| Title: | The Analysis of Dark Adaptation Data |
|---|---|
| Description: | The recovery of visual sensitivity in a dark environment is known as dark adaptation. In a clinical or research setting the recovery is typically measured after a dazzling flash of light and can be described by the Mahroo, Lamb and Pugh (MLP) model of dark adaptation. The functions in this package take dark adaptation data and use nonlinear regression to find the parameters of the model that 'best' describe the data. They do this by firstly, generating rapid initial objective estimates of data adaptation parameters, then a multi-start algorithm is used to reduce the possibility of a local minimum. There is also a bootstrap method to calculate parameter confidence intervals. The functions rely upon a 'dark' list or object. This object is created as the first step in the workflow and parts of the object are updated as it is processed. |
| Authors: | Jeremiah MF Kelly [aut, cre, cph] |
| Maintainer: | Jeremiah MF Kelly <[email protected]> |
| License: | GPL-3 |
| Version: | 0.9.9 |
| Built: | 2025-02-18 06:58:13 UTC |
| Source: | https://github.com/emkayoh/dark |
A series of scripts to find the parameters of dark adaptation.
| Package: | Dark |
| Type: | Package |
| Version: | 0.9.9 |
| Date: | 2016-06-1 |
| License: | GPL-3 |
Dark adaptation is the recovery of visual sensitivity in a dark environment and can be described by a physiological model. This package contains a series of functions to analyse data collected during dark adaptation.
The functions use the Mahroo Lamb and Pugh (MLP) model of dark adaptation. The functions in this package take dark adaptation data and find the parameters of the model that 'best fit' the data.
The functions generate rapid initial objective estimates of data adaptation parameters, a multi-start algorithm to reduce possibility of a local minimum. There is a bootstrap method to calculate parameter confidence intervals. There are also ancillary functions to facilitate the analysis.
The functions rely upon a *dark* list or object. This object is created by the first function and parts are added to the object as it is processed.
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
Maintainer: Jeremiah MF Kelly <[email protected]>
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.
set.seed(1234) Time<- seq(0,20) tmp<- TestData(Time) P<-Start(tmp,1000) MSC<-ModelSelect(tmp, P) tmp2<-BestFit(tmp, MSC) tmp3<-MultiStart(tmp2,10) BootDark(tmp3,50)set.seed(1234) Time<- seq(0,20) tmp<- TestData(Time) P<-Start(tmp,1000) MSC<-ModelSelect(tmp, P) tmp2<-BestFit(tmp, MSC) tmp3<-MultiStart(tmp2,10) BootDark(tmp3,50)
The Akaike information criterion corrected for small sample size is a measure of the relative quality of a model. The AICc is calculated from a 'dark' object.
AICc(obj)AICc(obj)
obj |
A dark object This object must have at least the following elements:
|
The value returned is an indication of the information lost by fitting a particular model to the data, and is only of merit when compared to the value from another model.
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
See https://en.wikipedia.org/wiki/Akaike_information_criterion.
K. Burnham and D. Anderson. Model selection and multi-model inference: a practical information- theoretic approach. Springer, 2002.
Sakamoto, Y., Ishiguro, M., and Kitagawa G. (1986). Akaike Information Criterion Statistics. D. Reidel Publishing Company.
AICc(dark)AICc(dark)
This script takes a dark object, a list of parameters and AICc scores from ModelSelect to chose a model and then return optimised values for the parameter estimates. Analysis of the data can be halted here if wished.
However, a MultiStart check can be useful if it is suspected that a local minimum has been found. Furthermore, BootDark will provide confidence intervals for the parameter estimates.
BestFit(obj, MSC, draw)BestFit(obj, MSC, draw)
obj |
A dark object |
MSC |
A list from the function |
draw |
A flag to indicate whether a figure should be drawn. |
A list with the following elements:
call |
the last function call on the data |
time |
time of observations |
thrs |
thresholds |
resid |
residuals of best model fit |
fit |
fitted thresholds for the optimal model and parameters |
thet |
seed parameters of TestData, null if not TestData |
sse |
sum of squared error used in TestData |
val |
calculated sum of squared errors |
data |
source of the data |
opt |
optimal parameter estimates |
Mod |
optimal model |
Pn |
number of parameters required by the model to fit the data |
AIC |
AICc scores for the three models fitted |
R2 |
an indication of the 'goodness' of fit |
This function makes extensive use of optim.
