative of blood plasma concentration, because they lack shape parameters, and gamma distributions, or their convolutions, do in fact fit the derivatives. In the case of drug persistence in the body, without proper derivative fitting, there is no hope of predicting future plasma concentration of drugs using SET heuristics, whereas fitting of derivatives may permit more exact extrapolation. When one plots SET derivatives from actual data fits, the result is a wiggly curve, with one bump for each exponential term, which is pathognomonic for overfitting.

The GD and ED$_{n\geq2}$ are not respectively nested because one cannot reduce either model to be equal to the other by choosing particular values for their parameters. Now, let us cut to the chase. The gamma distribution has a shape parameter, and SET formulas do not. As a consequence, SET formulas do not fit the derivative of blood plasma concentration, because they lack shape parameters, and gamma distributions, or their convolutions, do in fact fit the derivatives. In the case of drug persistence in the body, without proper derivative fitting, there is no hope of predicting future plasma concentration of drugs using SET heuristics, whereas fitting of derivatives may permit more exact extrapolation. When one plots SET derivatives from actual data fits, the result is a wiggly curve, with one bump for each exponential term, which is pathognomonic for overfitting. For another example of a non-nested models exhibiting problematic AIC values, in that case for $n$ of small to moderate size, see this answer.

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Carl
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This merited a comment by @whuber "... It is indeed possible to parameterize the ED$_2$ family with a scale parameter and two shape parameters; for instance, one could take $\lambda_1$ as an inverse scale parameter, leaving $\lambda_2>\lambda_1$ and $p_1$ as shape parameters. I cannot see any connection whatsoever between such considerations and derivatives unless "derivative" means something unusual in this context...." The response to which was "There is indeed an inefficient mutability of shape for an ED$_2$. Using multiple parameters to emulate a shape parameter is inefficient in the sense that the full range of shapes that a solitary shape parameter offers is not properly rendered.... One can reduce the error of fitting to zero by using a sufficient number of parameters. However.. Consider overfitting a curve with a polynomial. One can reduce the error of fitting to zero by using a sufficient number of parameters. However, unless the physics of the problem is coincidentally an exact polynomial shape, that perfect goodness of fit is meaningless in terms of extrapolation, and the fit may be "wiggly" between the samples fit. That is, overfitting does not tell us what a good model is, and if one does not consider what the slope is between or among samples, the model itself may have achieved a pyrrhic goodness of fit." 

Indeed, ED$_2$ is inflexible enough that exact solutions for four time-samples are sometimes complex field, i.e., not real and not physical. In one study of 413 subjects, eight results (1.9%) with four time-samples solutions had unphysical exponential coefficients

This merited a comment by @whuber "... It is indeed possible to parameterize the ED$_2$ family with a scale parameter and two shape parameters; for instance, one could take $\lambda_1$ as an inverse scale parameter, leaving $\lambda_2>\lambda_1$ and $p_1$ as shape parameters. I cannot see any connection whatsoever between such considerations and derivatives unless "derivative" means something unusual in this context...." The response to which was "There is indeed an inefficient mutability of shape for an ED$_2$. Using multiple parameters to emulate a shape parameter is inefficient in the sense that the full range of shapes that a solitary shape parameter offers is not properly rendered.... One can reduce the error of fitting to zero by using a sufficient number of parameters. However, unless the physics of the problem is coincidentally an exact polynomial shape, that perfect goodness of fit is meaningless in terms of extrapolation, and the fit may be "wiggly" between the samples fit. That is, overfitting does not tell us what a good model is, and if one does not consider what the slope is between or among samples, the model itself may have achieved a pyrrhic goodness of fit." Indeed, ED$_2$ is inflexible enough that exact solutions for four time-samples are sometimes complex field, i.e., not real and not physical. In one study of 413 subjects, eight results (1.9%) with four time-samples solutions had unphysical exponential coefficients

