Setup

library(tidyverse)
library(here)
library(lubridate)
library(ggthemes)
library(langcog)
library(mirt)
library(knitr)

pilot_data_filtered <- read_csv(file = here::here('data/preprocessed_data/all_preprocessed_data.csv')) %>%
  mutate(word1 = str_replace(word1, ' ', '.')) %>%
  mutate(word2 = str_replace(word2, ' ', '.')) %>%
  mutate(item_pair = paste0(word1,'_',word2))

d_wide_all<- pilot_data_filtered %>%
  ungroup() %>%
  select(sub_id, item_pair, correct) %>%
  arrange(item_pair) %>%
  ungroup() %>%
  pivot_wider(names_from=item_pair, values_from=correct, values_fn = ~mean(.x)) %>%
  ungroup()

d_mat_all <- d_wide_all %>%
  select(-sub_id) %>%
  data.frame %>%
  data.matrix 

rownames(d_mat_all) <- d_wide_all$sub_id

Get subject data

school_meta <- read_csv(here::here('data/rocketship_data/cs01-metadata-age.csv')) %>%
  as_tibble() %>%
  select(pid, grade, age)

sub_data_age_cleaned <- pilot_data_filtered %>%
  filter(! cohort %in% c('school')) %>%
  distinct(age, pid) %>%
  mutate(age = str_replace(age, '\\+', '')) %>%
  mutate(age = str_replace(age, 'Adult', '20')) %>%
  mutate(age = as.numeric(age)) %>%
  full_join(school_meta %>% select(pid,age))

Run iterative 2PL IRT model with all data

With guess rate of 0.5 Removes items that have slopes <.7

outliers <- TRUE
maxiter <- 20
iteration <- 0
df_good <- d_mat_all
aminmax <- c(.7, Inf) # Keep items with positive slopes over .9

# Model priors specified in loop

while (outliers > 0 & iteration<maxiter){
  iteration <- iteration + 1;
  start.dim <- dim(df_good)[2]-1
  mm = (
  'F = 1-%d,
  PRIOR = (1-%d, a1, norm, .2, 1),
  PRIOR = (1-%d, d, norm, 0, 2)'
  )
  mm = mirt.model(sprintf(mm,start.dim,start.dim,start.dim))
  m <- mirt(df_good, model = mm,itemtype = '2PL',guess=0.5) # 2AFC. Guess Rate = 0.5
  co <- coef(m,simplify=TRUE, IRTpars = FALSE) # Get coeeficients
  co <- tibble::rownames_to_column(as.data.frame(co$items),'words')
  ggplot(co, aes(a1, d)) + geom_point(size=3)
  # ggsave(sprintf('2PL-ModelParams_%d.png',iteration))
  # Remove items with low or extreme slope and refit
  df_good <- df_good[,which(co$a1>aminmax[1] & co$a1<aminmax[2])]
  end.dim <- dim(df_good)[2]-1
  outliers <- sum(!(co$a1>aminmax[1] & co$a1<aminmax[2]))
  print(sprintf('2PL ITERATION %d. STARTED WITH %d ITEMS. %d OUTLIERS REMOVED. %d ITEMS RETAINED.',iteration,start.dim,outliers,end.dim))
}

