# hexad: Create hexad binomial family In perbrock/sensR: Thurstonian Models for Sensory Discrimination

## Create hexad binomial family

### Description

Creates af binomial family object with the inverse link function equal to the psychometric function for the unspecified Hexad test.

### Usage

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### Value

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

### Note

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

### Author(s)

Karolina Stachlewska

### References

Eberhardt, K., Aubry, V., & Robinson, K. (2008). A thurstonian model for the unspecified hexad test. In 2008 Sensometrics Meeting 'Discover a New World of Data' (E-5). Kraft Foods.

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

### Examples

``````
## Estimating d-prime using glm for an unspecified Hexad test:
xt <- matrix(c(10, 5), ncol = 2) ## data: 10 correct answers, 5 incorrect
res <- glm(xt ~ 1, family = hexad)
summary(res)
## Equivalent to (Estimate and Std. Error):

## Extended example plotting the profile likelihood
## data: 10 correct answers, 9 incorrect
xt <- matrix(c(10, 9), ncol = 2)
summary(res <- glm(xt ~ 1, family = hexad))
N <- 100
dev <- double(N)
delta <- seq(1e-4, 3, length = N)
for(i in 1:N)
dev[i] <- glm(xt ~ -1 + offset(delta[i]),
plot(delta, exp(-dev/2), type = "l",
xlab = expression(delta),
ylab = "Normalized Profile Likelihood")
## Add Normal approximation:
lines(delta, exp(-(delta - coef(res))^2 /
(2 * vcov(res))), lty = 2)
## Add confidence limits:
level <- c(0.95, 0.99)
lim <- sapply(level, function(x) exp(-qchisq(x, df=1)/2) )
abline(h = lim, col = "grey")

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perbrock/sensR documentation built on Nov. 5, 2023, 10:41 a.m.