This merited a comment by @whuber "... It is indeed possible to parameterize the ED$_2$ family with a scale parameter and two shape parameters; for instance, one could take $\lambda_1$ as an inverse scale parameter, leaving $\lambda_2>\lambda_1$ and $p_1$ as shape parameters. I cannot see any connection whatsoever between such considerations and derivatives unless "derivative" means something unusual in this context...." The response to which was "There is indeed an inefficient mutability of shape for an ED$_2$. Using multiple parameters to emulate a shape parameter is inefficient in the sense that the full range of shapes that a solitary shape parameter offers is not properly rendered.... One can reduce the error of fitting to zero by using a sufficient number of parameters... Consider overfitting a curve with a polynomial. One can reduce the error of fitting to zero by using a sufficient number of parameters. However, unless the physics of the problem is coincidentally an exact polynomial shape, that perfect goodness of fit is meaningless in terms of extrapolation, and the fit may be "wiggly" between the samples fit. That is, overfitting does not tell us what a good model is, and if one does not consider what the slope is between or among samples, the model itself may have achieved a pyrrhic goodness of fit." 

Indeed, ED$_2$ is inflexible enough that exact solutions for four time-samples are sometimes complex field, i.e., not real and not physical. In one study of 413 subjects, eight results (1.9%) with four time-samples solutions had unphysical exponential coefficients

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Carl
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This merited a comment by @whuber "... It is indeed possible to parameterize the ED$_2$ family with a scale parameter and two shape parameters; for instance, one could take $\lambda_1$ as an inverse scale parameter, leaving $\lambda_2>\lambda_1$ and $p_1$ as shape parameters. I cannot see any connection whatsoever between such considerations and derivatives unless "derivative" means something unusual in this context...." The response to which was "There is indeed an inefficient mutability of shape for an ED$_2$. Using multiple parameters to emulate a shape parameter is inefficient in the sense that the full range of shapes that a solitary shape parameter offers is not properly rendered.... One can reduce the error of fitting to zero by using a sufficient number of parameters. However, unless the physics of the problem is coincidentally an exact polynomial shape, that perfect goodness of fit is meaningless in terms of extrapolation, and the fit may be "wiggly" between the samples fit. That is, overfitting does not tell us what a good model is, and if one does not consider what the slope is between or among samples, the model itself may have achieved a pyrrhic goodness of fit." Indeed, ED$_2$ is inflexible enough that exact solutions for four time-samples are sometimes complex field, i.e., not real and not physical. In one study of 413 subjects, eight results (1.9%) with four time-samples solutions had unphysical exponential coefficients

Now let us consider a non-nested model with respect to that latter equation. The gamma distribution (GD) is given by

Now let us consider a non-nested model with respect to that latter equation. The gamma distribution (GD) is given by

This merited a comment by @whuber "... It is indeed possible to parameterize the ED$_2$ family with a scale parameter and two shape parameters; for instance, one could take $\lambda_1$ as an inverse scale parameter, leaving $\lambda_2>\lambda_1$ and $p_1$ as shape parameters. I cannot see any connection whatsoever between such considerations and derivatives unless "derivative" means something unusual in this context...." The response to which was "There is indeed an inefficient mutability of shape for an ED$_2$. Using multiple parameters to emulate a shape parameter is inefficient in the sense that the full range of shapes that a solitary shape parameter offers is not properly rendered.... One can reduce the error of fitting to zero by using a sufficient number of parameters. However, unless the physics of the problem is coincidentally an exact polynomial shape, that perfect goodness of fit is meaningless in terms of extrapolation, and the fit may be "wiggly" between the samples fit. That is, overfitting does not tell us what a good model is, and if one does not consider what the slope is between or among samples, the model itself may have achieved a pyrrhic goodness of fit." Indeed, ED$_2$ is inflexible enough that exact solutions for four time-samples are sometimes complex field, i.e., not real and not physical. In one study of 413 subjects, eight results (1.9%) with four time-samples solutions had unphysical exponential coefficients

Now let us consider a non-nested model with respect to that latter equation. The gamma distribution (GD) is given by

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Carl
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