Title:	Model-Free Estimation of a Psychometric Function
Version:	1.2.1
Description:	Local linear estimation of psychometric functions. Provides functions for nonparametric estimation of a psychometric function and for estimation of a derived threshold and slope, and their standard deviations and confidence intervals.For more details see Zychaluk and Foster (2009) <doi:10.3758/APP.71.6.1414> and Foster and Zychaluk (2007) <doi:10.1109/MSP.2007.4286564>.
URL:	https://personalpages.manchester.ac.uk/staff/d.h.foster/software-modelfree/latest/home.html
License:	LGPL (≥ 3)
Encoding:	UTF-8
RoxygenNote:	7.3.2
Imports:	SparseM, PolynomF, methods
Depends:	R (≥ 2.10)
LazyData:	true
NeedsCompilation:	no
Packaged:	2025-05-22 14:33:50 UTC; kamil
Author:	Ivan Marin-Franch [aut], Kamila Zychaluk [aut, cre, cph], David H. Foster [aut]
Maintainer:	Kamila Zychaluk <Kamila.Zychaluk@liverpool.ac.uk>
Repository:	CRAN
Date/Publication:	2025-05-22 15:50:07 UTC

Auditory detection of a gap in noise

Description

A 300-ms noise burst containing a gap of 2–8 ms duration or no gap was presented to one ear of a subject. The symbols in the figure below show the proportion of responses "gap" as a function of gap duration. There were 12 trials with each gap duration and 84 trials with no gap. See https://personalpages.manchester.ac.uk/staff/d.h.foster/software-modelfree/latest/examples/Baker_etalR.html

Usage

data("Baker_etal")

Format

A data frame with 8 rows and 3 columns.

x

stimulus level

r

number of successes

m

number of trials

References

Baker, R. J., Jayewardene, D., Sayle, C., & Saeed, S. “Failure to find asymmetry in auditory gap detection”, Laterality: Asymmetries of Body, Brain and Cognition, 13, 1-21, 2008.

Examples

data("Baker_etal")
x = Schofield_etal$x
r = Schofield_etal$r
m = Schofield_etal$m
plot( x, r / m, xlim = c( 0.16, 7.83 ), ylim = c( -0.01, 1.01 ), type = "p", pch="*" )

Discrimination of pitch

Description

The subject had to identify the interval containing a tone whose fundamental frequency was different from that in the other two intervals. The symbols in the figure below show the proportion of correct responses as the difference between the tones varied. There were 3–49 trials at each stimulus level. See https://personalpages.manchester.ac.uk/staff/d.h.foster/software-modelfree/latest/examples/CarcagnoR.html

Usage

data("Carcagno")

Format

A data frame with 8 rows and 3 columns.

x

stimulus level

r

number of successes

m

number of trials

References

Unpublished data from S. Carcagno, Lancaster University, July 2008.

Examples

data("Carcagno")
x = Carcagno$x
r = Carcagno$r
m = Carcagno$m
plot( x, r / m, xlim = c( 1.95, 4.35 ), ylim = c( 0.24, 0.99 ), type = "p", pch="*" )

Visual detection of path deviation

Description

The subject was presented with the image of a dot moving rightwards on a linear path until it reached the midline of the display, when it changed direction either upwards or downwards. The subject had to indicate the direction. The symbols in the figure below show the proportion of correct responses in 30 trials as the deviation varied from –3 to 3 units. See https://personalpages.manchester.ac.uk/staff/d.h.foster/software-modelfree/latest/examples/Levi_TripathyR.html

Usage

data("Levi_Tripathy")

Format

A data frame with 7 rows and 3 columns.

x

stimulus level

r

number of successes

m

number of trials

References

Levi, D. M. & Tripathy, S. P. “Is the ability to identify deviations in multiple trajectories compromised by amblyopia?”, Journal of Vision, 6(12), 1367-1379, 2006.

