Extended Time Analysis: Part 2 - Latent Variable Modeling (IRT)
nitaked
7/6/2018
Data
allData is a list with 20 objects. 4 are the Winter 2018 exam files, 14 are the past exam files. 2 are gender and time cluster information for Winter 2018.
| allData_Elements | Name |
|---|---|
| 1 | WN2018_E4 |
| 2 | WN2018_E3 |
| 3 | WN2018_E2 |
| 4 | WN2018_E1 |
| 5 | WN2016_E1 |
| 6 | WN2015_E4 |
| 7 | WN2015_E3 |
| 8 | WN2015_E2 |
| 9 | WN2015_E1 |
| 10 | WN2014_E4 |
| 11 | WN2014_E3 |
| 12 | WN2014_E2 |
| 13 | WN2014_E1 |
| 14 | WN2013_E4 |
| 15 | WN2013_E3 |
| 16 | WN2013_E2 |
| 17 | WN2013_E1 |
| 18 | FA2004_E3 |
| 19 | WN2018_gender_3cluster |
| 20 | WN2018_gender_2cluster |
41 Repeated Questions - matched to WN2018 term and original term
| Number | WN2018_Info | OriginalTerm_Info |
|---|---|---|
| 1 | WN2018_E4_Q1 | WN2013_E4_Q6 |
| 2 | WN2018_E4_Q5 | WN2013_E4_Q4 |
| 3 | WN2018_E4_Q7 | WN2015_E4_Q3 |
| 4 | WN2018_E4_Q13 | WN2013_E4_Q7 |
| 5 | WN2018_E4_Q14 | WN2013_E4_Q10 |
| 6 | WN2018_E4_Q16 | WN2015_E4_Q17 |
| 7 | WN2018_E4_Q17 | WN2015_E4_Q14 |
| 8 | WN2018_E4_Q18 | WN2015_E4_Q15 |
| 9 | WN2018_E4_Q19 | WN2014_E4_Q12 |
| 10 | WN2018_E4_Q20 | WN2013_E4_Q19 |
| 11 | WN2018_E4_Q21 | WN2013_E4_Q24 |
| 12 | WN2018_E4_Q22 | WN2015_E4_Q19 |
| 13 | WN2018_E3_Q4 | WN2015_E3_Q4 |
| 14 | WN2018_E3_Q5 | WN2013_E3_Q5 |
| 15 | WN2018_E3_Q6 | FA2004_E3_Q5 |
| 16 | WN2018_E3_Q7 | WN2014_E3_Q7 |
| 17 | WN2018_E3_Q9 | WN2015_E3_Q9 |
| 18 | WN2018_E3_Q12 | FA2004_E3_Q12 |
| 19 | WN2018_E3_Q13 | WN2013_E3_Q13 |
| 20 | WN2018_E3_Q17 | FA2004_E3_Q17 |
| 21 | WN2018_E3_Q18 | WN2013_E3_Q18 |
| 22 | WN2018_E2_Q1 | WN2013_E2_Q1 |
| 23 | WN2018_E2_Q2 | WN2015_E2_Q2 |
| 24 | WN2018_E2_Q4 | WN2014_E2_Q4 |
| 25 | WN2018_E2_Q7 | WN2014_E2_Q7 |
| 26 | WN2018_E2_Q8 | WN2013_E2_Q8 |
| 27 | WN2018_E2_Q11 | WN2013_E2_Q11 |
| 28 | WN2018_E2_Q12 | WN2013_E2_Q13 |
| 29 | WN2018_E2_Q13 | WN2014_E2_Q13 |
| 30 | WN2018_E2_Q14 | WN2013_E2_Q14 |
| 31 | WN2018_E2_Q19 | WN2015_E2_Q19 |
| 32 | WN2018_E1_Q2 | WN2016_E1_Q2 |
| 33 | WN2018_E1_Q3 | WN2014_E4_Q4 |
| 34 | WN2018_E1_Q4 | WN2013_E1_Q4 |
| 35 | WN2018_E1_Q5 | WN2014_E1_Q5 |
| 36 | WN2018_E1_Q6 | WN2014_E4_Q6 |
| 37 | WN2018_E1_Q8 | WN2013_E1_Q8 |
| 38 | WN2018_E1_Q9 | WN2016_E1_Q8 |
| 39 | WN2018_E1_Q12 | WN2015_E1_Q12 |
| 40 | WN2018_E1_Q16 | WN2013_E1_Q16 |
| 41 | WN2018_E1_Q19 | WN2014_E1_Q19 |
Data in format for Item Response Theory
17 exam files.