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
tmp <- TestData(0:20) P<-Start(tmp,100) MSC<-ModelSelect(tmp, P) BestFit(tmp, MSC)tmp <- TestData(0:20) P<-Start(tmp,100) MSC<-ModelSelect(tmp, P) BestFit(tmp, MSC)
A script using bootstrap techniques to calculate confidence intervals for parameter estimates from a 'dark' object.
BootDark(obj, R, graph, progress = F)BootDark(obj, R, graph, progress = F)
obj |
A 'dark' object. |
R |
The number of repeats for the bootstrap calculations. |
graph |
A flag to indicate whether a figure should be drawn. |
progress |
A flag to indicate whether a progress bar should be drawn to the console. This might be preferred if using a large number of repeats. |
The script calculates bootstrap estimates of confidence intervals by sampling the residuals without replacement. The seven parameter model 'P7c' is always used. If 'P3' or 'P5c' have been found elsewhere to be a better fit then this will be confirmed by bootstrapping the 'P7c' model.
Returns a list 'out'
out$time |
times of observations |
out$thrs |
thresholds |
out$opt |
optimised parameter estimates |
out$Mod |
the name of the optimal model |
out$Pn |
number of parameters needed to describe the data |
out$AIC |
the AICc scores for the three models |
out$fit |
fitted values for the optimal parameter estimates |
out$resd |
residuals of the best fits |
out$R2 |
the coefficient of determination |
out$Bootstrap |
bootstrap parameter estimates, 2.5%, 50% and 97.5% |
out$weight |
the reciprocal of the CI |
out$valid |
an indication whether the parameter estimate is valid |
out$data |
the source of the data |
out$call |
updates the call label on the object |
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
B. Efron. Bootstrap methods: another look at the jackknife. The Annals of Statistics, 7(1):1-26, 1979.
B. Efron. Nonparametric estimates of standard error: The jackknife, the bootstrap and other methods. Biometrika, 68(3):589, 1981.
set.seed(1234) Time<- seq(0,20) tmp<- TestData(Time) P<-Start(tmp,1000) MSC<-ModelSelect(tmp, P) tmp2<-BestFit(tmp, MSC) tmp3<-MultiStart(tmp2,10) BootDark(tmp3,50)set.seed(1234) Time<- seq(0,20) tmp<- TestData(Time) P<-Start(tmp,1000) MSC<-ModelSelect(tmp, P) tmp2<-BestFit(tmp, MSC) tmp3<-MultiStart(tmp2,10) BootDark(tmp3,50)
This data was extracted from Figure 1 in Rushton's paradox: rod dark adaptation after flash photolysis, E.N.Pugh Jr. The Journal of Physiology, 1975.
data("dark")data("dark")
dark is a list of 15 items, that are used or created by the functions in this package.
The items are:
$time: the time of observations
$thrs: the thresholds
$fit: thresholds predicted by the model
$resid: residuals between the fitted model and observed data
$R2: the coefficient of determination
$Bootstrap: a table of quantiles (2.5%, 50% and 97.5%) for the parameter estimates from bootstrap methods
$weight: the parameter estimate divided by the 95% quantile range
$valid: an integer array indicating whether the quantile range encloses zero.
$opt: parameter estimates of the optimal model
$Mod: a string describing the optimal model
$Pn: the number of parameters in the optimal model
$AIC: an array with the AICc scores for the three models
$val: sum of residuals squared
$call: the last function call that produced the object
$data: the source of the data
E. Pugh. Rushton's paradox: rod dark adaptation after flash photolysis. The Journal of Physiology, 248(2):413, 1975.
https://physoc.onlinelibrary.wiley.com/doi/abs/10.1113/jphysiol.1975.sp010982
https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1975.sp010982
data(dark) ## load(dark)data(dark) ## load(dark)
A function to remove multiple button presses, i.e. data that has multiple values for the same threshold.
Declutter(tmp, delta)Declutter(tmp, delta)
tmp |
a 'dark' object with at least two elements; tmp$time and tmp$thrs. |
delta |
The minimum time in seconds between responses. Thresholds set within two seconds of each other are discarded apart from the first threshold. |
In early data collected with analogue equipment it was possible for a subject to return multiple button presses when setting just one threshold. This data is characterised by clusters of points within a very short time. This function removes the extra presses. It is rarely needed for data collected from digital equipment.
Returns an object with the same elements as 'tmp' but with object$time and object$thrs altered.
