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 likelyhood value. They are intended to be optimized using
constrOptim
in the tcplFit
function.
1 2 3 4 5 | 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-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.
The log-likelyhood.
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.
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.
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