## 
Iteration: 1, Log-Lik: -56576.090, Max-Change: 19.79992
Iteration: 2, Log-Lik: -43505.654, Max-Change: 10.32434
Iteration: 3, Log-Lik: -42380.588, Max-Change: 4.02271
Iteration: 4, Log-Lik: -42164.092, Max-Change: 2.13244
Iteration: 5, Log-Lik: -42106.750, Max-Change: 0.47059
Iteration: 6, Log-Lik: -42084.497, Max-Change: 0.10578
Iteration: 7, Log-Lik: -42074.445, Max-Change: 0.08024
Iteration: 8, Log-Lik: -42069.250, Max-Change: 0.06239
Iteration: 9, Log-Lik: -42066.279, Max-Change: 0.04749
Iteration: 10, Log-Lik: -42064.519, Max-Change: 0.03698
Iteration: 11, Log-Lik: -42063.458, Max-Change: 0.02859
Iteration: 12, Log-Lik: -42062.814, Max-Change: 0.02243
Iteration: 13, Log-Lik: -42061.855, Max-Change: 0.00552
Iteration: 14, Log-Lik: -42061.828, Max-Change: 0.00377
Iteration: 15, Log-Lik: -42061.814, Max-Change: 0.00319
Iteration: 16, Log-Lik: -42061.791, Max-Change: 0.00461
Iteration: 17, Log-Lik: -42061.789, Max-Change: 0.00175
Iteration: 18, Log-Lik: -42061.789, Max-Change: 0.00080
Iteration: 19, Log-Lik: -42061.788, Max-Change: 0.00038
Iteration: 20, Log-Lik: -42061.788, Max-Change: 0.00037
Iteration: 21, Log-Lik: -42061.788, Max-Change: 0.00037
Iteration: 22, Log-Lik: -42061.787, Max-Change: 0.00163
Iteration: 23, Log-Lik: -42061.787, Max-Change: 0.00116
Iteration: 24, Log-Lik: -42061.787, Max-Change: 0.00087
Iteration: 25, Log-Lik: -42061.787, Max-Change: 0.00028
Iteration: 26, Log-Lik: -42061.787, Max-Change: 0.00027
Iteration: 27, Log-Lik: -42061.787, Max-Change: 0.00133
Iteration: 28, Log-Lik: -42061.787, Max-Change: 0.00113
Iteration: 29, Log-Lik: -42061.787, Max-Change: 0.00087
Iteration: 30, Log-Lik: -42061.787, Max-Change: 0.00066
Iteration: 31, Log-Lik: -42061.787, Max-Change: 0.00022
Iteration: 32, Log-Lik: -42061.787, Max-Change: 0.00106
Iteration: 33, Log-Lik: -42061.787, Max-Change: 0.00080
Iteration: 34, Log-Lik: -42061.787, Max-Change: 0.00018
Iteration: 35, Log-Lik: -42061.787, Max-Change: 0.00018
Iteration: 36, Log-Lik: -42061.787, Max-Change: 0.00087
Iteration: 37, Log-Lik: -42061.787, Max-Change: 0.00062
Iteration: 38, Log-Lik: -42061.787, Max-Change: 0.00047
Iteration: 39, Log-Lik: -42061.787, Max-Change: 0.00036
Iteration: 40, Log-Lik: -42061.787, Max-Change: 0.00014
Iteration: 41, Log-Lik: -42061.787, Max-Change: 0.00069
Iteration: 42, Log-Lik: -42061.787, Max-Change: 0.00040
Iteration: 43, Log-Lik: -42061.787, Max-Change: 0.00012
Iteration: 44, Log-Lik: -42061.787, Max-Change: 0.00058
Iteration: 45, Log-Lik: -42061.787, Max-Change: 0.00040
Iteration: 46, Log-Lik: -42061.787, Max-Change: 0.00010
Iteration: 47, Log-Lik: -42061.787, Max-Change: 0.00049
Iteration: 48, Log-Lik: -42061.787, Max-Change: 0.00025
Iteration: 49, Log-Lik: -42061.787, Max-Change: 0.00008
## [1] "2PL ITERATION 1. STARTED WITH 392 ITEMS. 77 OUTLIERS REMOVED. 315 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -45533.039, Max-Change: 14.34072
Iteration: 2, Log-Lik: -34411.410, Max-Change: 6.52685
Iteration: 3, Log-Lik: -33395.206, Max-Change: 4.59254
Iteration: 4, Log-Lik: -33190.415, Max-Change: 1.07201
Iteration: 5, Log-Lik: -33135.889, Max-Change: 0.18865
Iteration: 6, Log-Lik: -33114.669, Max-Change: 0.10683
Iteration: 7, Log-Lik: -33103.998, Max-Change: 0.08372
Iteration: 8, Log-Lik: -33098.133, Max-Change: 0.06558
Iteration: 9, Log-Lik: -33094.706, Max-Change: 0.05089
Iteration: 10, Log-Lik: -33092.665, Max-Change: 0.03964
Iteration: 11, Log-Lik: -33091.441, Max-Change: 0.03064
Iteration: 12, Log-Lik: -33090.701, Max-Change: 0.02401
Iteration: 13, Log-Lik: -33089.599, Max-Change: 0.00651
Iteration: 14, Log-Lik: -33089.583, Max-Change: 0.00338
Iteration: 15, Log-Lik: -33089.574, Max-Change: 0.00215
Iteration: 16, Log-Lik: -33089.566, Max-Change: 0.00164
Iteration: 17, Log-Lik: -33089.563, Max-Change: 0.00135
Iteration: 18, Log-Lik: -33089.562, Max-Change: 0.00113
Iteration: 19, Log-Lik: -33089.559, Max-Change: 0.00077
Iteration: 20, Log-Lik: -33089.559, Max-Change: 0.00042
Iteration: 21, Log-Lik: -33089.559, Max-Change: 0.00023
Iteration: 22, Log-Lik: -33089.559, Max-Change: 0.00049
Iteration: 23, Log-Lik: -33089.559, Max-Change: 0.00040
Iteration: 24, Log-Lik: -33089.559, Max-Change: 0.00022
Iteration: 25, Log-Lik: -33089.559, Max-Change: 0.00032
Iteration: 26, Log-Lik: -33089.559, Max-Change: 0.00025
Iteration: 27, Log-Lik: -33089.559, Max-Change: 0.00014
Iteration: 28, Log-Lik: -33089.559, Max-Change: 0.00019
Iteration: 29, Log-Lik: -33089.559, Max-Change: 0.00023
Iteration: 30, Log-Lik: -33089.559, Max-Change: 0.00013
Iteration: 31, Log-Lik: -33089.559, Max-Change: 0.00004
## [1] "2PL ITERATION 2. STARTED WITH 315 ITEMS. 2 OUTLIERS REMOVED. 313 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -45268.116, Max-Change: 14.28993
Iteration: 2, Log-Lik: -34194.024, Max-Change: 6.56276
Iteration: 3, Log-Lik: -33214.664, Max-Change: 4.20871
Iteration: 4, Log-Lik: -33008.581, Max-Change: 1.37019
Iteration: 5, Log-Lik: -32950.802, Max-Change: 0.19505
Iteration: 6, Log-Lik: -32928.749, Max-Change: 0.11032
Iteration: 7, Log-Lik: -32917.666, Max-Change: 0.08567
Iteration: 8, Log-Lik: -32911.590, Max-Change: 0.06696
Iteration: 9, Log-Lik: -32908.044, Max-Change: 0.05190
Iteration: 10, Log-Lik: -32905.934, Max-Change: 0.04049
Iteration: 11, Log-Lik: -32904.669, Max-Change: 0.03113
Iteration: 12, Log-Lik: -32903.906, Max-Change: 0.02441
Iteration: 13, Log-Lik: -32902.771, Max-Change: 0.00664
Iteration: 14, Log-Lik: -32902.755, Max-Change: 0.00347
Iteration: 15, Log-Lik: -32902.746, Max-Change: 0.00211
Iteration: 16, Log-Lik: -32902.738, Max-Change: 0.00171
Iteration: 17, Log-Lik: -32902.735, Max-Change: 0.00141
Iteration: 18, Log-Lik: -32902.734, Max-Change: 0.00119
Iteration: 19, Log-Lik: -32902.730, Max-Change: 0.00090
Iteration: 20, Log-Lik: -32902.730, Max-Change: 0.00049
Iteration: 21, Log-Lik: -32902.730, Max-Change: 0.00028
Iteration: 22, Log-Lik: -32902.730, Max-Change: 0.00052
Iteration: 23, Log-Lik: -32902.730, Max-Change: 0.00044
Iteration: 24, Log-Lik: -32902.730, Max-Change: 0.00025
Iteration: 25, Log-Lik: -32902.730, Max-Change: 0.00034
Iteration: 26, Log-Lik: -32902.730, Max-Change: 0.00025
Iteration: 27, Log-Lik: -32902.730, Max-Change: 0.00015
Iteration: 28, Log-Lik: -32902.730, Max-Change: 0.00020
Iteration: 29, Log-Lik: -32902.730, Max-Change: 0.00019
Iteration: 30, Log-Lik: -32902.730, Max-Change: 0.00011
