BoneProfileR (version 4.0)

BP_flexit: Return the flexit for BoneProfileR models

Description

Return a vector with the probabilities. The flexit equation is published in:
Abreu-Grobois, F.A., Morales-Mérida, B.A., Hart, C.E., Guillon, J.-M., Godfrey, M.H., Navarro, E. & Girondot, M. (2020) Recent advances on the estimation of the thermal reaction norm for sex ratios. PeerJ, 8, e8451.
If dose < P then \((1 + (2^K1 - 1) * exp(4 * S1 * (P - x)))^(-1/K1)\)
If dose > P then \(1-((1 + (2^K2 - 1) * exp(4 * S2 * (x - P)))^(-1/K2)\)
with:
$$S1 = (2^(K1 - 1) * S * K1)/(2^K1 - 1)$$ $$S2 = (2^(K2 - 1) * S * K2)/(2^K2 - 1)$$
New in version 4.7-3 and larger:

If \(2^K1\) is too large to be estimated, the approximation \(S1 = S*K1/2\) is used.
Demonstration:
$$S1 = (2^(K1 - 1) * S * K1)/(2^K1 - 1)$$ $$S1 = exp(log((2^(K1 - 1) * S * K1)/(2^K1 - 1)))$$ $$S1 = exp(log(2^(K1 - 1)) + log(S * K1) - log(2^K1 - 1))$$ When \(K1\) is very large, \(2^K1 - 1 = 2^K1\) then $$S1 = exp((K1 - 1) * log(2) + log(S * K1) - K1 * log(2))$$ $$S1 = exp((K1 * log(2) - log(2) + log(S * K1) - K1 * log(2))$$ $$S1 = exp(log(S * K1)- log(2))$$ $$S1 = S * K1 / 2$$ If \(2^K2\) is too large to be estimated, the approximation \(S2 = S*K2/2\) is used.

If \((1 + (2^K1 - 1) * exp(4 * S1 * (P - x)))^(-1/K1)\) is not finite, the following approximation is used:
$$exp((-1/K1)*(K1*log(2)+(4*S1*(P-x))))$$ If \(1-((1 + (2^K2 - 1) * exp(4 * S2 * (x - P)))^(-1/K2)\) is not finite, the following approximation is used:
$$1 - exp((-1/K2)*(K2*log(2)+(4*S2*(x - P))))$$

Usage

BP_flexit(
  x,
  par = NULL,
  P = NULL,
  S = NULL,
  K1 = NULL,
  K2 = NULL,
  Min = 0,
  Max = 1,
  zero = 1e-10,
  error0 = 1e-10,
  error1 = 1 - 1e-10
)

Value

A vector with the probabilities

Arguments

x

The values at which the flexit model must be calculated

par

The vector with P, S, K1, and K2 values

P

P value

S

S value

K1

K1 value

K2

K2 value

Min

Min value for scaled flexit model

Max

Max value for scaled flexit model

zero

Value to replace zero

error0

Value to return if an error is observed toward 0

error1

Value to return if an error is observed toward 1

Author

Marc Girondot

Details

Return the flexit value

Examples

n <- flexit(x=1:100, par=c(P=50, S=0.001, K1=0.01, K2=0.02))
n <- flexit(x=1:100, P=50, S=0.001, K1=0.01, K2=0.02)

1/(1+exp(0.01*4*(50-1:100)))
flexit(1:100, P=50, S=0.01, K1=1, K2=1)