triangle: Create triangle binomial family

In perbrock/sensR: Thurstonian Models for Sensory Discrimination

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 own—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.

See Also

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")
## 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")

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