Examples

data("Levi_Tripathy")
x = Levi_Tripathy$x
r = Levi_Tripathy$r
m = Levi_Tripathy$m
plot( x, r / m, xlim = c( -2.87, 2.87 ), ylim = c( 0.03, 0.97 ), type = "p", pch="*" )

Detection of a flash of light

Description

A flash of light of variable intensity was presented repeatedly at a fixed location in the visual field of a subject who reported whether the flash was visible. There were 3–20 trials at each stimulus level. See https://personalpages.manchester.ac.uk/staff/d.h.foster/software-modelfree/latest/examples/Miranda_HensonR.html

Usage

data("Miranda_Henson")

Format

A data frame with 10 rows and 3 columns.

x

stimulus level

r

number of successes

m

number of trials

References

Miranda, M. A. & Henson, D. B. “Perimetric sensitivity and response variability in glaucoma with single-stimulus automated perimetry and multiple-stimulus perimetry with verbal feedback”, Acta Ophthalmologica, 86, 202-206, 2008.

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
plot( x, r / m, xlim = c( 0.1, 1.302 ), ylim = c( 0.0165, 0.965 ), type = "p", pch="*" )

Discrimination of image approximations

Description

The subject was shown an image of a natural scene and an approximation of this image based on principal component analysis. The task was to distinguish between the images. The symbols in the figure below show the proportion of correct responses as a function of number of components in the approximation. There were 200 trials at each level pooled over a range of natural scenes. See https://personalpages.manchester.ac.uk/staff/d.h.foster/software-modelfree/latest/examples/Nascimento_etalR.html

Usage

data("Nascimento_etal")

Format

A data frame with 8 rows and 3 columns.

x

stimulus level

r

number of successes

m

number of trials

References

Nascimento, S.M.C., Foster, D.H., & Amano, K. “Psychophysical estimates of the number of spectral-reflectance basis functions needed to reproduce natural scenes”, Journal of the Optical Society of America A-Optics Image Science and Vision, 22 (6), 1017-1022, 2005.

Examples

data("Nascimento_etal")
x = Schofield_etal$x
r = Schofield_etal$r
m = Schofield_etal$m
plot( x, r / m, xlim = c( 1.17, 7.8 ), ylim = c( 0.47, 1.03 ), type = "p", pch="*" )

Induction of a visual motion aftereffect

Description

The subject was presented with a moving adaptation stimulus, followed by a test stimulus. The symbols in the figure below show the proportion of responses in which the subject indicated motion of the test stimulus in the same direction as the adapting stimulus, either up or down, as a function of relative modulation depth. There were 10 trials at each stimulus level. See https://personalpages.manchester.ac.uk/staff/d.h.foster/software-modelfree/latest/examples/Schofield_etalR.html

Usage

data("Schofield_etal")

Format

A data frame with 7 rows and 3 columns.

x

stimulus level

r

number of successes

m

number of trials

References

Schofield, A. J., Ledgeway, T., & Hutchinson, C. V. “Asymmetric transfer of the dynamic motion aftereffect between first- and second-order cues and among different second-order cues”, Journal of Vision, 7(8), 1-12, 2007.

Examples

data("Schofield_etal")
x = Schofield_etal$x
r = Schofield_etal$r
m = Schofield_etal$m
plot( x, r / m, xlim = c( 2, 98.2 ), ylim = c( 0.02, 0.98 ), type = "p", pch="*" )

Discrimination of "porthole" views of natural scenes

Description

The subject was presented with a display split into two parts, one containing a pair of patches from the same image, the other a pair from different images, and the subject had to judge which pair came from the same image. The symbols in the figure below show the proportion of correct responses in 200 trials as a function of patch separation. See https://personalpages.manchester.ac.uk/staff/d.h.foster/software-modelfree/latest/examples/Xie_GriffinR.html

Usage

data("Xie_Griffin")

Format

A data frame with 10 rows and 3 columns.

x

stimulus level

r

number of successes

m

number of trials

References

Xie, Y. & Griffin, L. D. “A 'portholes' experiment for probing perception of small patches of natural images”, Perception, 36, 315, 2007.

Examples

data("Xie_Griffin")
x = Xie_Griffin$x
r = Xie_Griffin$r
m = Xie_Griffin$m
plot( x, r / m, xlim = c( 0.25, 8.76 ), ylim = c( 0.52, 0.99 ), type = "p", pch="*" )

Bootstrap bandwidth for local polynomial estimator of a psychometric function

Description

This function finds a bootstrap estimate of the optimal bandwidth h for a local polynomial estimate of the psychometric function with specified guessing and lapsing rates.