# Fall 2004 in a different format, worry about later (allData[[18]])
allDataLTM <- list()
for (i in 1:(length(allData) - 3)) {
allDataLTM[[i]] <- allData[[i]][c(9:38)]
allDataLTM[[i]] <- allDataLTM[[i]][, colSums(allDataLTM[[i]] != 0) > 0]
}Latent Variable Modeling
diff_discr_list <- list()
# Do this for all 17 exam files...
diff_discr_list[[1]] <- data.frame(summary(ltm(allDataLTM[[1]] ~ z1))$coefficients)Plot difficulty versus discrimination for each exam question
This only shows the 25 questions from Winter 2018 final exam. Next steps to plot all the repeated questions, in the original term and Winter 2018 term.
ggplot(coefTable[[1]], aes(Difficulty, Discrimination, color = Question)) +
geom_point() + geom_text(aes(label=Question),
vjust = -.7, hjust = -.7, size = 3) +
geom_errorbar(aes(Difficulty,
ymin = Discrimination - Standard.Error.Discr,
ymax = Discrimination + Standard.Error.Discr), width = .1) +
geom_errorbarh(aes(xmin = Difficulty - Standard.Error.Diff,
xmax = Difficulty + Standard.Error.Diff,
Discrimination), height = .06)
Repeated Questions
Winter 2018 Exam Questions
WN2018Table_E4 <- coefTable[[1]][c(1,5,7,13,14,16,17,18,19,20,21,22),] %>%
mutate(Winter2018 = c("E4_Q1", "E4_Q5", "E4_Q7", "E4_Q13", "E4_Q14",
"E4_Q16", "E4_Q17", "E4_Q18", "E4_Q19",
"E4_Q20", "E4_Q21", "E4_Q22")) %>%
mutate(WN2018Exam = "E4")
WN2018Table_E3 <- coefTable[[2]][c(4,5,6,7,9,12,13,17,18),] %>%
mutate(Winter2018 = c("E3_Q4", "E3_Q5", "E3_Q6", "E3_Q7", "E3_Q9",
"E3_Q12", "E3_Q13", "E3_Q17", "E3_Q18")) %>%
mutate(WN2018Exam = "E3")
WN2018Table_E2 <- coefTable[[3]][c(1,2,4,7,8,11,12,13,14,19),] %>%
mutate(Winter2018 = c("E2_Q1", "E2_Q2", "E2_Q4", "E2_Q7", "E2_Q8",
"E2_Q11", "E2_Q12", "E2_Q13", "E2_Q14", "E2_Q19")) %>%
mutate(WN2018Exam = "E2")
WN2018Table_E1 <- coefTable[[4]][c(2,3,4,5,6,8,9,12,16,19),] %>%
mutate(Winter2018 = c("E1_Q2", "E1_Q3", "E1_Q4", "E1_Q5", "E1_Q6",
"E1_Q8", "E1_Q9", "E1_Q12", "E1_Q16", "E1_Q19")) %>%
mutate(WN2018Exam = "E1")
WN2018Table <- rbind(WN2018Table_E1, WN2018Table_E2) %>%
rbind(WN2018Table_E3) %>% rbind(WN2018Table_E4) %>% mutate(Term = "WN2018")ggplot(WN2018Table, aes(Difficulty, Discrimination, color = Question)) +
geom_point() +
geom_errorbar(aes(Difficulty,
ymin = Discrimination - Standard.Error.Discr,
ymax = Discrimination + Standard.Error.Discr), width = .1) +
geom_errorbarh(aes(xmin = Difficulty - Standard.Error.Diff,
xmax = Difficulty + Standard.Error.Diff,
Discrimination), height = .06) + geom_text(aes(label=Question),
vjust = -.7, hjust = -.7, size = 3) + facet_wrap(~Info)
Original Exam Questions
ggplot(OGTable, aes(Difficulty, Discrimination, color = Question)) +
geom_point() +
geom_errorbar(aes(Difficulty,
ymin = Discrimination - Standard.Error.Discr,
