Models: Model objective functions

Description Usage Arguments Details Value Constant Model (cnst) Gain-Loss Model (gnls) Hill Model (hill)

Description

These functions take in the dose-response data and the model parameters, and return a likelihood value. They are intended to be optimized using constrOptim in the tcplFit function.

Usage

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tcplObjCnst(p, resp)

tcplObjGnls(p, lconc, resp)

tcplObjHill(p, lconc, resp)

tcplObjCnst(p, resp)

tcplObjGnls(p, lconc, resp)

tcplObjHill(p, lconc, resp)

Arguments

p

Numeric, the parameter values. See details for more information.

resp

Numeric, the response values

lconc

Numeric, the log10 concentration values

Details

These functions produce an estimated value based on the model and given parameters for each observation. Those estimated values are then used with the observed values and a scale term to calculate the log-likelihood.

Let t(z,ν) be the Student's t-distribution with ν degrees of freedom, y[i] be the observed response at the ith observation, and μ[i] be the estimated response at the ith observation. We calculate z[i] as:

z[i] = (y[i] - μ[i])/e^σ

where σ is the scale term. Then the log-likelihood is:

sum_{i=1}^{n} [ln(t(z[i], 4)) - σ]

Where n is the number of observations.

Value

The log-likelihood.

Constant Model (cnst)

tcplObjCnst calculates the likelyhood for a constant model at 0. The only parameter passed to tcplObjCnst by p is the scale term σ. The constant model value μ[i] for the ith observation is given by:

μ[i] = 0

tcplObjCnst calculates the likelyhood for a constant model at 0. The only parameter passed to tcplObjCnst by p is the scale term σ. The constant model value μ[i] for the ith observation is given by:

μ[i] = 0

Gain-Loss Model (gnls)

tcplObjGnls calculates the likelyhood for a 5 parameter model as the product of two Hill models with the same top and both bottoms equal to 0. The parameters passed to tcplObjGnls by p are (in order) top (\mathit{tp}), gain log AC50 (\mathit{ga}), gain hill coefficient (gw), loss log AC50 \mathit{la}, loss hill coefficient \mathit{lw}, and the scale term (σ). The gain-loss model value μ[i] for the ith observation is given by:

g[i] = 1/(1 + 10^(ga - x[i])*gw)

l[i] = 1/(1 + 10^(x[i] - la)*lw)

μ[i] = tp*g[i]*l[i]

where x[i] is the log concentration for the ith observation.

tcplObjGnls calculates the likelyhood for a 5 parameter model as the product of two Hill models with the same top and both bottoms equal to 0. The parameters passed to tcplObjGnls by p are (in order) top (\mathit{tp}), gain log AC50 (\mathit{ga}), gain hill coefficient (gw), loss log AC50 \mathit{la}, loss hill coefficient \mathit{lw}, and the scale term (σ). The gain-loss model value μ[i] for the ith observation is given by:

g[i] = 1/(1 + 10^(ga - x[i])*gw)

l[i] = 1/(1 + 10^(x[i] - la)*lw)

μ[i] = tp*g[i]*l[i]

where x[i] is the log concentration for the ith observation.

Hill Model (hill)

tcplObjHill calculates the likelyhood for a 3 parameter Hill model with the bottom equal to 0. The parameters passed to tcplObjHill by p are (in order) top (\mathit{tp}), log AC50 (\mathit{ga}), hill coefficient (\mathit{gw}), and the scale term (σ). The hill model value μ[i] for the ith observation is given by:

μ[i] = tp/(1 + 10^(ga - x[i])*gw)

where x[i] is the log concentration for the ith observation.

tcplObjHill calculates the likelyhood for a 3 parameter Hill model with the bottom equal to 0. The parameters passed to tcplObjHill by p are (in order) top (\mathit{tp}), log AC50 (\mathit{ga}), hill coefficient (\mathit{gw}), and the scale term (σ). The hill model value μ[i] for the ith observation is given by:

μ[i] = tp/(1 + 10^(ga - x[i])*gw)

where x[i] is the log concentration for the ith observation.


USEPA/CompTox-ToxCast-tcpl documentation built on May 5, 2019, 4:48 p.m.