Usage

bandwidth_bootstrap( r, m, x, H, N, h0 = NULL, link = "logit",
                     guessing = 0, lapsing = 0, K = 2, p = 1,
                     ker = "dnorm", maxiter = 50, tol = 1e-6, method = "all")

Arguments

Value

⁠h ⁠ bootstrap bandwidth for the chosen "method"; if no "method" is specified, then it has three components: $pscale, $eta-scale and $deviance

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
numxfit <- 199; # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
# Find a cross-validation bandwidth
bwd_min <- min( diff( x ) )
bwd_max <- max( x ) - min( x )
# This might take a few minutes
niter <- 500 # Note number of bootstrap iterations should be at least 500
bwd <- bandwidth_bootstrap( r, m, x, c( bwd_min, bwd_max ),niter, method="deviance")
pfit <- locglmfit( xfit, r, m, x, bwd )$pfit
# Plot the fitted curve
plot( x, r / m, xlim = c( 0.1, 1.302 ), ylim = c( 0.0165, 0.965 ), type = "p", pch="*" )
lines(xfit, pfit )

Cross-validation bandwidth for local polymnomial estimator of a psychometric function

Description

This function finds the cross-validation bandwidth for a local polynomial estimate of the psychometric function with specified guessing and lapsing rates.

Usage

bandwidth_cross_validation( r, m, x, H, link = "logit", guessing = 0,
                           lapsing = 0, K = 2, p = 1, ker = "dnorm",
                           maxiter = 50, tol = 1e-6, method = "all")

Arguments

Value

⁠h ⁠ cross-validation bandwidth for the chosen "method"; if no "method" is specified, then it has three components: $pscale, $etascale and $deviance

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
numxfit <- 199; # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
# Find a cross-validation bandwidth
bwd_min <- min( diff( x ) )
bwd_max <- max( x ) - min( x )
bwd <- bandwidth_cross_validation( r, m, x, c( bwd_min, bwd_max ) )
bwd <- bwd$deviance # Choose the estimate based on cross-validated deviance
pfit <- locglmfit( xfit, r, m, x, bwd )$pfit
# Plot the fitted curve
plot( x, r / m, xlim = c( 0.1, 1.302 ), ylim = c( 0.0165, 0.965 ), type = "p", pch="*" )
lines(xfit, pfit )

Plug-in bandwidth for local polynomial estimator of a psychometric function

Description

The function calculates an estimate of the AMISE optimal bandwidth for a local polynomial estimate of the psychometric function.

The function calculates an estimate of the AMISE optimal bandwidth for a local polynomial estimate of the psychometric function.

Usage

bandwidth_plugin( r, m, x, link = "logit", guessing = 0,
                   lapsing = 0, K = 2, p = 1, ker = "dnorm" )

bandwidth_plugin( r, m, x, link = "logit", guessing = 0,
                   lapsing = 0, K = 2, p = 1, ker = "dnorm" )

Arguments

Value

⁠h ⁠ plug-in bandwidth (ISE optimal on eta-scale)

⁠h ⁠ plug-in bandwidth (ISE optimal on eta-scale)

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
numxfit <- 199; # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
# Find a plug-in bandwidth
bwd <- bandwidth_plugin( r, m, x)
pfit <- locglmfit( xfit, r, m, x, bwd )$pfit
# Plot the fitted curve
plot( x, r / m, xlim = c( 0.1, 1.302 ), ylim = c( 0.0165, 0.965 ), type = "p", pch="*" )
lines(xfit, pfit )
data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
numxfit <- 199; # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
# Find a plug-in bandwidth
bwd <- bandwidth_plugin( r, m, x)
pfit <- locglmfit( xfit, r, m, x, bwd )$pfit
# Plot the fitted curve
plot( x, r / m, xlim = c( 0.1, 1.302 ), ylim = c( 0.0165, 0.965 ), type = "p", pch="*" )
lines(xfit, pfit )

Maximum likelihood parameter estimates for a psychometric function with guessing and lapsing rates

Description

This function finds the maximum likelihood estimates of the parameters of the psychometric function with guessing and lapsing rates, only guessing rate, or only lapsing rate.