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
set.seed(123) Time <-c(0, 0.02, 1, 2, 3, 3.02, 5, 6, 6.02, 7, 9, 9.02, 11, 12, 12.02, 13, 15, 15.02, 16, 18, 18.02, 20) # with duplicated times set.seed(1234) tmp <- TestData(Time, sse=0.05) ## Not run: plot(tmp$time, tmp$thrs, ylim=c(-4,0)) tmp <- Declutter(tmp) ## Not run: points(tmp$time, tmp$thrs, col='red', pch=16)set.seed(123) Time <-c(0, 0.02, 1, 2, 3, 3.02, 5, 6, 6.02, 7, 9, 9.02, 11, 12, 12.02, 13, 15, 15.02, 16, 18, 18.02, 20) # with duplicated times set.seed(1234) tmp <- TestData(Time, sse=0.05) ## Not run: plot(tmp$time, tmp$thrs, ylim=c(-4,0)) tmp <- Declutter(tmp) ## Not run: points(tmp$time, tmp$thrs, col='red', pch=16)
A template function that gets the data from a file and converts it to a dark object for use by other scripts. The script can be modified to format the data. A dark object has time data in minutes and thresholds in log units. If the data have been collected in other units then the script should convert them.
The script defaults to returning data generated by TestData.
GetData(path, .....)GetData(path, .....)
path |
This is the location of the data and will usually be a file path string. |
..... |
This can be any other values that might be needed to identify the data, e.g. subject number or study reference. |
This script can be altered in any way desired and then saved with a different name. I suggest the format 'GetData....R', where the ellipsis describes the data in some way.
A dark object with at least two elements
time |
the time elapsed after measurements begin in minutes |
thrs |
the thresholds recorded in log units |
other possible values include
data |
the name of the data source |
init |
initial estimates of the optimal model parameters |
opt |
optimal estimates of the optimal model parameters |
resid |
the residuals of the data for an optimal model |
... |
others to be added |
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
set.seed(1234) tmp <- GetData()set.seed(1234) tmp <- GetData()
This function is used to transition from 'off' to 'on'.
H(x, k = 100, t)H(x, k = 100, t)
x |
is the measured time. |
k |
is the transition constant, set arbitrarily high. |
t |
is the time at which the transition occurs. |
This helper function used in P5c and P7c enables the optim function to find parameters three times as quickly than if the transitions between the phases are modelled by a logical function e.g. a step function.
For times before 't' the output is less than or equal to 0.5, after this time the the output is greater than 0.5. As 'k' grows larger the rate of transition from 0 to 1 increases.
H is a logistic function that maps inputs to a values between zero and one
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
The logistic function: https://en.wikipedia.org/wiki/Logistic_function
The step function: https://en.wikipedia.org/wiki/Heaviside_step_function
x <- seq(0, 20, by=0.1) k <- 10 t <- 10 op <- par(las=1, bty='n') ## Not run: plot(x,H(x,k,t), 'l') par(op)x <- seq(0, 20, by=0.1) k <- 10 t <- 10 op <- par(las=1, bty='n') ## Not run: plot(x,H(x,k,t), 'l') par(op)
Returns a list with two elements; an array of AICc scores indexed by the number of parameters in the model considered and a matrix of parameters with three rows, one for each model.
ModelSelect(obj, P)ModelSelect(obj, P)
obj |
A 'dark' object. |
P |
Is a matrix with seven columns and at least one row. The values of each element can be zero. |
This is a brute-force method to make a first estimate of the optimal model parameters.
The matrix 'P' holds rows of possible parameter values. Each row is passed to the 3, 5, and 7 parameter models and the sum of residuals squared is calculated for the given times (obj$time) and thresholds (obj$thrs). So for each row in 'P' there is a score for each model. Then for each model the row which yields the lowest SSE is chosen as a starting point for optimisation. The optimised parameters are stored in 'param' and once the three parameter arrays have been found their AICc scores are found and returned as AIC.
Returns a list
AIC |
An array of seven values with AIC scores at the index of model parameter count. |
param |
A three row by seven column matrix. Each row containing the optimised parameters for each model. |
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
https://en.wikipedia.org/wiki/Brute-force_search
set.seed(1234) tmp<- TestData(0:20) P<-Start(tmp) ModelSelect(tmp,P)set.seed(1234) tmp<- TestData(0:20) P<-Start(tmp) ModelSelect(tmp,P)
Given a dark object, obj, this function repeatedly optimises the parameters in the vicinity of the seed array. The width of the search is dependent upon the value of spread.
