P3 {Dark}

Three parameter model.

Description

The three parameter model. A simple exponential decay.

Usage

P3(a, X)

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	(minutes)

X

The times when the model predicts thresholds.

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.

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.

Author(s)

Jeremiah MF Kelly

Faculty of Life Sciences, The University of Manchester, M13 9PL, UK

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'