# Data importing

data <- read.table("C:/cho_athay_preacher_2012.data.txt",header=T,fill=T)



# Call library

library(lme4)


# Variable type change

data$ITEM <- as.factor(data$item)

data$TIME <- as.factor(data$time)

data$GROUP <- as.factor(data$group)




# Model 1: Embretson descriptive model for unidimensional tests

M1 <- lmer(y ~ -1+ITEM+(Q1 + Q2 + Q3-1|person), data, binomial("logit"))


# Model 2: Embretson descriptive model for unidimensional tests

M2 <- lmer(y ~ 1 + TIME*GROUP  + operation + measurement + representation + (1|item) + (Q1 + Q2 + Q3-1|person), data, binomial("logit"))


# Creating Q_{d[i]t} for Models 3, 4, 5, and 6

data$operationQ1 <- (data$operation)*(data$Q1)

data$operationQ2 <- (data$operation)*(data$Q2)

data$operationQ3 <- (data$operation)*(data$Q3)


data$measurementQ1 <- (data$measurement)*(data$Q1)

data$measurementQ2 <- (data$measurement)*(data$Q2)

data$measurementQ3 <- (data$measurement)*(data$Q3)



data$representationQ1 <- (data$representation)*(data$Q1)

data$representationQ2 <- (data$representation)*(data$Q2)

data$representationQ3 <- (data$representation)*(data$Q3)



# Model 3: Descriptive longitudinal models for multidimensional tests

M3 <- lmer(y ~ -1 + ITEM + (operationQ1 + operationQ2 + operationQ3 - 1|person) + (measurementQ1 + measurementQ2 + measurementQ3 -1|person) + (representationQ1 + 
representationQ2 + representationQ3 -1|person), data, binomial("logit"))




# Model 4: Explanatory longitudinal models for multidimensional tests


M4 <- lmer(y ~ 1 + TIME*GROUP  + operation + measurement + representation + (1|item)  + (operationQ1 + operationQ2 + operationQ3 - 1|person) + (measurementQ1 + 
measurementQ2 + measurementQ3 -1|person) + (representationQ1 + representationQ2 + representationQ3 -1|person), data, binomial("logit"))



# Model 5: Descriptive bi-factor longitudinal models for multidimensional tests


M5 <- lmer(y ~ -1 + ITEM + (Q1-1|person) + (Q2-1|person) + (Q3-1|person) + (operationQ1-1|person) + (operationQ2-1|person) +( operationQ3-1|person) + 
(measurementQ1-1|person) + (measurementQ2-1|person) + (measurementQ3 -1|person) + (representationQ1-1|person) + (representationQ2-1|person) + (representationQ3 
-1|person), data, binomial("logit"))




# Model 6: Explanatory bi-factor longitudinal models for multidimensional tests


M6 <- lmer(y ~ 1 + TIME*GROUP  + operation + measurement + representation  + (1|item) + (Q1-1|person) + (Q2-1|person) + (Q3-1|person) + 
(operationQ1-1|person) + (operationQ2-1|person) +( operationQ3-1|person) + (measurementQ1-1|person) + (measurementQ2-1|person) + (measurementQ3 -1|person) + 
(representationQ1-1|person) + (representationQ2-1|person) + (representationQ3 -1|person), data, binomial("logit"))


# Model comparisons

anova(M1,M2,M3,M4,M5,M6)