library(ltm)
library(mirt)

data <- read.csv("neuroticism500.csv", header = T, row.names = 1)
head(data)

#########################
# Graded response model #
#########################

# Fit Graded Response Model using library ltm in R. 
# Provide table with discrimination and location parameters for each item.
?grm

(fit.grm2 <- grm(data))
summary(fit.grm2)
coef(fit.grm2)

# using mirt library
fit.grm2.mirt <- mirt(data, 1, itemtype = "graded")
coef(fit.grm2.mirt, simplify = T)

# Fit 1PL version of Graded Response Model (with equal discriminations for all items). 
# Provide table with discrimination and location parameters for each item.

(fit.grm1 <- grm(data, constrained = TRUE))
coef(fit.grm1)

# s mirtem
s <- 'F = 1-5
      CONSTRAIN = (1-5, a1)'
s <- mirt.model(s)
fit.grm1.mirt <- mirt(data, s, itemtype = "graded")
coef(fit.grm1.mirt, simplify = T)

# Use some criteria to decide between these two models.
anova(fit.grm1, fit.grm2) 

# using mirt library
anova(fit.grm1.mirt, fit.grm2.mirt) 

# Plot Category Response Curves for all items (provide 5 figures)
par(mfrow = c(2, 3))
plot(fit.grm2) 
par(mfrow = c(1, 1))

# using mirt
plot(fit.grm2.mirt, type = "trace")
plot(fit.grm2.mirt, type = "trace", facet_items = F)

# Looking at the figures, suggest at least one response category in at least one item 
# that might be good to merge with another category.

# Plot Item Information Curves, preferably all in one plot.
plot(fit.grm2, type = "IIC", items = NULL)
# Which item is the most informative for average respondent? 
# using mirt
plot(fit.grm2.mirt, type = "infotrace", facet_items = F)

# Plot Test information Function.
plot(fit.grm2, type = "IIC", items = 0) 
# For what type of respondents is the instrument most informative?
# using mirt
plot(fit.grm2.mirt, type = "info")

# Provide table with response patterns, estimated latent trait scores (factor scores) 
# and their standard errors for first 10 respondents.
factor.scores(fit.grm2, resp.patterns = data)$score.dat[1:10, ]


###########################################
# Generalized Partial Credit Model (GPCM) #
###########################################

# Fit Generalized Partial Credit Model using library ltm in R. 
# Provide table with discrimination and location parameters for each item.

?gpcm
(fit.gpcm <- gpcm(data, constraint = "gpcm"))
summary(fit.gpcm)
coef(fit.gpcm)

# using mirt
fit.gpcm.mirt <- mirt(data, 1, itemtype = "gpcm")
coef(fit.gpcm.mirt, simplify = T)

# Fit 1PL version of Generalized Partial Credit Model 
# (with equal discriminations for all items). 
# Provide table with discrimination and location parameters for each item.
(fit.gpcm1pl <- gpcm(data, constraint = "1PL"))
coef(fit.gpcm1pl)

# using mirt
s <- 'F = 1-5
      CONSTRAIN = (1-5, a1)'
s <- mirt.model(s)
fit.gpcm1pl.mirt <- mirt(data, s, itemtype = "gpcm")
coef(fit.gpcm1pl.mirt, simplify = T)

# Use some criteria to decide between these two models.
anova(fit.gpcm1pl, fit.gpcm)
# using mirt
anova(fit.gpcm1pl.mirt, fit.gpcm.mirt)

# Plot Category Response Curves for all items (in 5 figures).
par(mfrow = c(2, 3))
plot(fit.gpcm)
par(mfrow = c(1, 1))

# using mirt
plot(fit.gpcm.mirt, type = "trace")
plot(fit.gpcm.mirt, type = "trace", facet_items = F)

# Plot Item Information Curves, preferably all in one plot.
plot(fit.gpcm, type = "IIC", items = NULL)
# using mirt
plot(fit.gpcm.mirt, type = "infotrace", facet_items = F)

# Plot Test information Function.
plot(fit.gpcm, type = "IIC", items = 0)
# s mirtem
plot(fit.gpcm.mirt, type = "info")


# Use some criteria to decide between GRM and GPCM.
AIC(fit.grm2)
AIC(fit.gpcm)

BIC(fit.grm2)
BIC(fit.gpcm)

#################
# Nominal model #
#################

# using mirt
fit.nomi.mirt <- mirt(data, 1, itemtype = "nominal")
coef(fit.nomi.mirt, simplify = T)

# ICC
plot(fit.nomi.mirt, type = "trace")
plot(fit.nomi.mirt, type = "trace", facet_items = F)

# IIC
plot(fit.nomi.mirt, type = "infotrace", facet_items = F)

# TIF
plot(fit.nomi.mirt, type = "info")