#CURVAS CARACTERISTICAS DOS ITEMS MODELO DE 2 PARAMETROS
#########################################################

par(mfrow=c(1,2))

#discriminacao constante, mudando a dificuldade
###############################################
a=1
theta=seq(-5,5,by=0.1)

b=0
eta=a*(theta-b)
pl=plogis(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")

b=-2
eta=a*(theta-b)
pl2=plogis(eta)
lines(theta,pl2,col=3,type="l",lwd=3)

b=2
eta=a*(theta-b)
pl3=plogis(eta)
lines(theta,pl3,col=6,type="l",lwd=3)

legend(1.5,0.3,c(expression(b==0), expression(b==-2), expression(b==2)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)

#dificuldade constante, mudando a discriminacao
###############################################
b=0
theta=seq(-5,5,by=0.1)

a=1
eta=a*(theta-b)
pl=plogis(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")

a=0.5
eta=a*(theta-b)
pl2=plogis(eta)
lines(theta,pl2,col=3,type="l",lwd=3)

a=1.5
eta=a*(theta-b)
pl3=plogis(eta)
lines(theta,pl3,col=6,type="l",lwd=3)

legend(1.5,0.3,c(expression(a==1), expression(a==0.5), expression(a==1.5)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)
text(1,0.05,"y=1",lwd=3)






#CURVAS CARACTERISTICAS DOS ITEMS MODELO DE 3 PARAMETROS
#########################################################

par(mfrow=c(2,2))

#discriminacao constante, mudando a dificuldade para c=0.1
##########################################################
c=0.1


a=1
theta=seq(-5,5,by=0.1)

b=0
eta=a*(theta-b)
pl=c+(1-c)*plogis(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")

b=-2
eta=a*(theta-b)
pl2=c+(1-c)*plogis(eta)
lines(theta,pl2,col=3,type="l",lwd=3)

b=2
eta=a*(theta-b)
pl3=c+(1-c)*plogis(eta)
lines(theta,pl3,col=6,type="l",lwd=3)

legend(1.5,0.3,c(expression(b==0), expression(b==-2), expression(b==2)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)

#dificuldade constante, mudando a discriminacao para c=0.1
##########################################################
b=0
theta=seq(-5,5,by=0.1)

a=1
eta=a*(theta-b)
pl=c+(1-c)*plogis(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")

a=0.5
eta=a*(theta-b)
pl2=c+(1-c)*plogis(eta)
lines(theta,pl2,col=3,type="l",lwd=3)

a=1.5
eta=a*(theta-b)
pl3=c+(1-c)*plogis(eta)
lines(theta,pl3,col=6,type="l",lwd=3)

legend(1.5,0.3,c(expression(a==1), expression(a==0.5), expression(a==1.5)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)
text(1,0.05,"y=1",lwd=3)

#discriminacao constante, mudando a dificuldade para c=0.1
##########################################################
c=0.2


a=1
theta=seq(-5,5,by=0.1)

b=0
eta=a*(theta-b)
pl=c+(1-c)*plogis(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")

b=-2
eta=a*(theta-b)
pl2=c+(1-c)*plogis(eta)
lines(theta,pl2,col=3,type="l",lwd=3)

b=2
eta=a*(theta-b)
pl3=c+(1-c)*plogis(eta)
lines(theta,pl3,col=6,type="l",lwd=3)

legend(1.5,0.3,c(expression(b==0), expression(b==-2), expression(b==2)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)

#dificuldade constante, mudando a discriminacao para c=0.1
##########################################################
b=0
theta=seq(-5,5,by=0.1)

a=1
eta=a*(theta-b)
pl=c+(1-c)*plogis(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")

a=0.5
eta=a*(theta-b)
pl2=c+(1-c)*plogis(eta)
lines(theta,pl2,col=3,type="l",lwd=3)

a=1.5
eta=a*(theta-b)
pl3=c+(1-c)*plogis(eta)
lines(theta,pl3,col=6,type="l",lwd=3)

legend(1.5,0.3,c(expression(a==1), expression(a==0.5), expression(a==1.5)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)
text(1,0.05,"y=1",lwd=3)


#CURVAS CARACTERISTICAS DOS ITEMS MODELO DE 2 PARAMETROS NORMAL
#########################################################

par(mfrow=c(1,2))

#discriminacao constante, mudando a dificuldade
###############################################
a=1
theta=seq(-5,5,by=0.1)

b=0
eta=a*(theta-b)
pl=pnorm(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")

b=-2
eta=a*(theta-b)
pl2=pnorm(eta)
lines(theta,pl2,col=3,type="l",lwd=3)

b=2
eta=a*(theta-b)
pl3=pnorm(eta)
lines(theta,pl3,col=6,type="l",lwd=3)

legend(1.5,0.3,c(expression(b==0), expression(b==-2), expression(b==2)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)

#dificuldade constante, mudando a discriminacao
###############################################
b=0
theta=seq(-5,5,by=0.1)

a=1
eta=a*(theta-b)
pl=pnorm(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")

a=0.5
eta=a*(theta-b)
pl2=pnorm(eta)
lines(theta,pl2,col=3,type="l",lwd=3)

a=1.5
eta=a*(theta-b)
pl3=pnorm(eta)
lines(theta,pl3,col=6,type="l",lwd=3)

legend(1.5,0.3,c(expression(a==1), expression(a==0.5), expression(a==1.5)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)
text(1,0.05,"y=1",lwd=3)


#CURVAS CARACTERISTICAS DOS ITEMS MODELO DE 2 PARAMETROS NORMAL
#E NORMAL APROXIMADO PELA LOGISTICA
#########################################################

par(mfrow=c(1,2))

#discriminacao constante, mudando a dificuldade
###############################################
a=1
theta=seq(-5,5,by=0.1)

b=0
eta=a*(theta-b)
pl=pnorm(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")
pp=plogis(1.702*eta)
lines(theta,pp,lty=1,col=10,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")



b=-2
eta=a*(theta-b)
pl2=pnorm(eta)
lines(theta,pl2,col=3,type="l",lwd=3)
pp=plogis(1.702*eta)
lines(theta,pp,lty=1,col=10,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")


b=2
eta=a*(theta-b)
pl3=pnorm(eta)
lines(theta,pl3,col=6,type="l",lwd=3)
pp=plogis(1.702*eta)
lines(theta,pp,lty=1,col=10,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")


legend(1.5,0.3,c(expression(b==0), expression(b==-2), expression(b==2)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)

#dificuldade constante, mudando a discriminacao
###############################################
b=0
theta=seq(-5,5,by=0.1)

a=1
eta=a*(theta-b)
pl=pnorm(eta)
plot(theta,pl,lty=1,col=1,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")
pp=plogis(1.702*eta)
lines(theta,pp,lty=1,col=10,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")


a=0.5
eta=a*(theta-b)
pl2=pnorm(eta)
lines(theta,pl2,col=3,type="l",lwd=3)
pp=plogis(1.702*eta)
lines(theta,pp,lty=1,col=10,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")


a=1.5
eta=a*(theta-b)
pl3=pnorm(eta)
lines(theta,pl3,col=6,type="l",lwd=3)
pp=plogis(1.702*eta)
lines(theta,pp,lty=1,col=10,xlab=expression(theta),ylab="probability of correct response",cex.lab=1.5,cex.axis=1.2,lwd=3,type="l")


legend(1.5,0.3,c(expression(a==1), expression(a==0.5), expression(a==1.5)),col=c(1,3,6),lty=1,text.width=1.2,lwd=3)
abline(v=0,h=.5,lty=3)
text(1,0.05,"y=1",lwd=3)