```
if (FALSE) {
# the example may occasionally fail due to a starting values - integration mismatch.
# Fit an SDT for a 4 alternative ranking task (Kellen, Klauer, & Singmann, 2012).
ranking.data <- structure(c(39, 80, 75, 35, 61, 54, 73, 52, 44, 63, 40, 48, 80,
49, 43, 80, 68, 53, 81, 60, 60, 65, 49, 58, 69, 75, 71, 47, 44,
85, 23, 9, 11, 21, 12, 21, 14, 20, 19, 15, 29, 13, 14, 15, 22,
11, 12, 16, 13, 20, 20, 9, 26, 19, 13, 9, 14, 15, 24, 9, 19,
7, 9, 26, 16, 14, 6, 17, 21, 14, 20, 18, 5, 19, 17, 5, 11, 21,
4, 9, 15, 17, 7, 17, 11, 11, 9, 19, 20, 3, 19, 4, 5, 18, 11,
11, 7, 11, 16, 8, 11, 21, 1, 17, 18, 4, 9, 10, 2, 11, 5, 9, 18,
6, 7, 5, 6, 19, 12, 3), .Dim = c(30L, 4L))
expSDTrank <- function(Q, param.names, n.params, tmp.env){
e <- vector("numeric",4)
mu <- Q[1]
ss <- Q[2]
G1<-function(x){
((pnorm(x)^3)*dnorm(x,mean=mu,sd=ss))
}
G2<-function(x){
((pnorm(x)^2)*dnorm(x,mean=mu,sd=ss)*(1-pnorm(x)))*3
}
G3<-function(x){
(pnorm(x)*dnorm(x,mean=mu,sd=ss)*(1-pnorm(x))^2)*3
}
e[1] <- integrate(G1,-Inf,Inf,rel.tol = .Machine$double.eps^0.5)$value
e[2] <- integrate(G2,-Inf,Inf,rel.tol = .Machine$double.eps^0.5)$value
e[3] <- integrate(G3,-Inf,Inf,rel.tol = .Machine$double.eps^0.5)$value
e[4] <- 1-e[1]-e[2]-e[3]
return(e)
}
SDTrank <- function(Q, data, param.names, n.params, tmp.env, lower.bound, upper.bound){
e<-vector("numeric",4)
mu <- Q[1]
ss <- Q[2]
G1<-function(x){
((pnorm(x)^3)*dnorm(x,mean=mu,sd=ss))
}
G2<-function(x){
((pnorm(x)^2)*dnorm(x,mean=mu,sd=ss)*(1-pnorm(x)))*3
}
G3<-function(x){
(pnorm(x)*dnorm(x,mean=mu,sd=ss)*(1-pnorm(x))^2)*3
}
e[1] <- integrate(G1,-Inf,Inf,rel.tol = .Machine$double.eps^0.5)$value
e[2] <- integrate(G2,-Inf,Inf,rel.tol = .Machine$double.eps^0.5)$value
e[3] <- integrate(G3,-Inf,Inf,rel.tol = .Machine$double.eps^0.5)$value
e[4] <- 1-e[1]-e[2]-e[3]
LL <- -sum(data[data!=0]*log(e[data!=0]))
return(LL)
}
fit.mptinr(ranking.data, SDTrank, c("mu", "sigma"), 4, prediction = expSDTrank,
lower.bound = c(0,0.1), upper.bound = Inf)
}
```

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