# threeAFC: Create 3-AFC binomial family In perbrock/sensR: Thurstonian Models for Sensory Discrimination

 threeAFC R Documentation

## Create 3-AFC binomial family

### Description

Creates a copy of the binomial family with the inverse link function changed to equal the 3-AFC psychometric function and correspondingly changed link function and derivative of the inverse link function.

### Usage

``````threeAFC()
``````

### Value

A binomial family object for models. Among other things it inludes the psychometric function as `linkinv` and the inverse psychometric function (for direct dprime computation) as `linkfun`.

### Note

Several functions in this package makes use of the function, but it may also be used on its ownâ€”see the example below.

### Author(s)

Rune Haubo B Christensen and Per Bruun Brockhoff

### References

Brockhoff, P.B. and Christensen, R.H.B. (2010). Thurstonian models for sensory discrimination tests as generalized linear models. Food Quality and Preference, 21, pp. 330-338.

`triangle`, `twoAFC`, `tetrad`, `duotrio`, `discrim`, `discrimPwr`, `discrimSim`, `AnotA`, `discrimSS`, `samediff`, `findcr`

### Examples

``````
## Estimating d-prime using glm for a 3-AFC test:
xt <- matrix(c(10, 5), ncol = 2) ## data: 10 correct answers, 5 incorrect
res <- glm(xt ~ 1, family = threeAFC)
summary(res)
## Equivalent to (Estimate and Std. Error):
discrim(10, 15, method="threeAFC")

## Extended example plotting the profile likelihood
## data: 10 correct answers, 5 incorrect
xt <- matrix(c(10, 2), ncol = 2)
summary(res <- glm(xt ~ 1, family = threeAFC))#, etastart = etastart))
N <- 100
dev <- double(N)
level <- c(0.95, 0.99)
delta <- seq(1e-4, 5, length = N)
for(i in 1:N)
dev[i] <- glm(xt ~ -1 + offset(delta[i]),
family = threeAFC)\$deviance
plot(delta, exp(-dev/2), type = "l",
xlab = expression(delta),
ylab = "Normalized Profile Likelihood")