Iteration: 31, Log-Lik: -32902.730, Max-Change: 0.00015
Iteration: 32, Log-Lik: -32902.730, Max-Change: 0.00021
Iteration: 33, Log-Lik: -32902.730, Max-Change: 0.00012
Iteration: 34, Log-Lik: -32902.730, Max-Change: 0.00005
## [1] "2PL ITERATION 3. STARTED WITH 313 ITEMS. 1 OUTLIERS REMOVED. 312 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -45166.577, Max-Change: 14.26319
Iteration: 2, Log-Lik: -34125.901, Max-Change: 6.38952
Iteration: 3, Log-Lik: -33158.924, Max-Change: 4.72414
Iteration: 4, Log-Lik: -32951.540, Max-Change: 0.94181
Iteration: 5, Log-Lik: -32899.472, Max-Change: 0.19987
Iteration: 6, Log-Lik: -32878.482, Max-Change: 0.10925
Iteration: 7, Log-Lik: -32867.910, Max-Change: 0.08422
Iteration: 8, Log-Lik: -32862.102, Max-Change: 0.06570
Iteration: 9, Log-Lik: -32858.711, Max-Change: 0.05085
Iteration: 10, Log-Lik: -32856.695, Max-Change: 0.03953
Iteration: 11, Log-Lik: -32855.486, Max-Change: 0.03054
Iteration: 12, Log-Lik: -32854.757, Max-Change: 0.02392
Iteration: 13, Log-Lik: -32853.675, Max-Change: 0.00650
Iteration: 14, Log-Lik: -32853.659, Max-Change: 0.00318
Iteration: 15, Log-Lik: -32853.650, Max-Change: 0.00213
Iteration: 16, Log-Lik: -32853.640, Max-Change: 0.00151
Iteration: 17, Log-Lik: -32853.638, Max-Change: 0.00124
Iteration: 18, Log-Lik: -32853.637, Max-Change: 0.00132
Iteration: 19, Log-Lik: -32853.637, Max-Change: 0.00053
Iteration: 20, Log-Lik: -32853.636, Max-Change: 0.00046
Iteration: 21, Log-Lik: -32853.636, Max-Change: 0.00041
Iteration: 22, Log-Lik: -32853.635, Max-Change: 0.00082
Iteration: 23, Log-Lik: -32853.635, Max-Change: 0.00045
Iteration: 24, Log-Lik: -32853.635, Max-Change: 0.00152
Iteration: 25, Log-Lik: -32853.635, Max-Change: 0.00223
Iteration: 26, Log-Lik: -32853.635, Max-Change: 0.00132
Iteration: 27, Log-Lik: -32853.635, Max-Change: 0.00077
Iteration: 28, Log-Lik: -32853.635, Max-Change: 0.00026
Iteration: 29, Log-Lik: -32853.635, Max-Change: 0.00016
Iteration: 30, Log-Lik: -32853.635, Max-Change: 0.00044
Iteration: 31, Log-Lik: -32853.635, Max-Change: 0.00078
Iteration: 32, Log-Lik: -32853.635, Max-Change: 0.00045
Iteration: 33, Log-Lik: -32853.635, Max-Change: 0.00027
Iteration: 34, Log-Lik: -32853.635, Max-Change: 0.00009
## [1] "2PL ITERATION 4. STARTED WITH 312 ITEMS. 1 OUTLIERS REMOVED. 311 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -45097.534, Max-Change: 14.26793
Iteration: 2, Log-Lik: -34052.958, Max-Change: 6.45949
Iteration: 3, Log-Lik: -33084.504, Max-Change: 5.46831
Iteration: 4, Log-Lik: -32903.522, Max-Change: 0.49257
Iteration: 5, Log-Lik: -32834.266, Max-Change: 0.18552
Iteration: 6, Log-Lik: -32809.106, Max-Change: 0.11158
Iteration: 7, Log-Lik: -32796.886, Max-Change: 0.08827
Iteration: 8, Log-Lik: -32790.305, Max-Change: 0.06942
Iteration: 9, Log-Lik: -32786.489, Max-Change: 0.05385
Iteration: 10, Log-Lik: -32784.227, Max-Change: 0.04200
Iteration: 11, Log-Lik: -32782.874, Max-Change: 0.03227
Iteration: 12, Log-Lik: -32782.060, Max-Change: 0.02530
Iteration: 13, Log-Lik: -32780.856, Max-Change: 0.00673
Iteration: 14, Log-Lik: -32780.838, Max-Change: 0.00360
Iteration: 15, Log-Lik: -32780.828, Max-Change: 0.00218
Iteration: 16, Log-Lik: -32780.820, Max-Change: 0.00177
Iteration: 17, Log-Lik: -32780.818, Max-Change: 0.00146
Iteration: 18, Log-Lik: -32780.816, Max-Change: 0.00123
Iteration: 19, Log-Lik: -32780.812, Max-Change: 0.00093
Iteration: 20, Log-Lik: -32780.812, Max-Change: 0.00050
Iteration: 21, Log-Lik: -32780.812, Max-Change: 0.00029
Iteration: 22, Log-Lik: -32780.812, Max-Change: 0.00054
Iteration: 23, Log-Lik: -32780.812, Max-Change: 0.00047
Iteration: 24, Log-Lik: -32780.812, Max-Change: 0.00027
Iteration: 25, Log-Lik: -32780.812, Max-Change: 0.00036
Iteration: 26, Log-Lik: -32780.812, Max-Change: 0.00029
Iteration: 27, Log-Lik: -32780.812, Max-Change: 0.00017
Iteration: 28, Log-Lik: -32780.812, Max-Change: 0.00021
Iteration: 29, Log-Lik: -32780.812, Max-Change: 0.00026
Iteration: 30, Log-Lik: -32780.812, Max-Change: 0.00015
Iteration: 31, Log-Lik: -32780.812, Max-Change: 0.00005
## [1] "2PL ITERATION 5. STARTED WITH 311 ITEMS. 1 OUTLIERS REMOVED. 310 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -45034.012, Max-Change: 14.22868
Iteration: 2, Log-Lik: -34025.133, Max-Change: 6.43184
Iteration: 3, Log-Lik: -33038.876, Max-Change: 4.12162
Iteration: 4, Log-Lik: -32830.431, Max-Change: 1.52145
Iteration: 5, Log-Lik: -32772.626, Max-Change: 0.19167
Iteration: 6, Log-Lik: -32750.933, Max-Change: 0.10944
Iteration: 7, Log-Lik: -32740.106, Max-Change: 0.08493
Iteration: 8, Log-Lik: -32734.203, Max-Change: 0.06633
Iteration: 9, Log-Lik: -32730.769, Max-Change: 0.05131
Iteration: 10, Log-Lik: -32728.732, Max-Change: 0.03983
Iteration: 11, Log-Lik: -32727.515, Max-Change: 0.03078
Iteration: 12, Log-Lik: -32726.781, Max-Change: 0.02409
Iteration: 13, Log-Lik: -32725.697, Max-Change: 0.00654
Iteration: 14, Log-Lik: -32725.681, Max-Change: 0.00321
Iteration: 15, Log-Lik: -32725.672, Max-Change: 0.00215
Iteration: 16, Log-Lik: -32725.662, Max-Change: 0.00153
Iteration: 17, Log-Lik: -32725.660, Max-Change: 0.00125
Iteration: 18, Log-Lik: -32725.659, Max-Change: 0.00132
Iteration: 19, Log-Lik: -32725.658, Max-Change: 0.00053
Iteration: 20, Log-Lik: -32725.658, Max-Change: 0.00047
Iteration: 21, Log-Lik: -32725.657, Max-Change: 0.00041
Iteration: 22, Log-Lik: -32725.657, Max-Change: 0.00083
Iteration: 23, Log-Lik: -32725.657, Max-Change: 0.00045
Iteration: 24, Log-Lik: -32725.657, Max-Change: 0.00154
Iteration: 25, Log-Lik: -32725.656, Max-Change: 0.00227
Iteration: 26, Log-Lik: -32725.656, Max-Change: 0.00134
Iteration: 27, Log-Lik: -32725.656, Max-Change: 0.00078
Iteration: 28, Log-Lik: -32725.656, Max-Change: 0.00026
Iteration: 29, Log-Lik: -32725.656, Max-Change: 0.00017
Iteration: 30, Log-Lik: -32725.656, Max-Change: 0.00045
Iteration: 31, Log-Lik: -32725.656, Max-Change: 0.00080
Iteration: 32, Log-Lik: -32725.656, Max-Change: 0.00046
Iteration: 33, Log-Lik: -32725.656, Max-Change: 0.00028
Iteration: 34, Log-Lik: -32725.656, Max-Change: 0.00009
## [1] "2PL ITERATION 6. STARTED WITH 310 ITEMS. 1 OUTLIERS REMOVED. 309 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -45034.221, Max-Change: 14.13620
Iteration: 2, Log-Lik: -33945.875, Max-Change: 6.45192
Iteration: 3, Log-Lik: -32982.702, Max-Change: 5.51773
Iteration: 4, Log-Lik: -32802.754, Max-Change: 0.47821