MultiStart(obj, repeats, draw, spread, debug)MultiStart(obj, repeats, draw, spread, debug)
obj |
A dark object containing at least;
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repeats |
The number of times the algorithm is repeated |
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draw |
A flag indicating whether a figure should be drawn. |
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spread |
The amount by which the seed array should be varied. A larger value gives a greater range of possible starting points. |
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debug |
A flag used in debugging the software. |
To reduce the possibility of selecting non-optimal parameter estimates, the optimisation is repeated in the region of initial estimates. The
Returns a list;
time |
times of threshold setting |
out$thrs |
observed thresholds |
out$resid |
residuals |
out$fit |
optimal fitted values |
out$thet |
seed parameters if test data |
out$sse |
sum of squared residuals if test data |
out$data |
source of the data |
out$opt |
optimal parameter estimates of the chosen model |
out$Mod |
name of the optimal model |
out$Pn |
the number of parameters needed to describe the data |
out$AIC |
array of AICc scores |
out$val |
calculated sum of squared residuals |
out$R2 |
the coefficient of determination |
out$warning |
if none of the nearby values converge |
out$call |
updates the function call label |
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
Nelder, J.A.; Mead, R. 1965: A simplex for function minimization. Comput. J. 7, 308-313
set.seed(1234) Time<- seq(0,20) tmp<- TestData(Time) P<-Start(tmp,1000) MSC<-ModelSelect(tmp, P) tmp2<-BestFit(tmp, MSC) tmp3<-MultiStart(tmp2,10)set.seed(1234) Time<- seq(0,20) tmp<- TestData(Time) P<-Start(tmp,1000) MSC<-ModelSelect(tmp, P) tmp2<-BestFit(tmp, MSC) tmp3<-MultiStart(tmp2,10)
The three parameter model. A simple exponential decay.
P3(a, X)P3(a, X)
a |
An array of parameters;
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X |
The times when the model predicts thresholds. |
This function has three roles, to calculate the thresholds for given parameters a and times X. If missing X, then the function calls the values x and y from the .Globalenv and calculates the sum of residuals squared error (SSE) for a. If a is an array of length 1L or boolean then a description of the model is returned.
The use of the function H rather than an impulse function gives a three-fold increase is speed for the optim function.
The output depends upon the input.
If the input is an array of length 1L or a boolean then a list is returned
Pn |
number of parameters |
Mod |
name of the model |
If a parameter array is passed then the sum of residuals squared is calculated. This is used by optim to optimise the parameter estimates.
Passing a parameter array and a series of putative times causes the function to return predicted thresholds.
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
O. Mahroo and T. Lamb. Recovery of the human photopic electroretinogram after bleaching exposures: estimation of pigment regeneration kinetics. The Journal of Physiology, 554(2):417, 2004.
T. Lamb and E. Pugh. Dark adaptation and the retinoid cycle of vision. Progress in Retinal and Eye Research, 23(3):307-380, 2004.
set.seed(1234) x <- 0:20 a <- c(-1.00, 1.00, 1.00, -0.24, 6.00, 0.20, 13.00) tmp <- TestData(x, a) y <- tmp$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'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$resid P3(TRUE) # Describes the model P3(a) # The sum of squared residuals P3(a,x) # The fitted thresholds for given parameters 'theta' and times 'x'
The five parameter model. An exponential decay followed by a linear phase.
P5c(a,X)P5c(a,X)
a |
An array of parameters;
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X |
The times when the model predicts thresholds. |
This function has three roles, to calculate the thresholds for given parameters a and times X. If missing X, then the function calls the values x and y from the .Globalenv and calculates the sum of residuals squared error (SSE) for a. If a is an array of length 1L or boolean then a description of the model is returned.
The use of the function H rather than an impulse function gives a three-fold increase is speed for the optim function.
If the input is an array of length 1L or a boolean then a list is returned
Pn |
number of parameters |
Mod |
name of the model |
If a parameter array is passed then the sum of residuals squared is calculated. This is used by optim to optimise the parameter estimates.
Passing a parameter array and a series of putative times causes the function to return predicted thresholds.
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
O. Mahroo and T. Lamb. Recovery of the human photopic electroretinogram after bleaching exposures: estimation of pigment regeneration kinetics. The Journal of Physiology, 554(2):417, 2004.
