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#                L7 - IRT MODELS FOR ORDINAL AND NOMINAL ITEMS                     #
#                                    NMST570                                       #
#                             Last update: 01/12/2020                              #
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# Slides available at http://www.cs.cas.cz/martinkova/NMST570.html
# HW assignment available at http://www.cs.cas.cz/hladka/documents/NMST570_2020_HW7.pdf

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# Loading data #####################################################################
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data <- read.csv("neuroticism500.csv", header = TRUE, row.names = 1)
head(data)
summary(data)

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# Loading packages #################################################################
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library(mirt)

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# Ex. 3.2. #########################################################################
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#-----------------------------------------------------------------------------------
# 1. fit GRM model with mirt package with the same discrimination for all items

### open help for function mirt()
?mirt

### to fit GRM model with mirt() function. You need to specify data, model and itemtype
### first we need to specify constraints for parameter a:
s <- 'F = 1-5
CONSTRAIN = (1-5, a1)'
### this mean that we assume one latent trait for all 5 items and we constrain 
### parameter a to be the same for all items
### itemtype = "graded" means that we assumed GRM model for all items
### replace ???
fitGRM1 <- mirt(data = ???, model = s, itemtype = ???)
summary(fitGRM1)

### print estimated parameters, replace ???
coef(???, simplify = TRUE)

#-----------------------------------------------------------------------------------
# 2. fit GRM model with mirt package with no constrain

### simply use model = 1
### itemtype = "graded" means that we assumed GRM model for all items
### replace ???
fitGRM2 <- mirt(data = ???, model = ???, itemtype = ???)
summary(fitGRM2)

### print estimated parameters, replace ???
coef(???, simplify = TRUE)

#-----------------------------------------------------------------------------------
# 3. decide between two models

### help for anova
??anova.SingleGroupClass

### now compare both models with anova() function
### replace ???
anova(???, ???)

#-----------------------------------------------------------------------------------
# 4. category response curve

### help for plot
??plot.SingleGroupClass

### plot category response curve
### you need to specify model and type. For category response curve use type = "trace"
### replace ???
plot(???, type = ???)

#-----------------------------------------------------------------------------------
# 5. item information curve

### item information curve
### you need to specify model and type. For item information curve use type = "infotrace"
### to plot all curves in one model use argument facet_items = F
### replace ???
plot(???, type = ???)

#-----------------------------------------------------------------------------------
# 6. test information curve

### test information curve
### you need to specify model and type. For test information curve use type = "infoSE"
### replace ???
plot(???, type = ???)