Iteration: 5, Log-Lik: -32736.305, Max-Change: 0.17983
Iteration: 6, Log-Lik: -32712.416, Max-Change: 0.10692
Iteration: 7, Log-Lik: -32700.923, Max-Change: 0.08592
Iteration: 8, Log-Lik: -32694.729, Max-Change: 0.06694
Iteration: 9, Log-Lik: -32691.183, Max-Change: 0.07152
Iteration: 10, Log-Lik: -32689.085, Max-Change: 0.08870
Iteration: 11, Log-Lik: -32687.822, Max-Change: 0.21776
Iteration: 12, Log-Lik: -32687.022, Max-Change: 0.80753
Iteration: 13, Log-Lik: -32686.213, Max-Change: 5.05328
Iteration: 14, Log-Lik: -32676.275, Max-Change: 0.67228
Iteration: 15, Log-Lik: -32670.227, Max-Change: 0.04731
Iteration: 16, Log-Lik: -32670.113, Max-Change: 0.01785
Iteration: 17, Log-Lik: -32670.085, Max-Change: 0.00601
Iteration: 18, Log-Lik: -32670.073, Max-Change: 0.00256
Iteration: 19, Log-Lik: -32670.067, Max-Change: 0.00192
Iteration: 20, Log-Lik: -32670.063, Max-Change: 0.00162
Iteration: 21, Log-Lik: -32670.060, Max-Change: 0.00133
Iteration: 22, Log-Lik: -32670.055, Max-Change: 0.00078
Iteration: 23, Log-Lik: -32670.055, Max-Change: 0.00049
Iteration: 24, Log-Lik: -32670.055, Max-Change: 0.00028
Iteration: 25, Log-Lik: -32670.055, Max-Change: 0.00085
Iteration: 26, Log-Lik: -32670.055, Max-Change: 0.00096
Iteration: 27, Log-Lik: -32670.055, Max-Change: 0.00054
Iteration: 28, Log-Lik: -32670.055, Max-Change: 0.00019
Iteration: 29, Log-Lik: -32670.055, Max-Change: 0.00012
Iteration: 30, Log-Lik: -32670.055, Max-Change: 0.00042
Iteration: 31, Log-Lik: -32670.055, Max-Change: 0.00056
Iteration: 32, Log-Lik: -32670.055, Max-Change: 0.00033
Iteration: 33, Log-Lik: -32670.055, Max-Change: 0.00020
Iteration: 34, Log-Lik: -32670.055, Max-Change: 0.00007
## [1] "2PL ITERATION 7. STARTED WITH 309 ITEMS. 1 OUTLIERS REMOVED. 308 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -44825.487, Max-Change: 14.24352
Iteration: 2, Log-Lik: -33857.838, Max-Change: 6.41549
Iteration: 3, Log-Lik: -32898.186, Max-Change: 5.34328
Iteration: 4, Log-Lik: -32710.381, Max-Change: 0.43914
Iteration: 5, Log-Lik: -32639.407, Max-Change: 0.19417
Iteration: 6, Log-Lik: -32613.616, Max-Change: 0.11356
Iteration: 7, Log-Lik: -32601.157, Max-Change: 0.08977
Iteration: 8, Log-Lik: -32594.437, Max-Change: 0.06951
Iteration: 9, Log-Lik: -32590.589, Max-Change: 0.05401
Iteration: 10, Log-Lik: -32588.314, Max-Change: 0.04210
Iteration: 11, Log-Lik: -32586.955, Max-Change: 0.03232
Iteration: 12, Log-Lik: -32586.139, Max-Change: 0.02531
Iteration: 13, Log-Lik: -32584.937, Max-Change: 0.00688
Iteration: 14, Log-Lik: -32584.919, Max-Change: 0.00363
Iteration: 15, Log-Lik: -32584.909, Max-Change: 0.00220
Iteration: 16, Log-Lik: -32584.901, Max-Change: 0.00179
Iteration: 17, Log-Lik: -32584.898, Max-Change: 0.00147
Iteration: 18, Log-Lik: -32584.896, Max-Change: 0.00123
Iteration: 19, Log-Lik: -32584.892, Max-Change: 0.00090
Iteration: 20, Log-Lik: -32584.892, Max-Change: 0.00048
Iteration: 21, Log-Lik: -32584.892, Max-Change: 0.00028
Iteration: 22, Log-Lik: -32584.892, Max-Change: 0.00055
Iteration: 23, Log-Lik: -32584.892, Max-Change: 0.00057
Iteration: 24, Log-Lik: -32584.892, Max-Change: 0.00033
Iteration: 25, Log-Lik: -32584.892, Max-Change: 0.00037
Iteration: 26, Log-Lik: -32584.892, Max-Change: 0.00052
Iteration: 27, Log-Lik: -32584.892, Max-Change: 0.00030
Iteration: 28, Log-Lik: -32584.892, Max-Change: 0.00010
Iteration: 29, Log-Lik: -32584.892, Max-Change: 0.00006
## [1] "2PL ITERATION 8. STARTED WITH 308 ITEMS. 2 OUTLIERS REMOVED. 306 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -44615.890, Max-Change: 14.18950
Iteration: 2, Log-Lik: -33612.461, Max-Change: 6.40974
Iteration: 3, Log-Lik: -32652.900, Max-Change: 4.08619
Iteration: 4, Log-Lik: -32448.724, Max-Change: 1.46209
Iteration: 5, Log-Lik: -32391.052, Max-Change: 0.20188
Iteration: 6, Log-Lik: -32369.679, Max-Change: 0.10869
Iteration: 7, Log-Lik: -32359.098, Max-Change: 0.08407
Iteration: 8, Log-Lik: -32353.360, Max-Change: 0.06545
Iteration: 9, Log-Lik: -32350.038, Max-Change: 0.05054
Iteration: 10, Log-Lik: -32348.076, Max-Change: 0.03918
Iteration: 11, Log-Lik: -32346.907, Max-Change: 0.03020
Iteration: 12, Log-Lik: -32346.205, Max-Change: 0.02357
Iteration: 13, Log-Lik: -32345.178, Max-Change: 0.00613
Iteration: 14, Log-Lik: -32345.162, Max-Change: 0.00341
Iteration: 15, Log-Lik: -32345.153, Max-Change: 0.00216
Iteration: 16, Log-Lik: -32345.145, Max-Change: 0.00164
Iteration: 17, Log-Lik: -32345.143, Max-Change: 0.00135
Iteration: 18, Log-Lik: -32345.141, Max-Change: 0.00112
Iteration: 19, Log-Lik: -32345.138, Max-Change: 0.00072
Iteration: 20, Log-Lik: -32345.138, Max-Change: 0.00038
Iteration: 21, Log-Lik: -32345.138, Max-Change: 0.00021
Iteration: 22, Log-Lik: -32345.138, Max-Change: 0.00050
Iteration: 23, Log-Lik: -32345.138, Max-Change: 0.00057
Iteration: 24, Log-Lik: -32345.138, Max-Change: 0.00032
Iteration: 25, Log-Lik: -32345.138, Max-Change: 0.00045
Iteration: 26, Log-Lik: -32345.138, Max-Change: 0.00064
Iteration: 27, Log-Lik: -32345.138, Max-Change: 0.00037
Iteration: 28, Log-Lik: -32345.138, Max-Change: 0.00014
Iteration: 29, Log-Lik: -32345.138, Max-Change: 0.00008
## [1] "2PL ITERATION 9. STARTED WITH 306 ITEMS. 1 OUTLIERS REMOVED. 305 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -44277.468, Max-Change: 14.37600
Iteration: 2, Log-Lik: -33408.728, Max-Change: 6.54879
Iteration: 3, Log-Lik: -32480.911, Max-Change: 4.58045
Iteration: 4, Log-Lik: -32272.028, Max-Change: 0.98148
Iteration: 5, Log-Lik: -32220.211, Max-Change: 0.19648
Iteration: 6, Log-Lik: -32199.394, Max-Change: 0.10870
Iteration: 7, Log-Lik: -32189.041, Max-Change: 0.08363
Iteration: 8, Log-Lik: -32183.408, Max-Change: 0.06499
Iteration: 9, Log-Lik: -32180.144, Max-Change: 0.05015
Iteration: 10, Log-Lik: -32178.215, Max-Change: 0.03887
Iteration: 11, Log-Lik: -32177.065, Max-Change: 0.02996
Iteration: 12, Log-Lik: -32176.375, Max-Change: 0.02339
Iteration: 13, Log-Lik: -32175.366, Max-Change: 0.00599
Iteration: 14, Log-Lik: -32175.351, Max-Change: 0.00314
Iteration: 15, Log-Lik: -32175.342, Max-Change: 0.00214
Iteration: 16, Log-Lik: -32175.334, Max-Change: 0.00170
Iteration: 17, Log-Lik: -32175.332, Max-Change: 0.00144
Iteration: 18, Log-Lik: -32175.330, Max-Change: 0.00118
Iteration: 19, Log-Lik: -32175.327, Max-Change: 0.00025
Iteration: 20, Log-Lik: -32175.327, Max-Change: 0.00071
Iteration: 21, Log-Lik: -32175.327, Max-Change: 0.00072