T. Lamb and E. Pugh. Dark adaptation and the retinoid cycle of vision. Progress in Retinal and Eye Research, 23(3):307-380, 2004.
set.seed(1234) x <- 0:20 a <- c(-1.00, 1.00, 1.00, -0.24, 6.00, 0.20, 13.00) tmp <- TestData(x, a) y <- tmp$resid P5c(TRUE) # Describes the model P5c(a) # The sum of squared residuals P5c(a,x) # The fitted thresholds for given parameters 'theta' and times 'x'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 P5c(TRUE) # Describes the model P5c(a) # The sum of squared residuals P5c(a,x) # The fitted thresholds for given parameters 'theta' and times 'x'
An exponential decay followed by a second exponential decay.
P6c(a, X)P6c(a, X)
a |
An array of parameters;
note that the cone threshold is a[1] + a[5] log10(lum) |
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X |
The times in minutes when the model predicts thresholds. |
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.
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.
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
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.
set.seed(1234) x <- 0:20 a <- c(-2, 2, 1/2, 10, 3, 1/8) # P6c(TRUE) # Describes the model # P6c(a) # The sum of squared residuals # P6c(a,x) # The fitted thresholds for given parameters 'a' and times 'x'set.seed(1234) x <- 0:20 a <- c(-2, 2, 1/2, 10, 3, 1/8) # P6c(TRUE) # Describes the model # P6c(a) # The sum of squared residuals # P6c(a,x) # The fitted thresholds for given parameters 'a' and times 'x'
The seven parameter model. An exponential decay followed by two linear phases.
P7c(a, X)P7c(a, X)
a |
An array of parameters;
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X |
The times when the model predicts thresholds. |
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.
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.
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
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.
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'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$resid # P7c(TRUE) # Describes the model # P7c(a) # The sum of squared residuals # P7c(a,x) # The fitted thresholds for given parameters 'a' and times 'x'
A function to build an array of starting parameters from a dark object.
Start(obj, Reps)Start(obj, Reps)
obj |
A dark object |
Reps |
The number of rows in the array. |
The array of starting parameters is built from the time and threshold data in the object, obj.
Each parameter is assumed to have a possible range given the data.
Each range is constructed as follows; the time points; alpha (cone-rod transition minutes) and beta (rod-rod transition minutes) are assumed to fall in the first and second halves of the time data respectively (obj$time).
The cone threshold is assumed to be in the upper half of the threshold data (obj$thrs log units). The cone coefficient (log units) or threshold at time zero is presumed to be positive and the same values are used for the time constants ( minutes).
The rate of rod recovery S2, and the combined parameter -(S2 + S3) are ranged between -0.6 and 0 log units/minute.
These ranges of possible values are complied into an array by sampling without replacement from each range for each parameter.
Output is an array of seven columns and number of rows = 'Reps'.
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
set.seed(1234) tmp<-TestData(0:20) Start(tmp, 10)set.seed(1234) tmp<-TestData(0:20) Start(tmp, 10)
This script creates data in the form of a dark object from specified times, parameters, and level of variability. It is used for testing and developing other scripts. Presently only the seven parameter model and its subsets are implemented.
TestData(x, theta, sse, repeatable)TestData(x, theta, sse, repeatable)
x |
the times at which observations are made. |
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theta |
the parameters of the Mahroo Lamb Pugh model
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sse |
the variability of the data |
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repeatable |
a boolean flag that ensures that the function can return the same values each time it is called. |
The parameters values chosen as defaults are entirely arbitrary. The sixth parameter is the negative sum of the rates of rod recovery called S2 and S3
The function returns a dark object with the following components;
call |
a label describing the last call the object was subject to |
time |
the time observations |
thrs |
thresholds |
resid |
residuals |
fit |
thresholds predicted in the absence of noise |
thet |
parameters passed to the function |
sse |
the sum of squared residuals value used to describe the variability in the data |
val |
the actual sse of the generated data |
data |
the name of the data source |
Jeremiah MF Kelly
Mumac Ltd, SK7 6NR, GB
L. Patryas, N. R. Parry, D. Carden, D. H. Baker, J. M. Kelly, T. Aslam, and I. J. Murray. Assessment of age changes and repeatability for computer-based rod dark adaptation. Graefe's Archive for Clinical and Experimental Ophthalmology, pages 1-7, 2013.
set.seed(1234) x <- seq(0,20) tmp <- TestData(x) tmpset.seed(1234) x <- seq(0,20) tmp <- TestData(x) tmp