Init
Sys.setenv(LANG = "en") # make R environment in english
library(kirkegaard)
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load_packages(
mirt,
rms
)
## Loading required package: stats4
## Loading required package: lattice
theme_set(theme_bw())
options(
digits = 3
)
Analysis
Basic
d$Is_English_one_of_your_native_languages %>% table2()
## # A tibble: 3 × 3
## Group Count Percent
## <chr> <dbl> <dbl>
## 1 Yes 436 98.9
## 2 No 5 1.13
## 3 <NA> 0 0
Overall fit
#fit model
good_items_fit = mirt(
itemdata %>% select(-id),
model = 1,
itemtype = "2PL",
verbose = F,
technical = list(NCYCLES = 2000)
)
good_items_fit
##
## Call:
## mirt(data = itemdata %>% select(-id), model = 1, itemtype = "2PL",
## verbose = F, technical = list(NCYCLES = 2000))
##
## Full-information item factor analysis with 1 factor(s).
## Converged within 1e-04 tolerance after 328 EM iterations.
## mirt version: 1.42
## M-step optimizer: BFGS
## EM acceleration: Ramsay
## Number of rectangular quadrature: 61
## Latent density type: Gaussian
##
## Log-likelihood = -36583
## Estimated parameters: 438
## AIC = 74042
## BIC = 75833; SABIC = 74443
good_items_fit %>% summary()
## F1 h2
## a_specific_number 0.456 0.2083
## a_type_of_brass_instrument 0.877 0.7699
## a_type_of_drapery 0.652 0.4257
## a_type_of_fabric_101 0.744 0.5532
## a_type_of_fabric_98 0.700 0.4895
## a_type_of_grasshopper 0.803 0.6452
## a_type_of_hat 0.574 0.3293
## a_type_of_heating_unit 0.498 0.2478
## a_type_of_magistrate_position 0.746 0.5566
## a_type_of_mathematical_operation 0.569 0.3240
## a_type_of_overshoe 0.495 0.2455
## a_type_of_plant 0.734 0.5392
## a_type_of_religious_teacher 0.779 0.6073
## a_type_of_rock 0.321 0.1028
## a_type_of_skirts 0.642 0.4126
## a_type_of_smokeless_powder 0.467 0.2178
## a_type_of_sound 0.490 0.2403
## a_type_of_sword 0.356 0.1265
## a_type_of_volcanic_crater 0.666 0.4441
## a_type_of_wavy_form 0.706 0.4986
## actionable_negligence 0.769 0.5916
## advisory 0.723 0.5231
## advocate 0.702 0.4921
## almighty 0.914 0.8357
## amazement 0.661 0.4366
## amenability 0.740 0.5471
## auspices 0.688 0.4727
## barely_able_to_read_and_write 0.841 0.7067
## because 0.680 0.4628
## berate 0.836 0.6993
## blade 0.783 0.6130
## blend 0.683 0.4659
## blunder 0.860 0.7401
## bow 0.751 0.5647
## brief 0.432 0.1866
## bring_about 0.790 0.6240
## carelessly_or_hastily_put_together 0.609 0.3711
## celebration 0.719 0.5167
## cheat 0.806 0.6497
## clay_pigeon_shooting 0.767 0.5885
## coarse 0.776 0.6028
## collect_or_study_insects 0.626 0.3922
## colossal 0.713 0.5078
## commotion 0.903 0.8150
## complainer 0.795 0.6323
## confiscate 0.909 0.8268
## congratulate 0.591 0.3491
## contemplate 0.468 0.2186
## convoy 0.855 0.7303
## couch 0.651 0.4239