Iteration: 22, Log-Lik: -32175.327, Max-Change: 0.00043
Iteration: 23, Log-Lik: -32175.327, Max-Change: 0.00027
Iteration: 24, Log-Lik: -32175.327, Max-Change: 0.00015
Iteration: 25, Log-Lik: -32175.327, Max-Change: 0.00033
Iteration: 26, Log-Lik: -32175.327, Max-Change: 0.00016
Iteration: 27, Log-Lik: -32175.327, Max-Change: 0.00009
## [1] "2PL ITERATION 10. STARTED WITH 305 ITEMS. 1 OUTLIERS REMOVED. 304 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -44200.600, Max-Change: 14.36555
Iteration: 2, Log-Lik: -33398.884, Max-Change: 6.53100
Iteration: 3, Log-Lik: -32467.470, Max-Change: 5.28902
Iteration: 4, Log-Lik: -32284.420, Max-Change: 0.47666
Iteration: 5, Log-Lik: -32210.688, Max-Change: 0.19409
Iteration: 6, Log-Lik: -32185.987, Max-Change: 0.11059
Iteration: 7, Log-Lik: -32174.163, Max-Change: 0.08706
Iteration: 8, Log-Lik: -32167.851, Max-Change: 0.06825
Iteration: 9, Log-Lik: -32164.213, Max-Change: 0.05282
Iteration: 10, Log-Lik: -32162.070, Max-Change: 0.04110
Iteration: 11, Log-Lik: -32160.795, Max-Change: 0.03150
Iteration: 12, Log-Lik: -32160.032, Max-Change: 0.02461
Iteration: 13, Log-Lik: -32158.916, Max-Change: 0.00620
Iteration: 14, Log-Lik: -32158.900, Max-Change: 0.00352
Iteration: 15, Log-Lik: -32158.891, Max-Change: 0.00222
Iteration: 16, Log-Lik: -32158.883, Max-Change: 0.00168
Iteration: 17, Log-Lik: -32158.880, Max-Change: 0.00138
Iteration: 18, Log-Lik: -32158.878, Max-Change: 0.00115
Iteration: 19, Log-Lik: -32158.875, Max-Change: 0.00068
Iteration: 20, Log-Lik: -32158.875, Max-Change: 0.00036
Iteration: 21, Log-Lik: -32158.875, Max-Change: 0.00099
Iteration: 22, Log-Lik: -32158.875, Max-Change: 0.00155
Iteration: 23, Log-Lik: -32158.875, Max-Change: 0.00091
Iteration: 24, Log-Lik: -32158.875, Max-Change: 0.00051
Iteration: 25, Log-Lik: -32158.875, Max-Change: 0.00019
Iteration: 26, Log-Lik: -32158.875, Max-Change: 0.00012
Iteration: 27, Log-Lik: -32158.875, Max-Change: 0.00032
Iteration: 28, Log-Lik: -32158.875, Max-Change: 0.00054
Iteration: 29, Log-Lik: -32158.875, Max-Change: 0.00031
Iteration: 30, Log-Lik: -32158.875, Max-Change: 0.00018
Iteration: 31, Log-Lik: -32158.875, Max-Change: 0.00006
## [1] "2PL ITERATION 11. STARTED WITH 304 ITEMS. 1 OUTLIERS REMOVED. 303 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -44171.594, Max-Change: 14.49327
Iteration: 2, Log-Lik: -33353.687, Max-Change: 7.69781
Iteration: 3, Log-Lik: -32404.800, Max-Change: 4.86473
Iteration: 4, Log-Lik: -32236.212, Max-Change: 0.72904
Iteration: 5, Log-Lik: -32173.325, Max-Change: 0.19843
Iteration: 6, Log-Lik: -32149.987, Max-Change: 0.11048
Iteration: 7, Log-Lik: -32138.716, Max-Change: 0.08601
Iteration: 8, Log-Lik: -32132.694, Max-Change: 0.06689
Iteration: 9, Log-Lik: -32129.229, Max-Change: 0.05159
Iteration: 10, Log-Lik: -32127.192, Max-Change: 0.03995
Iteration: 11, Log-Lik: -32125.983, Max-Change: 0.03075
Iteration: 12, Log-Lik: -32125.258, Max-Change: 0.02394
Iteration: 13, Log-Lik: -32124.207, Max-Change: 0.00635
Iteration: 14, Log-Lik: -32124.191, Max-Change: 0.00348
Iteration: 15, Log-Lik: -32124.181, Max-Change: 0.00221
Iteration: 16, Log-Lik: -32124.173, Max-Change: 0.00167
Iteration: 17, Log-Lik: -32124.171, Max-Change: 0.00137
Iteration: 18, Log-Lik: -32124.169, Max-Change: 0.00114
Iteration: 19, Log-Lik: -32124.166, Max-Change: 0.00075
Iteration: 20, Log-Lik: -32124.166, Max-Change: 0.00040
Iteration: 21, Log-Lik: -32124.166, Max-Change: 0.00022
Iteration: 22, Log-Lik: -32124.166, Max-Change: 0.00050
Iteration: 23, Log-Lik: -32124.166, Max-Change: 0.00057
Iteration: 24, Log-Lik: -32124.166, Max-Change: 0.00032
Iteration: 25, Log-Lik: -32124.166, Max-Change: 0.00043
Iteration: 26, Log-Lik: -32124.166, Max-Change: 0.00061
Iteration: 27, Log-Lik: -32124.166, Max-Change: 0.00035
Iteration: 28, Log-Lik: -32124.166, Max-Change: 0.00013
Iteration: 29, Log-Lik: -32124.166, Max-Change: 0.00008
## [1] "2PL ITERATION 12. STARTED WITH 303 ITEMS. 1 OUTLIERS REMOVED. 302 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -44216.134, Max-Change: 37.64747
Iteration: 2, Log-Lik: -33269.401, Max-Change: 6.52420
Iteration: 3, Log-Lik: -32316.574, Max-Change: 4.54107
Iteration: 4, Log-Lik: -32136.606, Max-Change: 0.65019
Iteration: 5, Log-Lik: -32074.615, Max-Change: 0.17960
Iteration: 6, Log-Lik: -32051.276, Max-Change: 0.10989
Iteration: 7, Log-Lik: -32040.240, Max-Change: 0.08493
Iteration: 8, Log-Lik: -32034.433, Max-Change: 0.06596
Iteration: 9, Log-Lik: -32031.124, Max-Change: 0.05099
Iteration: 10, Log-Lik: -32029.191, Max-Change: 0.03888
Iteration: 11, Log-Lik: -32028.047, Max-Change: 0.03006
Iteration: 12, Log-Lik: -32027.364, Max-Change: 0.02342
Iteration: 13, Log-Lik: -32026.379, Max-Change: 0.00623
Iteration: 14, Log-Lik: -32026.363, Max-Change: 0.00316
Iteration: 15, Log-Lik: -32026.354, Max-Change: 0.00210
Iteration: 16, Log-Lik: -32026.347, Max-Change: 0.00173
Iteration: 17, Log-Lik: -32026.344, Max-Change: 0.00148
Iteration: 18, Log-Lik: -32026.343, Max-Change: 0.00122
Iteration: 19, Log-Lik: -32026.340, Max-Change: 0.00084
Iteration: 20, Log-Lik: -32026.339, Max-Change: 0.00047
Iteration: 21, Log-Lik: -32026.339, Max-Change: 0.00030
Iteration: 22, Log-Lik: -32026.339, Max-Change: 0.00077
Iteration: 23, Log-Lik: -32026.339, Max-Change: 0.00083
Iteration: 24, Log-Lik: -32026.339, Max-Change: 0.00052
Iteration: 25, Log-Lik: -32026.339, Max-Change: 0.00019
Iteration: 26, Log-Lik: -32026.339, Max-Change: 0.00011
Iteration: 27, Log-Lik: -32026.339, Max-Change: 0.00035
Iteration: 28, Log-Lik: -32026.339, Max-Change: 0.00053
Iteration: 29, Log-Lik: -32026.339, Max-Change: 0.00031
Iteration: 30, Log-Lik: -32026.339, Max-Change: 0.00019
Iteration: 31, Log-Lik: -32026.339, Max-Change: 0.00006
## [1] "2PL ITERATION 13. STARTED WITH 302 ITEMS. 2 OUTLIERS REMOVED. 300 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -43502.030, Max-Change: 14.63076
Iteration: 2, Log-Lik: -32796.879, Max-Change: 8.32444
Iteration: 3, Log-Lik: -31831.478, Max-Change: 5.11912
Iteration: 4, Log-Lik: -31668.117, Max-Change: 0.48556
Iteration: 5, Log-Lik: -31609.353, Max-Change: 0.16937
Iteration: 6, Log-Lik: -31587.009, Max-Change: 0.11159
Iteration: 7, Log-Lik: -31576.244, Max-Change: 0.08560
Iteration: 8, Log-Lik: -31570.503, Max-Change: 0.06601
Iteration: 9, Log-Lik: -31567.219, Max-Change: 0.05073
