Models {GladiaTOX} | R Documentation

## Model objective functions

### Description

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

### Usage

    gtoxObjCnst(p, resp)

    gtoxObjGnls(p, lconc, resp)

    gtoxObjHill(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-likelyhood.

Let t(z,ν) be the Student's t-ditribution 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-likelyhood is:

sum_{i=1}^{n} [ln(t(z[i], 4)) - σ]

Where n is the number of observations.

### Value

The log-likelyhood.

### Constant Model (cnst)

`gtoxObjCnst` calculates the likelyhood for a constant model at 0. The only parameter passed to `gtoxObjCnst` 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)

`gtoxObjGnls` 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 `gtoxObjGnls` 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)

`gtoxObjHill` calculates the likelyhood for a 3 parameter Hill model with the bottom equal to 0. The parameters passed to `gtoxObjHill` 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.

### Examples

    ## Load level 3 data for an assay endpoint ID
    dat <- gtoxLoadData(lvl=3L, type="mc", fld="aeid", val=3L)

    ## Compute fitting log-likelyhood
    gtoxObjCnst(1, dat$resp)

    ## Load level 3 data for an assay endpoint ID
    dat <- gtoxLoadData(lvl=3L, type="mc", fld="aeid", val=2L)

    ## Compute fitting log-likelyhood
    gtoxObjGnls(p=c(rep(0.5,5),1e-3), lconc=dat$logc, resp=dat$resp)

    ## Load level 3 data for an assay endpoint ID
    dat <- gtoxLoadData(lvl=3L, type="mc", fld="aeid", val=3L)

    ## Compute fitting log-likelyhood
    gtoxObjHill(c(rep(0,3), 1e-3), dat$logc, dat$resp)

[Package GladiaTOX version 1.0.0 Index]