Usage

binom_lims( r, m, x, gl = "both", link = "logit", p = 1, K = 2, initval = NULL )

Arguments

Value

⁠b ⁠estimated coefficients for the linear part

⁠guessing ⁠ estimated guessing rate (if estimated)

⁠lapsing ⁠ estimated lapsing rate (if estimated)

⁠fit ⁠ glm object to be used in evaluation of fitted values

Examples

data("Baker_etal")
x = Baker_etal$x
r = Baker_etal$r
m = Baker_etal$m
plot( x, r / m, xlim = c( 0.16, 7.83 ), ylim = c( -0.01, 1.01 ), type = "p", pch="*" )
val <- binomfit_lims( r, m, x, link = "probit" )
numxfit <- 199; # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
# Plot the fitted curve
pfit<-predict( val$fit, data.frame( x = xfit ), type = "response" )
lines(xfit, pfit )

Reverse Weibull model for the psychometric function

Description

This function finds the maximum likelihood estimates of the parameters of the reverse Weibull model for the psychometric function.

Usage

binom_revweib( r, m, x, p = 1, initK = 2, guessing = 0, lapsing = 0 )

Arguments

Value

⁠b ⁠ vector of estimated coefficients for the linear part

⁠K ⁠ estiamte of the power parameter in the reverse Weibull model

⁠fit ⁠ glm object to be used in evaluation of fitted values

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
numxfit <- 199; # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
val <- binom_revweib( r, m, x )
# Plot the fitted curve
plot( x, r / m, xlim = c( 0.1, 1.302 ), ylim = c( 0.0165, 0.965 ), type = "p", pch="*" )
pfit <- predict( val$fit, data.frame( x = xfit ), type = "response" )
lines(xfit, pfit, col = "green" )

Weibull model for the psychometric function

Description

This function finds the maximum likelihood estimates of the parameters of the Weibull model for the psychometric function.

Usage

binom_weib( r, m, x, p = 1, initK = 2, guessing = 0, lapsing = 0 )

Arguments

Value

⁠b ⁠ vector of estimated coefficients for the linear part

⁠K ⁠ estiamte of the power parameter in the Weibull model

⁠fit ⁠ glm object to be used in evaluation of fitted values

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
numxfit <- 199; # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
val <- binom_weib( r, m, x )
# Plot the fitted curve
plot( x, r / m, xlim = c( 0.1, 1.302 ), ylim = c( 0.0165, 0.965 ), type = "p", pch="*" )
pfit <- predict( val$fit, data.frame( x = xfit ), type = "response" )
lines(xfit, pfit, col = "red" )

Parameter estimates for a psychometric function with FIXED guessing and lapsing rates

Description

This function fits a binomial generalised linear model with fixed guessing and lapsing rates.

Usage

binomfit_lims( r, m, x, p = 1, link = "logit", guessing = 0, lapsing = 0, K = 2 )

Arguments

Value

⁠b ⁠ vector of estiamted coefficients for the linear part

⁠fit ⁠ glm object to be used in evaluation of fitted values

Examples

data("Carcagno")
x = Carcagno$x
r = Carcagno$r
m = Carcagno$m
plot( x, r / m, xlim = c( 1.95, 4.35 ), ylim = c( 0.24, 0.99 ), type = "p", pch="*" )
guess = 1/3; # guessing rate
laps = 0; # lapsing rate
val <- binomfit_lims( r, m, x, link = "probit", guessing = guess, lapsing = laps )
numxfit <- 199 # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
# Plot the fitted curve
pfit<-predict( val$fit, data.frame( x = xfit ), type = "response" )
lines(xfit, pfit )

Bootstrap confidence interval for the slope of a psychometric function

Description

Finds a bootstrap estimate of a confidence interval at a significance level alpha for the estimated slope for the local polynomial estimate of the psychometric function with guessing and lapsing rates. The confidence interval is based on bootstrap percentiles. See Efron & Tibshirani's "An introduction to the bootstrap", 1993

Usage

bootstrap_ci_sl( TH, r, m, x, N, h0, alpha = 0.05,
                 X = (max(x)-min(x))*(0:999)/999+min(x), link = "logit", guessing = 0,
                 lapsing = 0, K = 2, p = 1, ker = "dnorm", maxiter = 50, tol = 1e-6 )