Iteration: 10, Log-Lik: -31565.298, Max-Change: 0.03979
Iteration: 11, Log-Lik: -31564.153, Max-Change: 0.03018
Iteration: 12, Log-Lik: -31563.474, Max-Change: 0.02322
Iteration: 13, Log-Lik: -31562.540, Max-Change: 0.00502
Iteration: 14, Log-Lik: -31562.517, Max-Change: 0.00431
Iteration: 15, Log-Lik: -31562.503, Max-Change: 0.00314
Iteration: 16, Log-Lik: -31562.488, Max-Change: 0.00264
Iteration: 17, Log-Lik: -31562.485, Max-Change: 0.00146
Iteration: 18, Log-Lik: -31562.483, Max-Change: 0.00119
Iteration: 19, Log-Lik: -31562.480, Max-Change: 0.00067
Iteration: 20, Log-Lik: -31562.480, Max-Change: 0.00037
Iteration: 21, Log-Lik: -31562.480, Max-Change: 0.00118
Iteration: 22, Log-Lik: -31562.480, Max-Change: 0.00157
Iteration: 23, Log-Lik: -31562.480, Max-Change: 0.00089
Iteration: 24, Log-Lik: -31562.480, Max-Change: 0.00056
Iteration: 25, Log-Lik: -31562.480, Max-Change: 0.00021
Iteration: 26, Log-Lik: -31562.480, Max-Change: 0.00012
Iteration: 27, Log-Lik: -31562.480, Max-Change: 0.00008
## [1] "2PL ITERATION 14. STARTED WITH 300 ITEMS. 1 OUTLIERS REMOVED. 299 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -43305.621, Max-Change: 14.26489
Iteration: 2, Log-Lik: -32638.486, Max-Change: 7.54889
Iteration: 3, Log-Lik: -31731.980, Max-Change: 5.74525
Iteration: 4, Log-Lik: -31573.936, Max-Change: 0.35158
Iteration: 5, Log-Lik: -31513.249, Max-Change: 0.17291
Iteration: 6, Log-Lik: -31491.291, Max-Change: 0.10525
Iteration: 7, Log-Lik: -31480.998, Max-Change: 0.08248
Iteration: 8, Log-Lik: -31475.591, Max-Change: 0.06392
Iteration: 9, Log-Lik: -31472.518, Max-Change: 0.04943
Iteration: 10, Log-Lik: -31470.728, Max-Change: 0.03822
Iteration: 11, Log-Lik: -31469.663, Max-Change: 0.02900
Iteration: 12, Log-Lik: -31469.032, Max-Change: 0.02255
Iteration: 13, Log-Lik: -31468.158, Max-Change: 0.00466
Iteration: 14, Log-Lik: -31468.141, Max-Change: 0.00356
Iteration: 15, Log-Lik: -31468.130, Max-Change: 0.00228
Iteration: 16, Log-Lik: -31468.121, Max-Change: 0.00188
Iteration: 17, Log-Lik: -31468.118, Max-Change: 0.00152
Iteration: 18, Log-Lik: -31468.116, Max-Change: 0.00127
Iteration: 19, Log-Lik: -31468.112, Max-Change: 0.00082
Iteration: 20, Log-Lik: -31468.112, Max-Change: 0.00049
Iteration: 21, Log-Lik: -31468.112, Max-Change: 0.00029
Iteration: 22, Log-Lik: -31468.112, Max-Change: 0.00075
Iteration: 23, Log-Lik: -31468.112, Max-Change: 0.00101
Iteration: 24, Log-Lik: -31468.112, Max-Change: 0.00057
Iteration: 25, Log-Lik: -31468.112, Max-Change: 0.00019
Iteration: 26, Log-Lik: -31468.112, Max-Change: 0.00061
Iteration: 27, Log-Lik: -31468.112, Max-Change: 0.00077
Iteration: 28, Log-Lik: -31468.112, Max-Change: 0.00025
Iteration: 29, Log-Lik: -31468.112, Max-Change: 0.00015
Iteration: 30, Log-Lik: -31468.112, Max-Change: 0.00009
## [1] "2PL ITERATION 15. STARTED WITH 299 ITEMS. 1 OUTLIERS REMOVED. 298 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -43186.153, Max-Change: 14.48338
Iteration: 2, Log-Lik: -32628.740, Max-Change: 7.31660
Iteration: 3, Log-Lik: -31696.046, Max-Change: 4.51505
Iteration: 4, Log-Lik: -31517.105, Max-Change: 1.12462
Iteration: 5, Log-Lik: -31463.991, Max-Change: 0.18806
Iteration: 6, Log-Lik: -31444.002, Max-Change: 0.11346
Iteration: 7, Log-Lik: -31434.317, Max-Change: 0.08145
Iteration: 8, Log-Lik: -31429.130, Max-Change: 0.06293
Iteration: 9, Log-Lik: -31426.165, Max-Change: 0.04865
Iteration: 10, Log-Lik: -31424.432, Max-Change: 0.03762
Iteration: 11, Log-Lik: -31423.399, Max-Change: 0.02855
Iteration: 12, Log-Lik: -31422.788, Max-Change: 0.02220
Iteration: 13, Log-Lik: -31421.942, Max-Change: 0.00462
Iteration: 14, Log-Lik: -31421.925, Max-Change: 0.00352
Iteration: 15, Log-Lik: -31421.915, Max-Change: 0.00226
Iteration: 16, Log-Lik: -31421.906, Max-Change: 0.00186
Iteration: 17, Log-Lik: -31421.903, Max-Change: 0.00150
Iteration: 18, Log-Lik: -31421.901, Max-Change: 0.00125
Iteration: 19, Log-Lik: -31421.898, Max-Change: 0.00088
Iteration: 20, Log-Lik: -31421.898, Max-Change: 0.00053
Iteration: 21, Log-Lik: -31421.898, Max-Change: 0.00031
Iteration: 22, Log-Lik: -31421.898, Max-Change: 0.00069
Iteration: 23, Log-Lik: -31421.897, Max-Change: 0.00091
Iteration: 24, Log-Lik: -31421.897, Max-Change: 0.00052
Iteration: 25, Log-Lik: -31421.897, Max-Change: 0.00016
Iteration: 26, Log-Lik: -31421.897, Max-Change: 0.00053
Iteration: 27, Log-Lik: -31421.897, Max-Change: 0.00066
Iteration: 28, Log-Lik: -31421.897, Max-Change: 0.00024
Iteration: 29, Log-Lik: -31421.897, Max-Change: 0.00014
Iteration: 30, Log-Lik: -31421.897, Max-Change: 0.00008
## [1] "2PL ITERATION 16. STARTED WITH 298 ITEMS. 1 OUTLIERS REMOVED. 297 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -43063.191, Max-Change: 14.58058
Iteration: 2, Log-Lik: -32569.929, Max-Change: 6.93401
Iteration: 3, Log-Lik: -31657.052, Max-Change: 5.26143
Iteration: 4, Log-Lik: -31487.208, Max-Change: 0.37763
Iteration: 5, Log-Lik: -31425.672, Max-Change: 0.18529
Iteration: 6, Log-Lik: -31403.035, Max-Change: 0.11664
Iteration: 7, Log-Lik: -31392.324, Max-Change: 0.08370
Iteration: 8, Log-Lik: -31386.672, Max-Change: 0.06514
Iteration: 9, Log-Lik: -31383.455, Max-Change: 0.05047
Iteration: 10, Log-Lik: -31381.582, Max-Change: 0.03905
Iteration: 11, Log-Lik: -31380.467, Max-Change: 0.02917
Iteration: 12, Log-Lik: -31379.816, Max-Change: 0.02328
Iteration: 13, Log-Lik: -31378.878, Max-Change: 0.00558
Iteration: 14, Log-Lik: -31378.866, Max-Change: 0.00212
Iteration: 15, Log-Lik: -31378.861, Max-Change: 0.00192
Iteration: 16, Log-Lik: -31378.852, Max-Change: 0.00153
Iteration: 17, Log-Lik: -31378.851, Max-Change: 0.00079
Iteration: 18, Log-Lik: -31378.851, Max-Change: 0.00055
Iteration: 19, Log-Lik: -31378.851, Max-Change: 0.00045
Iteration: 20, Log-Lik: -31378.851, Max-Change: 0.00164
Iteration: 21, Log-Lik: -31378.851, Max-Change: 0.00190
Iteration: 22, Log-Lik: -31378.850, Max-Change: 0.00104
Iteration: 23, Log-Lik: -31378.850, Max-Change: 0.00064
Iteration: 24, Log-Lik: -31378.850, Max-Change: 0.00036
Iteration: 25, Log-Lik: -31378.850, Max-Change: 0.00062
Iteration: 26, Log-Lik: -31378.850, Max-Change: 0.00054
Iteration: 27, Log-Lik: -31378.850, Max-Change: 0.00033
Iteration: 28, Log-Lik: -31378.850, Max-Change: 0.00036
Iteration: 29, Log-Lik: -31378.850, Max-Change: 0.00030
Iteration: 30, Log-Lik: -31378.850, Max-Change: 0.00019
Iteration: 31, Log-Lik: -31378.850, Max-Change: 0.00023
