sensR (version 1.5-2)

tetrad: Create tetrad binomial family

Description

Creates a binomial family object with the inverse link function equal to the psychometric function for the unspecified method of tetrads.

Usage

tetrad()

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.

References

Ennis, J. M., Ennis, D. M., Yip, D., & O'Mahony, M. (1998). Thurstonian models for variants of the method of tetrads. British Journal of Mathematical and Statistical Psychology, 51, pp. 205-215.

Ennis, J. M., & Jesionka, V. (2011). The power of sensory discrimination methods revisited. Journal of Sensory Studies, 26, pp. 371-382.

See Also

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

Examples

# NOT RUN {
## Estimating d-prime using glm for a Tetrad test:
xt <- matrix(c(10, 5), ncol = 2) ## data: 10 correct answers, 5 incorrect
res <- glm(xt ~ 1, family = tetrad)
summary(res)
## Equivalent to (Estimate and Std. Error):
discrim(10, 15, method="tetrad")

# }
# NOT RUN {
## 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 = tetrad))
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 = tetrad)$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")

# }