Dark (version 0.9.9)

P3: Three parameter model.

Description

The three parameter model. A simple exponential decay.

Usage

P3(a, X)

Value

The output depends upon the input. If the input is an array of length 1L or a boolean then a list is returned

Pn

number of parameters

Mod

name of the model

If a parameter array is passed then the sum of residuals squared is calculated. This is used by optim to optimise the parameter estimates.

Passing a parameter array and a series of putative times causes the function to return predicted thresholds.

Arguments

a

An array of parameters;

a:	parameter	Units
	a[1]:	cone threshold
(log lum)	a[2]:	cone coefficient
(log lum)	a[3]:	cone time constant

X

The times when the model predicts thresholds.

Author

Jeremiah MF Kelly

Mumac Ltd, SK7 6NR, GB

Details

This function has three roles, to calculate the thresholds for given parameters a and times X. If missing X, then the function calls the values x and y from the .Globalenv and calculates the sum of residuals squared error (SSE) for a. If a is an array of length 1L or boolean then a description of the model is returned.

The use of the function H rather than an impulse function gives a three-fold increase is speed for the optim function.

References

O. Mahroo and T. Lamb. Recovery of the human photopic electroretinogram after bleaching exposures: estimation of pigment regeneration kinetics. The Journal of Physiology, 554(2):417, 2004.

T. Lamb and E. Pugh. Dark adaptation and the retinoid cycle of vision. Progress in Retinal and Eye Research, 23(3):307-380, 2004.

See Also

P5c,P6c,P7c

Examples

set.seed(1234)
x <- 0:20
a <- c(-1.00,  1.00,  1.00, -0.24,  6.00,  0.20, 13.00)
tmp <- TestData(x, a)
y <- tmp$resid

P3(TRUE)
# Describes the model

P3(a)
# The sum of squared residuals

P3(a,x)
# The fitted thresholds for given parameters 'theta' and times 'x'