Iteration: 32, Log-Lik: -31378.850, Max-Change: 0.00021
Iteration: 33, Log-Lik: -31378.850, Max-Change: 0.00013
Iteration: 34, Log-Lik: -31378.850, Max-Change: 0.00017
Iteration: 35, Log-Lik: -31378.850, Max-Change: 0.00022
Iteration: 36, Log-Lik: -31378.850, Max-Change: 0.00013
Iteration: 37, Log-Lik: -31378.850, Max-Change: 0.00005
## [1] "2PL ITERATION 17. STARTED WITH 297 ITEMS. 2 OUTLIERS REMOVED. 295 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -42928.172, Max-Change: 14.50660
Iteration: 2, Log-Lik: -32490.895, Max-Change: 6.35474
Iteration: 3, Log-Lik: -31585.405, Max-Change: 4.50152
Iteration: 4, Log-Lik: -31422.658, Max-Change: 1.28450
Iteration: 5, Log-Lik: -31372.383, Max-Change: 0.19192
Iteration: 6, Log-Lik: -31354.635, Max-Change: 0.10986
Iteration: 7, Log-Lik: -31346.029, Max-Change: 0.07722
Iteration: 8, Log-Lik: -31341.418, Max-Change: 0.05961
Iteration: 9, Log-Lik: -31338.791, Max-Change: 0.04597
Iteration: 10, Log-Lik: -31337.262, Max-Change: 0.03498
Iteration: 11, Log-Lik: -31336.362, Max-Change: 0.02706
Iteration: 12, Log-Lik: -31335.822, Max-Change: 0.02091
Iteration: 13, Log-Lik: -31335.090, Max-Change: 0.00470
Iteration: 14, Log-Lik: -31335.071, Max-Change: 0.00359
Iteration: 15, Log-Lik: -31335.061, Max-Change: 0.00241
Iteration: 16, Log-Lik: -31335.048, Max-Change: 0.00169
Iteration: 17, Log-Lik: -31335.046, Max-Change: 0.00140
Iteration: 18, Log-Lik: -31335.045, Max-Change: 0.00156
Iteration: 19, Log-Lik: -31335.044, Max-Change: 0.00060
Iteration: 20, Log-Lik: -31335.044, Max-Change: 0.00052
Iteration: 21, Log-Lik: -31335.043, Max-Change: 0.00045
Iteration: 22, Log-Lik: -31335.042, Max-Change: 0.00100
Iteration: 23, Log-Lik: -31335.042, Max-Change: 0.00054
Iteration: 24, Log-Lik: -31335.042, Max-Change: 0.00183
Iteration: 25, Log-Lik: -31335.042, Max-Change: 0.00276
Iteration: 26, Log-Lik: -31335.042, Max-Change: 0.00163
Iteration: 27, Log-Lik: -31335.042, Max-Change: 0.00096
Iteration: 28, Log-Lik: -31335.042, Max-Change: 0.00032
Iteration: 29, Log-Lik: -31335.042, Max-Change: 0.00020
Iteration: 30, Log-Lik: -31335.042, Max-Change: 0.00055
Iteration: 31, Log-Lik: -31335.042, Max-Change: 0.00098
Iteration: 32, Log-Lik: -31335.042, Max-Change: 0.00057
Iteration: 33, Log-Lik: -31335.042, Max-Change: 0.00034
Iteration: 34, Log-Lik: -31335.042, Max-Change: 0.00012
Iteration: 35, Log-Lik: -31335.042, Max-Change: 0.00007
## [1] "2PL ITERATION 18. STARTED WITH 295 ITEMS. 1 OUTLIERS REMOVED. 294 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -42971.881, Max-Change: 26.57850
Iteration: 2, Log-Lik: -32452.006, Max-Change: 6.13016
Iteration: 3, Log-Lik: -31545.626, Max-Change: 3.91902
Iteration: 4, Log-Lik: -31366.546, Max-Change: 1.27451
Iteration: 5, Log-Lik: -31311.972, Max-Change: 0.17905
Iteration: 6, Log-Lik: -31292.457, Max-Change: 0.10932
Iteration: 7, Log-Lik: -31283.345, Max-Change: 0.07765
Iteration: 8, Log-Lik: -31278.591, Max-Change: 0.05931
Iteration: 9, Log-Lik: -31275.920, Max-Change: 0.04560
Iteration: 10, Log-Lik: -31274.378, Max-Change: 0.03467
Iteration: 11, Log-Lik: -31273.476, Max-Change: 0.02680
Iteration: 12, Log-Lik: -31272.936, Max-Change: 0.02042
Iteration: 13, Log-Lik: -31272.222, Max-Change: 0.00510
Iteration: 14, Log-Lik: -31272.198, Max-Change: 0.00419
Iteration: 15, Log-Lik: -31272.184, Max-Change: 0.00332
Iteration: 16, Log-Lik: -31272.169, Max-Change: 0.00785
Iteration: 17, Log-Lik: -31272.166, Max-Change: 0.00128
Iteration: 18, Log-Lik: -31272.165, Max-Change: 0.00092
Iteration: 19, Log-Lik: -31272.164, Max-Change: 0.00067
Iteration: 20, Log-Lik: -31272.164, Max-Change: 0.00046
Iteration: 21, Log-Lik: -31272.163, Max-Change: 0.00039
Iteration: 22, Log-Lik: -31272.163, Max-Change: 0.00074
Iteration: 23, Log-Lik: -31272.163, Max-Change: 0.00048
Iteration: 24, Log-Lik: -31272.163, Max-Change: 0.00122
Iteration: 25, Log-Lik: -31272.162, Max-Change: 0.00214
Iteration: 26, Log-Lik: -31272.162, Max-Change: 0.00121
Iteration: 27, Log-Lik: -31272.162, Max-Change: 0.00070
Iteration: 28, Log-Lik: -31272.162, Max-Change: 0.00024
Iteration: 29, Log-Lik: -31272.162, Max-Change: 0.00064
Iteration: 30, Log-Lik: -31272.162, Max-Change: 0.00093
Iteration: 31, Log-Lik: -31272.162, Max-Change: 0.00032
Iteration: 32, Log-Lik: -31272.162, Max-Change: 0.00018
Iteration: 33, Log-Lik: -31272.162, Max-Change: 0.00011
Iteration: 34, Log-Lik: -31272.162, Max-Change: 0.00023
Iteration: 35, Log-Lik: -31272.162, Max-Change: 0.00010
Iteration: 36, Log-Lik: -31272.162, Max-Change: 0.00005
## [1] "2PL ITERATION 19. STARTED WITH 294 ITEMS. 2 OUTLIERS REMOVED. 292 ITEMS RETAINED."
## 
Iteration: 1, Log-Lik: -42524.883, Max-Change: 14.62557
Iteration: 2, Log-Lik: -32113.248, Max-Change: 6.62731
Iteration: 3, Log-Lik: -31198.678, Max-Change: 5.58434
Iteration: 4, Log-Lik: -31032.983, Max-Change: 0.39426
Iteration: 5, Log-Lik: -30971.316, Max-Change: 0.18858
Iteration: 6, Log-Lik: -30949.555, Max-Change: 0.11783
Iteration: 7, Log-Lik: -30939.538, Max-Change: 0.07942
Iteration: 8, Log-Lik: -30934.337, Max-Change: 0.06170
Iteration: 9, Log-Lik: -30931.415, Max-Change: 0.04768
Iteration: 10, Log-Lik: -30929.728, Max-Change: 0.03677
Iteration: 11, Log-Lik: -30928.731, Max-Change: 0.02780
Iteration: 12, Log-Lik: -30928.146, Max-Change: 0.02148
Iteration: 13, Log-Lik: -30927.351, Max-Change: 0.00505
Iteration: 14, Log-Lik: -30927.334, Max-Change: 0.00347
Iteration: 15, Log-Lik: -30927.324, Max-Change: 0.00233
Iteration: 16, Log-Lik: -30927.314, Max-Change: 0.00177
Iteration: 17, Log-Lik: -30927.312, Max-Change: 0.00143
Iteration: 18, Log-Lik: -30927.310, Max-Change: 0.00117
Iteration: 19, Log-Lik: -30927.307, Max-Change: 0.00083
Iteration: 20, Log-Lik: -30927.307, Max-Change: 0.00049
Iteration: 21, Log-Lik: -30927.307, Max-Change: 0.00028
Iteration: 22, Log-Lik: -30927.307, Max-Change: 0.00066
Iteration: 23, Log-Lik: -30927.307, Max-Change: 0.00082
Iteration: 24, Log-Lik: -30927.307, Max-Change: 0.00044
Iteration: 25, Log-Lik: -30927.307, Max-Change: 0.00015
Iteration: 26, Log-Lik: -30927.307, Max-Change: 0.00047
Iteration: 27, Log-Lik: -30927.307, Max-Change: 0.00057
Iteration: 28, Log-Lik: -30927.307, Max-Change: 0.00022
Iteration: 29, Log-Lik: -30927.307, Max-Change: 0.00013
Iteration: 30, Log-Lik: -30927.307, Max-Change: 0.00007
## [1] "2PL ITERATION 20. STARTED WITH 292 ITEMS. 1 OUTLIERS REMOVED. 291 ITEMS RETAINED."