## crease 0.762 0.5811
## cunning 0.639 0.4085
## deceit 0.575 0.3301
## deliberately 0.761 0.5790
## deprive 0.636 0.4043
## detectable 0.338 0.1142
## diatribes 0.579 0.3350
## disjoined 0.311 0.0970
## disrupt 0.791 0.6253
## distinct 0.275 0.0756
## divergence 0.796 0.6334
## dome 0.552 0.3046
## downfall 0.775 0.6010
## drink 0.851 0.7244
## elite 0.700 0.4896
## embarrassment 0.602 0.3624
## emphasize 0.881 0.7753
## empire 0.505 0.2554
## empty 0.759 0.5763
## entanglement 0.691 0.4775
## environment 0.659 0.4343
## excite 0.775 0.6010
## flammable 0.920 0.8466
## flatterer 0.868 0.7527
## flatteries 0.646 0.4178
## forever 0.799 0.6379
## gigantic 0.763 0.5826
## girl 0.779 0.6066
## goo 0.717 0.5147
## goodbye 0.820 0.6732
## greed 0.841 0.7073
## groan 0.851 0.7244
## gruesome 0.666 0.4434
## guarantee 0.283 0.0801
## gutter 0.658 0.4326
## harmfulness 0.523 0.2739
## hobby 0.806 0.6502
## hut 0.811 0.6582
## illness 0.491 0.2413
## impromptu 0.660 0.4359
## indescribable 0.762 0.5802
## intellectual 0.711 0.5054
## jargon 0.926 0.8573
## knowledgeable 0.817 0.6681
## lackadaisical 0.606 0.3676
## manager 0.868 0.7529
## meal 0.792 0.6277
## melodic 0.729 0.5313
## mutually 0.873 0.7630
## nonsense 0.861 0.7410
## nonsensical 0.872 0.7600
## not_coveted 0.664 0.4407
## pamper 0.590 0.3487
## penitentiary 0.528 0.2784
## perplexing 0.691 0.4768
## persistence 0.638 0.4075
## predetermine 0.542 0.2940
## pretender 0.857 0.7348
## questioning 0.662 0.4380
## quickly 0.657 0.4321
## rebellious 0.803 0.6452
## referee 0.772 0.5961
## referendum 0.525 0.2760
## relating_to_the_right 0.350 0.1227
## relevant 0.699 0.4890
## respectful 0.771 0.5937
## retailer 0.601 0.3612
## retract 0.524 0.2751
## ropes 0.799 0.6381
## sag 0.596 0.3548
## schemer 0.669 0.4478
## seize 0.793 0.6295
## sensitivity 0.717 0.5145
## shadows 0.658 0.4333
## sketch 0.655 0.4284
## slang 0.803 0.6442
## slave 0.481 0.2313
## sluggish 0.634 0.4020
## somber 0.606 0.3669
## spinelessness 0.632 0.4000
## sporadic 0.832 0.6916
## squad 0.975 0.9509
## stagger 0.652 0.4256
## stinking 0.877 0.7686
## stroll 0.872 0.7606
## stubborn_100 0.552 0.3050
## stubborn_143 0.654 0.4282
## stylish 0.693 0.4796
## summit 0.756 0.5713
## terminology 0.830 0.6882
## the_science_of_speech_sounds 0.751 0.5646
## transportation 0.298 0.0890
## tyrant 0.439 0.1932
## unhealthful 0.419 0.1756
## vile 0.881 0.7770
## vulgar 0.720 0.5181
## wandering 0.415 0.1724
## warning 0.637 0.4063
## wave 0.721 0.5199
## weaponry 0.676 0.4571
## 1of5_1 0.440 0.1938
## 1of5_2 0.289 0.0838
## 1of5_3 0.378 0.1431
## 1of5_4 0.311 0.0969
## 2of5_1 0.411 0.1685
## 2of5_2 0.536 0.2872
## 2of5_3 0.581 0.3376
## 2of5_4 0.619 0.3830
## 2of5_5 0.521 0.2714
## 2of5_6 0.736 