Created
January 13, 2019 20:33
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Submission for 2016 EM:IP Cover Showcase
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# Note: Code and graphic have been updated since original submission | |
### User input ----------------------------------------------------------------- | |
num_stu <- 20000 | |
num_testlet <- 6 | |
num_item <- 10 | |
set.seed(3567) | |
### Packages ------------------------------------------------------------------- | |
needed_packages <- c("tidyverse", "glue", "tidyselect", "colorblindr", | |
"hrbrthemes", "ggforce") | |
load_packages <- function(x) { | |
if (!(x %in% installed.packages())) { | |
install.packages(x) | |
} | |
suppressPackageStartupMessages(require(x, character.only = TRUE)) | |
} | |
vapply(needed_packages, load_packages, logical(1)) | |
### Simulate test -------------------------------------------------------------- | |
items <- crossing( | |
level = seq_len(5), | |
testlet = seq_len(num_testlet), | |
item = seq_len(num_item) | |
) %>% | |
filter(!(testlet == 1 & level == 5)) %>% | |
mutate( | |
nonmaster_prob = runif(n = nrow(.), min = 0.1, max = 0.4), | |
master_prob = runif(n = nrow(.), min = 0.6, max = 0.9) | |
) | |
profiles <- list( | |
c(0, 0, 0, 0, 0), | |
c(1, 0, 0, 0, 0), | |
c(1, 1, 0, 0, 0), | |
c(1, 1, 1, 0, 0), | |
c(1, 1, 1, 1, 0), | |
c(1, 1, 1, 1, 1) | |
) | |
profile_probs <- c(0.15, 0.35, 0.25, 0.12, 0.09, 0.04) | |
stu_profiles <- map(seq_len(num_stu), function(x) { | |
map_dbl(seq_len(num_testlet), function(x) { | |
sample(profiles, size = 1) %>% | |
flatten_dbl() %>% sum() | |
}) | |
}) | |
max_int <- function(x, m) { | |
as.integer(min(x, m)) | |
} | |
min_int <- function(x, m) { | |
as.integer(max(x, m)) | |
} | |
stu_bands <- map_dbl(.x = stu_profiles, .f = function(x, bands) { | |
poss <- (round(mean(x), 0) - 1):(round(mean(x), 0) + 1) | |
poss <- vapply(poss, max_int, integer(1), m = max(bands)) | |
poss <- vapply(poss, min_int, integer(1), m = min(bands)) | |
sample(poss, size = 1) | |
}, | |
bands = filter(items, testlet == 1) %>% pull(level) %>% unique()) | |
only_if <- function(condition) { | |
function(func) { | |
if (condition) { | |
func | |
} else { | |
function(., ...) . | |
} | |
} | |
} | |
sim_data <- map2_dfr(stu_profiles, stu_bands, function(profile, band, | |
items) { | |
stu_data <- list_along(unique(items$testlet)) | |
stu_levels <- list_along(unique(items$testlet)) %>% | |
set_names(nm = glue("rank_{seq_len(length(.))}")) | |
cur_level <- as.integer(band) | |
for (i in seq_along(stu_levels)) { | |
stu_levels[[i]] <- cur_level | |
master <- profile[i] >= cur_level | |
cur_testlet <- items %>% | |
filter(testlet == i, level == cur_level) %>% | |
mutate(rnd = runif(n = nrow(.), min = 0, max = 1)) %>% | |
only_if(master)(mutate)(score = | |
case_when(rnd <= master_prob ~ 1, TRUE ~ 0)) %>% | |
only_if(!master)(mutate)(score = | |
case_when(rnd <= nonmaster_prob ~ 1, TRUE ~ 0)) %>% | |
select(level, testlet, item, score) | |
stu_data[[i]] <- cur_testlet | |
pct_cor <- mean(cur_testlet$score) | |
if (pct_cor < 0.35) { | |
cur_level <- cur_level - 1 | |