Look at thetas by sub

thetas_by_all_subs <- fscores(m) %>%
  as_tibble() %>%
  add_column(pid = d_wide_all$sub_id) %>%
  rename(theta_2pl_all_data = `F`) %>%
  left_join(sub_data_age_cleaned)

thetas_by_age_all_data <- thetas_by_all_subs %>%
  group_by(age) %>%
  multi_boot_standard(col='theta_2pl_all_data') %>%
  filter(!is.na(age))

ggplot(data = thetas_by_all_subs, aes(x=age, y=theta_2pl_all_data, col=age)) +
    geom_jitter(width=.2, alpha=.2) +
  geom_smooth(method='lm', color='grey',alpha=.8)  +
  geom_pointrange(data=thetas_by_age_all_data,aes(x=age, y=mean, ymin=ci_lower, ymax =ci_upper), col='black', alpha=.5) +
  theme_few()  +
  ylab('Theta estimates') +
  xlab('Age') + 
  # facet_wrap(~model, nrow=2) +
  theme(legend.position='none') +
  theme(aspect.ratio=.75)

See which items were retained

Show items by difficulty

coefficients_pruned_items <- co %>%
  mutate(slope = a1, item_pair = words) %>%
  mutate(difficulty = -d) %>%
  arrange(-difficulty)

Get item info for rejoining

item_info_clip <- pilot_data_filtered %>%
  filter(cohort == 'prolific') %>%
  distinct(item_pair, wordPairing, cor) %>%
  rename(wordPairingClip = wordPairing)

Get item pc/responses overall

items_all_responses <- pilot_data_filtered %>%
  group_by(item_pair, word1, word2) %>%
  summarize(num_responses = length(correct), pc = mean(correct))

Add back in pc for sanity & and word pairing details

coefficients_pruned_items <- coefficients_pruned_items %>%
  left_join(items_all_responses) %>%
  left_join(item_info_clip) %>%
  mutate(wordPairingClip = replace_na(wordPairingClip, 'DAIVT'))

items_with_matches <- coefficients_pruned_items %>%
  group_by(word1) %>%
  mutate(num_pairs_retains = length(unique(word2))) %>%
  filter(num_pairs_retains>1)

Refit a model kicking with items without 2 distract ors

kept_items = items_with_matches$words

d_wide_model_subset<- pilot_data_filtered %>%
  ungroup() %>%
  filter(item_pair %in% kept_items) %>%
  select(sub_id, item_pair, correct) %>%
  arrange(item_pair) %>%
  ungroup() %>%
  pivot_wider(names_from=item_pair, values_from=correct, values_fn = ~mean(.x)) %>%
  ungroup()

d_mat_model_subset <- d_wide_model_subset %>%
  select(-sub_id) %>%
  data.frame %>%
  data.matrix

rownames(d_mat_model_subset) <- d_wide_model_subset$sub_id

Fit the 2PL model to this subset

start.dim = length(colnames(d_mat_model_subset))-1
mm = (
  'F = 1-%d,
PRIOR = (1-%d, a1, norm, .2, 1),
PRIOR = (1-%d, d, norm, 0, 2)'
)
mm = mirt.model(sprintf(mm,start.dim,start.dim,start.dim))

mod_2pl_priors_subset <- mirt::mirt(d_mat_model_subset, mm, itemtype='2PL', guess=.5,  upper=1, verbose=FALSE)

Get coefficients

coefficients_subset <- coef(mod_2pl_priors_subset,simplify=TRUE, IRTpars = FALSE) # Get coeeficients
coefficients_subset <- tibble::rownames_to_column(as.data.frame(coefficients_subset$items),'words')

Look at thetas by sub for refit model

all_thetas_with_matched_subset <- fscores(mod_2pl_priors_subset) %>%
  as_tibble() %>%
  add_column(pid = d_wide_model_subset$sub_id) %>%
  rename(theta_2pl_matched_data = `F`) %>%
  left_join(sub_data_age_cleaned)

thetas_by_age_matched_subset <- all_thetas_with_matched_subset %>%
  group_by(age) %>%
  multi_boot_standard(col='theta_2pl_matched_data') %>%
  filter(!is.na(age))

ggplot(data = all_thetas_with_matched_subset, aes(x=age, y=theta_2pl_matched_data, col=age)) +
    geom_jitter(width=.2, alpha=.2) +
  geom_smooth(method='lm', color='grey',alpha=.8)  +
  geom_pointrange(data=thetas_by_age_matched_subset,aes(x=age, y=mean, ymin=ci_lower, ymax =ci_upper), col='black', alpha=.5) +
  theme_few()  +
  ylab('Theta estimates') +
  xlab('Age') + 
  # facet_wrap(~model, nrow=2) +
  theme(legend.position='none') +
  theme(aspect.ratio=.75)

Look at items Show items by difficulty

coefficients_subset <- coefficients_subset %>%
  mutate(slope = a1, item_pair = words) %>%
  mutate(difficulty = -d) %>%
  arrange(-difficulty)

Get item info for rejoining

item_info_clip <- pilot_data_filtered %>%
  filter(cohort == 'prolific') %>%
  distinct(item_pair, wordPairing, cor) %>%
  rename(wordPairingClip = wordPairing)

Get item pc/responses overall

items_all_responses <- pilot_data_filtered %>%
  group_by(item_pair, word1, word2) %>%
  summarize(num_responses = length(correct), pc = mean(correct))

Add back in pc for sanity & and word pairing details

coefficients_pruned_items <- coefficients_pruned_items %>%
  left_join(items_all_responses) %>%
  left_join(item_info_clip) %>%
  mutate(wordPairingClip = replace_na(wordPairingClip, 'DAIVT'))

ggplot(data = coefficients_pruned_items, aes(x=difficulty, y=a1,col=wordPairingClip )) + 
  geom_point(alpha=.5) + 
  ggrepel::geom_label_repel(aes(label = item_pair), box.padding = 0.1, max.overlaps=20, size=3) +
  theme_few(base_size=10) + 
  xlab("IRT difficulty") +
  ylab("IRT discriminability (slope)")

by_word <- coefficients_pruned_items %>%
  filter(wordPairingClip %in% c('easy','hard')) %>%
  select(word1, difficulty, wordPairingClip) %>%
  pivot_wider(values_from = difficulty, names_from=wordPairingClip) %>%
  mutate(diff = hard - easy) %>%
  arrange(-diff) %>% 
  kable

Thetas with these two different models

thetas_by_all_subs <- thetas_by_all_subs %>%
  right_join(all_thetas_with_matched_subset)

ggplot(data = thetas_by_all_subs, aes(x=theta_2pl_all_data, y=theta_2pl_matched_data, col=age)) +
  geom_point(alpha=.8) +
  geom_smooth(method='lm', color='grey',alpha=.2)  +
  theme_few()  +
  ylab('Theta estimates') +
  xlab('Theta estimates') + 
  scale_color_viridis_c() +
  facet_wrap(~age, nrow=2) +
  theme(legend.position='right') +
  theme(aspect.ratio=.75)

Plot some individual items

thetas_for_plot <- seq(-6,6,.1)

irt2pl <- function(a, d, theta = seq(-6,6,.1)) {
  p = boot::inv.logit(a * (theta + d))
  return(p)
}

iccs <- coefficients_subset %>%
  filter(d > quantile(d, .9)) %>%
  split(.$item_pair) %>%
  map_df(function(d) {
    return(data_frame(item_pair = d$item_pair,
                      theta = thetas_for_plot, 
                      p = irt2pl(d$a1, d$d, thetas_for_plot)))
  })

ggplot(iccs,  
       aes(x = theta, y = p)) + 
  geom_line() + 
  facet_wrap(~item_pair) + 
  xlab("Ability") + 
  ylab("Probability of comprehension") +
  ggtitle('Easiest items')

Hardest items

iccs <- coefficients_subset %>%
  filter(d < quantile(d, .1)) %>%
  split(.$item_pair) %>%
  map_df(function(d) {
    return(data_frame(item_pair = d$item_pair,
                      theta = thetas_for_plot, 
                      p = irt2pl(d$a1, d$d, thetas_for_plot)))
  })

ggplot(iccs,  
       aes(x = theta, y = p)) + 
  geom_line() + 
  facet_wrap(~item_pair) + 
  xlab("Ability") + 
  ylab("Probability of comprehension") +
  ggtitle('Hardest items')

Partial compensatory model?

# same as partial credit models?
# 'PC2PL'

all_data_irt_march_14

Bria Long

2023-03-14

Setup

Get subject data

Run iterative 2PL IRT model with all data

Look at thetas by sub

See which items were retained

Show items by difficulty

Get item info for rejoining

Get item pc/responses overall

Add back in pc for sanity & and word pairing details

Refit a model kicking with items without 2 distract ors

Fit the 2PL model to this subset

Get coefficients

Look at thetas by sub for refit model

Look at items Show items by difficulty

Get item info for rejoining

Get item pc/responses overall

Add back in pc for sanity & and word pairing details

Thetas with these two different models

Plot some individual items

Hardest items

Partial compensatory model?