Arguments

Value

⁠ci ⁠ confidence interval based on bootstrap percentiles

⁠sl0 ⁠ slope estimate

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
bwd_min <- min( diff( x ) )
bwd_max <- max( x ) - min( x )
bwd <- bandwidth_cross_validation( r, m, x, c( bwd_min, bwd_max ), method = "deviance" )
prob <- 0.5 # Required threshold level
alpha <- 0.05 # Significance level for the confidence intervals
# This might take a few minutes
niter <- 1000 # Note number of bootstrap iterations should be at least 1000
ci_sl <- bootstrap_ci_sl( prob, r, m, x, niter, bwd, alpha ) # Be patient, slow process

Bootstrap confidence interval for a slope of a psychometric function

Description

Finds a bootstrap estimate of a confidence interval at a significance level alpha for the estimated threshold for the local polynomial estimate of the psychometric function with guessing and lapsing rates. The confidence interval is based on bootstrap percentiles. See Efron & Tibshirani's "An introduction to the bootstrap", 1993

Usage

bootstrap_ci_th( TH, r, m, x, N, h0, alpha = 0.05,
                 X = (max(x)-min(x))*(0:999)/999+min(x), link = "logit", guessing = 0,
                 lapsing = 0, K = 2, p = 1, ker = "dnorm", maxiter = 50, tol = 1e-6 )

Arguments

Value

⁠ci ⁠ confidence interval based on bootstrap percentiles

⁠th0 ⁠ threshold estimate

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
bwd_min <- min( diff( x ) )
bwd_max <- max( x ) - min( x )
bwd <- bandwidth_cross_validation( r, m, x, c( bwd_min, bwd_max ), method = "deviance" )
prob <- 0.5 # Required threshold level
alpha <- 0.05 # Significance level for the confidence intervals
# This might take a few minutes
niter <- 1000 # Note number of bootstrap iterations should be at least 1000
ci_th <- bootstrap_ci_th( prob, r, m, x, niter, bwd, alpha ) # Be patient, slow process

Bootstrap standard deviation for the slope of a psychometric function

Description

The function finds a bootstrap estimate of the standard deviation of the estimated slope for the local polynomial estimate of the psychometric function with guessing and lapsing rates.

Usage

bootstrap_sd_sl( TH, r, m, x, N, h0, X = (max(x)-min(x))*(0:999)/999+min(x),
                 link = "logit", guessing = 0, lapsing = 0, K = 2, p = 1,
                 ker = "dnorm", maxiter = 50, tol = 1e-6 )

Arguments

Value

⁠sd ⁠ bootstrap estimate of the standard deviation of the slope estimator

⁠sl0 ⁠ slope estimate

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
bwd_min <- min( diff( x ) )
bwd_max <- max( x ) - min( x )
bwd <- bandwidth_cross_validation( r, m, x, c( bwd_min, bwd_max ), method = "deviance" )
prob <- 0.5 # Required threshold level
# This might take a few minutes
niter <- 200 # Note number of bootstrap iterations should be at least 200
sd_sl <- bootstrap_sd_sl( prob, r, m, x, niter, bwd ) # Be patient, slow process

Bootstrap standard deviation for the slope of a psychometric function

Description

The function finds a bootstrap estimate of the standard deviation of the estimated threshold for the local polynomial estimate of the psychometric function with guessing and lapsing rates.

Usage

bootstrap_sd_th( TH, r, m, x, N, h0, X = (max(x)-min(x))*(0:999)/999+min(x),
                 link = "logit", guessing = 0, lapsing = 0, K = 2, p = 1,
                 ker = "dnorm", maxiter = 50, tol = 1e-6 )

Arguments

Value

⁠sd ⁠ bootstrap estimate of the standard deviation of the threshold estimator

⁠th0 ⁠ threshold estimate

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
bwd_min <- min( diff( x ) )
bwd_max <- max( x ) - min( x )
bwd <- bandwidth_cross_validation( r, m, x, c( bwd_min, bwd_max ), method = "deviance" )
prob <- 0.5 # Required threshold level
# This might take a few minutes
niter <- 200 # Note number of bootstrap iterations should be at least 200
th_sl <- bootstrap_sd_sl( prob, r, m, x, niter, bwd ) # Be patient, slow process

Complementary log-log link with guessing and lapsing rates Creates a complementary log-log link function; the guessing rate and lapsing rate are fixed, hence link is a function of only one variable.

