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

## Description

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

## Usage

 `1` ```hexad() ```

## 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 own—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`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```## 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): discrim(10, 15, method="hexad") ## 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]), family = hexad)\$deviance 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") ```