ymax = Discrimination + Standard.Error.Discr), width = .1) +
geom_errorbarh(aes(xmin = Difficulty - Standard.Error.Diff,
xmax = Difficulty + Standard.Error.Diff,
Discrimination), height = .06) + geom_text(aes(label=Question),
vjust = -.7, hjust = -.7, size = 3) + facet_wrap(~Info)
All Repeated Questions
FullTable <- rbind(WN2018Table, OGTable)[c(9,8,7,1:6)]
FullTable$TermQuestion <- paste(FullTable$Info, FullTable$Question, sep = "_")
for (i in 1:nrow(FullTable)) {
if(FullTable$Term[i] == "WN2018") {
FullTable$TermQuestion[i] = ""
}
}Winter 2018 Exam 1 Questions - Coefficients for OG and WN2018 terms
ggplot(filter(FullTable, WN2018Exam == "E1"),
aes(Difficulty, Discrimination, color = Term)) +
geom_point() + facet_wrap(~Winter2018, ncol = 3) +
geom_errorbar(aes(ymin = Discrimination - Standard.Error.Discr,
ymax = Discrimination + Standard.Error.Discr),
width = .2) +
geom_errorbarh(aes(xmin = Difficulty - Standard.Error.Diff,
xmax = Difficulty + Standard.Error.Diff),
height = .1) +
geom_text(aes(label = TermQuestion), size = 2.5, x = -3, y = 1.75) + ylim(c(0,2))
Winter 2018 Exam 2 Questions - Coefficients for OG and WN2018 terms
ggplot(filter(FullTable, WN2018Exam == "E2"),
aes(Difficulty, Discrimination, color = Term)) +
geom_point() + facet_wrap(~Winter2018, ncol = 3) +
geom_errorbar(aes(ymin = Discrimination - Standard.Error.Discr,
ymax = Discrimination + Standard.Error.Discr),
width = .2) +
geom_errorbarh(aes(xmin = Difficulty - Standard.Error.Diff,
xmax = Difficulty + Standard.Error.Diff),
height = .1) +
geom_text(aes(label = TermQuestion), size = 2.5, x = -3, y = 1.75) + ylim(c(0,2))
Winter 2018 Exam 3 Questions - Coefficients for OG and WN2018 terms
The OG terms for 3 of these questions are not plotted, because they are from Fall 2004.
ggplot(filter(FullTable, WN2018Exam == "E3"),
aes(Difficulty, Discrimination, color = Term)) +
geom_point() + facet_wrap(~Winter2018, ncol = 3) +
geom_errorbar(aes(ymin = Discrimination - Standard.Error.Discr,
ymax = Discrimination + Standard.Error.Discr),
width = .2) +
geom_errorbarh(aes(xmin = Difficulty - Standard.Error.Diff,
xmax = Difficulty + Standard.Error.Diff),
height = .1) +
geom_text(aes(label = TermQuestion), size = 2.5, x = -1.75, y = 1.75) + ylim(c(0,2))
Winter 2018 Exam 4 Questions - Coefficients for OG and WN2018 terms
ggplot(filter(FullTable, WN2018Exam == "E4"),
aes(Difficulty, Discrimination, color = Term)) +
geom_point() + facet_wrap(~Winter2018, ncol = 3) +
geom_errorbar(aes(ymin = Discrimination - Standard.Error.Discr,
ymax = Discrimination + Standard.Error.Discr),
width = .2) +
geom_errorbarh(aes(xmin = Difficulty - Standard.Error.Diff,
xmax = Difficulty + Standard.Error.Diff),
height = .1) +
geom_text(aes(label = TermQuestion), size = 2.5, x = -3, y = 1.75) + ylim(c(0,2.5))