Dark (version 0.9.9)

P7c: Seven parameter model

Description

The seven parameter model. An exponential decay followed by two linear phases.

Usage

P7c(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
(minutes)	a[4]:	S2
(log lum/ minute)	a[5]:	alpha point
(minutes)	a[6]:	-(S2 + S3)
(log luminance)	a[7]:	beta point

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

P3,P5c,P6c

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

# P7c(TRUE)
# Describes the model

# P7c(a)
# The sum of squared residuals

# P7c(a,x)
# The fitted thresholds for given parameters 'a' and times 'x'