0.5414
## 2of5_7 0.375 0.1406
## 2of5_8 0.585 0.3427
## 2of5_9 0.554 0.3074
## 2of5_10 0.378 0.1428
## 2of5_11 0.371 0.1373
## 2of5_12 0.418 0.1749
## 2of5_13 0.491 0.2410
## 2of5_14 0.402 0.1612
## 2of5_15 0.677 0.4578
## 2of5_16 0.574 0.3299
## 2of5_17 0.679 0.4617
## 2of5_18 0.735 0.5400
## 2of5_19 0.447 0.1997
## 2of5_20 0.384 0.1477
## 2of5_21 0.514 0.2646
## 2of5_22 0.881 0.7754
## 2of5_23 0.310 0.0964
## 2of5_25 0.734 0.5394
## 2of5_26 0.711 0.5058
## 2of5_27 0.582 0.3385
## 2of5_28 0.275 0.0755
## 2of5_29 0.548 0.3007
## 2of5_30 0.552 0.3047
## 2of5_31 0.538 0.2900
## 2of5_32 0.627 0.3926
## 2of5_33 0.333 0.1111
## 2of5_34 0.453 0.2055
## 2of5_35 0.295 0.0871
## 2of5_36 0.764 0.5831
## 2of5_37 0.856 0.7335
## 3of5_1 0.271 0.0732
## 3of5_2 0.494 0.2441
## 3of5_3 0.476 0.2263
## 3of5_4 0.707 0.4992
## 3of5_5 0.329 0.1082
## 3of5_6 0.750 0.5630
## 3of5_7 0.594 0.3526
## 3of5_8 0.411 0.1690
## 3of5_10 0.850 0.7228
## 3of5_11 0.723 0.5220
## 3of5_12 0.546 0.2980
## 3of5_13 0.365 0.1330
## 3of5_14 0.508 0.2577
## 3of5_16 0.326 0.1065
## 3of5_17 0.386 0.1486
## 3of5_18 0.319 0.1018
## 3of5_20 0.553 0.3056
## 3of5_21 0.422 0.1781
## 3of5_22 0.443 0.1960
## 3of5_23 0.860 0.7398
## 3of5_24 0.549 0.3018
## 3of5_25 0.526 0.2766
## 3of5_26 0.709 0.5033
## 3of5_27 0.596 0.3551
## 3of5_28 0.413 0.1709
## 3of5_29 0.541 0.2926
## 3of5_30 0.510 0.2606
## 3of5_31 0.426 0.1812
## 3of5_32 0.576 0.3316
##
## SS loadings: 94.3
## Proportion Var: 0.431
##
## Factor correlations:
##
## F1
## F1 1
good_items_stats = itemstats(itemdata %>% select(-id))
good_items_stats$itemstats$loading = good_items_fit %>% get_loadings()
good_items_stats$itemstats$discrim = coef(good_items_fit, simplify = T)$items[, 1] %>% unname()
good_items_stats$itemstats$difficulty = -coef(good_items_fit, simplify = T)$items[, 2] %>% unname()
good_items_stats$itemstats
## N mean sd total.r total.r_if_rm
## a_specific_number 441 0.841 0.366 0.257 0.247
## a_type_of_brass_instrument 441 0.932 0.252 0.387 0.381
## a_type_of_drapery 441 0.823 0.382 0.389 0.380
## a_type_of_fabric_101 441 0.934 0.248 0.320 0.314
## a_type_of_fabric_98 441 0.755 0.431 0.479 0.470
## a_type_of_grasshopper 441 0.821 0.384 0.510 0.502
## a_type_of_hat 441 0.356 0.479 0.468 0.456
## a_type_of_heating_unit 441 0.871 0.336 0.248 0.239
## a_type_of_magistrate_position 441 0.898 0.303 0.357 0.350
## a_type_of_mathematical_operation 441 0.921 0.271 0.263 0.255
## a_type_of_overshoe 441 0.635 0.482 0.396 0.384
## a_type_of_plant 441 0.862 0.346 0.422 0.414
## a_type_of_religious_teacher 441 0.855 0.353 0.462 0.454
## a_type_of_rock 441 0.948 0.223 0.100 0.094
## a_type_of_skirts 441 0.828 0.378 0.386 0.377
## a_type_of_smokeless_powder 441 0.753 0.432 0.301 0.290
## a_type_of_sound 