Description

Complementary log-log link with guessing and lapsing rates Creates a complementary log-log link function; the guessing rate and lapsing rate are fixed, hence link is a function of only one variable.

Usage

comploglog_link(guessing = 0, lapsing = 0)

Arguments

Value

link complementary log-log link for use in all GLM functions

Deviance of a psychometric function

Description

This function calculates the deviance for the fitted values of the psychometric function pfit.

Usage

deviance2( r, m, pfit )

Arguments

Value

⁠D ⁠ deviance

Examples

data("Carcagno")
x = Carcagno$x
r = Carcagno$r
m = Carcagno$m
plot( x, r / m, xlim = c( 1.95, 4.35 ), ylim = c( 0.24, 0.99 ), type = "p", pch="*" )
guess = 1/3; # guessing rate
laps = 0; # lapsing rate
val <- binomfit_lims( r, m, x, link = "probit", guessing = guess, lapsing = laps )
pfit<-predict( val$fit, data.frame( x = x ), type = "response" )
d2 = deviance2( r, m, pfit )

Local polynomial estimator of a psychometric function

Description

Local polynomial estimator for the psychometric function and eta function (psychometric function transformed by link) for binomial data; also returns the hat matrix H.

Usage

locglmfit( xfit, r, m, x, h, returnH = FALSE, link = "logit",
               guessing = 0, lapsing = 0, K = 2, p = 1,
               ker = "dnorm", maxiter = 50, tol = 1e-6 )

Arguments

Value

⁠pfit ⁠ value of the local polynomial estimate at points xfit

⁠etafit ⁠ estimate of eta (link of pfit)

⁠H ⁠ hat matrix (OPTIONAL)

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
numxfit <- 199; # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
# Find a plug-in bandwidth
bwd <- bandwidth_plugin( r, m, x)
pfit <- locglmfit( xfit, r, m, x, bwd )$pfit
# Plot the fitted curve
plot( x, r / m, xlim = c( 0.1, 1.302 ), ylim = c( 0.0165, 0.965 ), type = "p", pch="*" )
lines(xfit, pfit )

Logit link with guessing and lapsing rates Creates a complementary logit link function; the guessing rate and lapsing rate are fixed, hence link is a function of only one variable.

Description

Logit link with guessing and lapsing rates Creates a complementary logit link function; the guessing rate and lapsing rate are fixed, hence link is a function of only one variable.

Usage

logit_link(guessing = 0, lapsing = 0)

Arguments

Value

link logit link for use in all GLM functions

Log-log link with guessing and lapsing rates

Description

Creates a log-log link function; the guessing rate and lapsing rate are fixed, hence link is a function of only one variable.

Usage

loglog_link(guessing = 0, lapsing = 0)

Arguments

Value

link log-log link for use in all GLM functions

Probit link with guessing and lapsing rates

Description

Creates a complementary log-log link function; the guessing rate and lapsing rate are fixed, hence link is a function of only one variable.

Usage

probit_link(guessing = 0, lapsing = 0)

Arguments

Value

link probit link for use in all GLM functions

Estimates of threshold and slope for a fitted psychometric function

Description

This function finds the approximate value of x (=x_th) for which the value of the estimated psychometric function is equal to 'thresh' and the approximate value of slope in x_th.

Usage

threshold_slope( pfit, xfit, thresh = 0.5 )

Arguments

Value

⁠x_th ⁠ estimated threshold

⁠slope ⁠ estimated value of slope, i.e. derivative of pfit at x_th

Examples

data("Miranda_Henson")
x = Miranda_Henson$x
r = Miranda_Henson$r
m = Miranda_Henson$m
numxfit <- 199; # Number of new points to be generated minus 1
xfit <- (max(x)-min(x)) * (0:numxfit) / numxfit + min(x)
# Find a plug-in bandwidth
bwd <- bandwidth_plugin( r, m, x)
pfit <- locglmfit( xfit, r, m, x, bwd )$pfit
prob <- 0.5 # Required threshold level
thr_sl <- threshold_slope( pfit, xfit, prob )