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

 triangle R Documentation

Create triangle binomial family

Description

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

Usage

``````triangle()
``````

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.

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

Examples

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

## 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 = triangle))
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 = triangle)\$deviance
plot(delta, exp(-dev/2), type = "l",
xlab = expression(delta),
ylab = "Normalized Profile Likelihood")