441 0.680 0.467 0.364 0.353
## a_type_of_sword 441 0.599 0.491 0.258 0.245
## a_type_of_volcanic_crater 441 0.855 0.353 0.380 0.371
## a_type_of_wavy_form 441 0.615 0.487 0.549 0.539
## actionable_negligence 441 0.841 0.366 0.449 0.440
## advisory 441 0.959 0.198 0.242 0.237
## advocate 441 0.751 0.433 0.502 0.492
## almighty 441 0.961 0.193 0.354 0.349
## amazement 441 0.918 0.274 0.305 0.298
## amenability 441 0.832 0.374 0.422 0.413
## auspices 441 0.494 0.501 0.558 0.548
## barely_able_to_read_and_write 441 0.880 0.326 0.473 0.466
## because 441 0.912 0.284 0.284 0.277
## berate 441 0.857 0.350 0.451 0.443
## blade 441 0.939 0.240 0.342 0.336
## blend 441 0.912 0.284 0.329 0.321
## blunder 441 0.961 0.193 0.230 0.225
## bow 441 0.596 0.491 0.595 0.586
## brief 441 0.571 0.495 0.429 0.417
## bring_about 441 0.868 0.338 0.438 0.430
## carelessly_or_hastily_put_together 441 0.866 0.341 0.312 0.304
## celebration 441 0.757 0.429 0.477 0.467
## cheat 441 0.723 0.448 0.577 0.569
## clay_pigeon_shooting 441 0.943 0.232 0.292 0.286
## coarse 441 0.941 0.236 0.340 0.333
## collect_or_study_insects 441 0.932 0.252 0.272 0.265
## colossal 441 0.823 0.382 0.419 0.410
## commotion 441 0.853 0.355 0.563 0.556
## complainer 441 0.839 0.368 0.483 0.475
## confiscate 441 0.896 0.306 0.483 0.476
## congratulate 441 0.887 0.317 0.294 0.285
## contemplate 441 0.902 0.297 0.242 0.234
## convoy 441 0.764 0.425 0.594 0.586
## couch 441 0.757 0.429 0.434 0.424
## crease 441 0.830 0.376 0.470 0.461
## cunning 441 0.796 0.403 0.369 0.359
## deceit 441 0.746 0.436 0.391 0.380
## deliberately 441 0.812 0.391 0.479 0.471
## deprive 441 0.837 0.370 0.386 0.377
## detectable 441 0.966 0.181 0.103 0.097
## diatribes 441 0.624 0.485 0.453 0.441
## disjoined 441 0.494 0.501 0.272 0.259
## disrupt 441 0.959 0.198 0.274 0.269
## distinct 441 0.857 0.350 0.186 0.176
## divergence 441 0.698 0.459 0.591 0.582
## dome 441 0.744 0.437 0.393 0.383
## downfall 441 0.898 0.303 0.407 0.400
## drink 441 0.769 0.422 0.558 0.550
## elite 441 0.853 0.355 0.384 0.376
## embarrassment 441 0.875 0.331 0.313 0.304
## emphasize 441 0.966 0.181 0.286 0.282
## empire 441 0.816 0.388 0.317 0.307
## empty 441 0.848 0.359 0.448 0.439
## entanglement 441 0.542 0.499 0.539 0.528
## environment 441 0.503 0.501 0.541 0.531
## excite 441 0.707 0.455 0.581 0.572
## flammable 441 0.986 0.116 0.223 0.220
## flatterer 441 0.844 0.364 0.558 0.551
## flatteries 441 0.732 0.443 0.482 0.472
## forever 441 0.864 0.343 0.453 0.445
## gigantic 441 0.952 0.213 0.242 0.237
## girl 441 0.875 0.331 0.418 0.410
## goo 441 0.971 0.169 0.219 0.215
## goodbye 441 0.948 0.223 0.326 0.320
## greed 441 0.649 0.478 0.668 0.660
## groan 441 0.912 0.284 0.391 0.384
## gruesome 441 