} else if (pct_cor >= 0.8) { | |
cur_level <- cur_level + 1 | |
} | |
cur_level <- vapply(cur_level, max_int, integer(1), max(items$level)) | |
cur_level <- vapply(cur_level, min_int, integer(1), min(items$level)) | |
} | |
bind_cols( | |
data_frame( | |
stu_data = list(bind_rows(stu_data)), | |
path = flatten_int(stu_levels) %>% paste(collapse = "") | |
), | |
as_data_frame(stu_levels) | |
) | |
}, items = items) | |
rm(list = setdiff(ls(), c("sim_data", "num_item", "num_stu", "num_testlet"))) | |
save(list = ls(), file = "~/Desktop/emip-2018-data.rda") | |
### Line plot ------------------------------------------------------------------ | |
load("~/Desktop/emip-2018-data.rda") | |
pattern_count <- sim_data %>% | |
filter(str_detect(path, "^2")) %>% | |
group_by(path, rank_6) %>% | |
summarize(n = n()) %>% | |
group_by(rank_6) %>% | |
top_n(10, wt = n) %>% | |
ungroup() %>% | |
select(path, n) | |
line_data <- pmap_dfr(pattern_count, function(path, n) { | |
pattern <- str_split(path, "") %>% flatten_chr() %>% as.integer() | |
pat_data <- data_frame(testlet = seq_along(pattern), level = pattern, | |
final_level = pattern[length(pattern)]) | |
ret_data <- data_frame( | |
pat_data = list(pat_data), | |
line_id = glue("{path}_{seq_len(n)}") | |
) %>% | |
unnest() | |
}) %>% | |
mutate(final_level = factor(final_level, levels = 1:5, | |
labels = c("Initial\nPrecursor", "Distal\nPrecursor", "Proximal\nPrecursor", | |
"Target", "Successor"))) | |
point_data <- sim_data %>% | |
rowid_to_column(var = "stu_id") %>% | |
filter(str_detect(path, "^2")) %>% | |
select(-stu_data, -path) %>% | |
gather(key = rank, value = level, -stu_id) %>% | |
mutate(rank = str_replace(rank, "rank_", "") %>% as.integer()) %>% | |
group_by(rank, level) %>% | |
summarize(num_stu = n()) | |
line_plot <- ggplot() + | |
geom_line(data = line_data, aes(x = testlet, y = level, group = line_id, | |
color = factor(final_level)), stat = "smooth", method = "loess", | |
alpha = 0.009, size = 1) + | |
geom_point(aes(x = point_data$rank, y = point_data$level, | |
size = point_data$num_stu), color = "black", alpha = 0.4) + | |
scale_x_continuous(lim = c(1, num_testlet), breaks = seq_len(num_testlet)) + | |
scale_y_continuous(lim = c(0, 6), breaks = seq_len(5), | |
labels = c("Initial\nPrecursor", "Distal\nPrecursor", "Proximal\nPrecursor", | |
"Target", "Successor")) + | |
scale_size_area(limits = c(0, num_stu), max_size = 25, | |
breaks = c(100, 500, seq(1000, 4000, 1000))) + | |
scale_color_OkabeIto() + | |
coord_cartesian(ylim = c(1, 5), xlim = c(1, num_testlet)) + | |
labs(x = "Testlet Number", y = "Linkage Level", size = "Number of\nStudents", | |
color = "Ending\nLinkage Level") + | |
theme_ipsum_ps() + | |
theme(legend.position = "bottom", legend.box = "vertical", | |
panel.grid.minor = element_blank()) + | |
guides( | |
color = guide_legend(nrow = 1, order = 1, override.aes = list(alpha = 1)), | |
size = guide_legend(nrow = 1, order = 2) | |
) | |
ggsave("line-plot.png", plot = line_plot, width = 12, height = 8, units = "in", | |
dpi = "retina") |
Author
wjakethompson
commented
Jan 13, 2019
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