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

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.

1 2 3 4 5 6 7 8 9 10 11 | ```
tcplObjCnst(p, resp)
tcplObjGnls(p, lconc, resp)
tcplObjHill(p, lconc, resp)
tcplObjCnst(p, resp)
tcplObjGnls(p, lconc, resp)
tcplObjHill(p, lconc, resp)
``` |

`p` |
Numeric, the parameter values. See details for more information. |

`resp` |
Numeric, the response values |

`lconc` |
Numeric, the log10 concentration values |

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.

The log-likelihood.

`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*

`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.

`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.

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