0.834 0.372 0.392 0.383
## guarantee 441 0.930 0.256 0.108 0.100
## gutter 441 0.941 0.236 0.223 0.217
## harmfulness 441 0.868 0.338 0.312 0.303
## hobby 441 0.880 0.326 0.443 0.436
## hut 441 0.889 0.315 0.454 0.446
## illness 441 0.717 0.451 0.334 0.323
## impromptu 441 0.626 0.484 0.513 0.503
## indescribable 441 0.955 0.208 0.291 0.286
## intellectual 441 0.943 0.232 0.296 0.290
## jargon 441 0.959 0.198 0.346 0.341
## knowledgeable 441 0.823 0.382 0.513 0.505
## lackadaisical 441 0.741 0.438 0.416 0.405
## manager 441 0.986 0.116 0.192 0.189
## meal 441 0.610 0.488 0.627 0.619
## melodic 441 0.873 0.333 0.422 0.414
## mutually 441 0.966 0.181 0.310 0.305
## nonsense 441 0.873 0.333 0.493 0.486
## nonsensical 441 0.973 0.163 0.306 0.301
## not_coveted 441 0.853 0.355 0.371 0.362
## pamper 441 0.467 0.499 0.452 0.441
## penitentiary 441 0.918 0.274 0.241 0.234
## perplexing 441 0.905 0.294 0.376 0.369
## persistence 441 0.862 0.346 0.350 0.341
## predetermine 441 0.916 0.278 0.256 0.249
## pretender 441 0.991 0.095 0.139 0.136
## questioning 441 0.900 0.300 0.343 0.335
## quickly 441 0.789 0.408 0.400 0.391
## rebellious 441 0.832 0.374 0.488 0.480
## referee 441 0.898 0.303 0.398 0.390
## referendum 441 0.397 0.490 0.440 0.428
## relating_to_the_right 441 0.698 0.459 0.290 0.277
## relevant 441 0.705 0.456 0.482 0.472
## respectful 441 0.859 0.348 0.422 0.414
## retailer 441 0.798 0.402 0.393 0.383
## retract 441 0.875 0.331 0.281 0.272
## ropes 441 0.857 0.350 0.417 0.409
## sag 441 0.719 0.450 0.460 0.449
## schemer 441 0.585 0.493 0.525 0.515
## seize 441 0.864 0.343 0.442 0.434
## sensitivity 441 0.728 0.446 0.511 0.502
## shadows 441 0.685 0.465 0.492 0.481
## sketch 441 0.721 0.449 0.474 0.464
## slang 441 0.821 0.384 0.481 0.473
## slave 441 0.776 0.418 0.361 0.350
## sluggish 441 0.746 0.436 0.479 0.469
## somber 441 0.662 0.474 0.488 0.478
## spinelessness 441 0.830 0.376 0.397 0.388
## sporadic 441 0.658 0.475 0.668 0.660
## squad 441 0.993 0.082 0.207 0.205
## stagger 441 0.769 0.422 0.441 0.431
## stinking 441 0.862 0.346 0.500 0.492
## stroll 441 0.698 0.459 0.670 0.663
## stubborn_100 441 0.864 0.343 0.282 0.273
## stubborn_143 441 0.871 0.336 0.404 0.396
## stylish 441 0.469 0.500 0.560 0.549
## summit 441 0.859 0.348 0.437 0.429
## terminology 441 0.739 0.440 0.588 0.580
## the_science_of_speech_sounds 441 0.964 0.187 0.218 0.213
## transportation 441 0.660 0.474 0.217 0.204
## tyrant 441 0.333 0.472 0.332 0.319
## unhealthful 441 0.435 0.496 0.329 0.316
## vile 441 0.948 0.223 0.358 0.352
## vulgar 441 0.610 0.488 0.533 0.522
## wandering 441 0.565 0.496 0.328 0.315
## warning 441 0.893 0.309 0.359 0.351
## wave 441 0.821 0.384 0.453 0.444
## weaponry 441 0.834 0.372 0.405 0.396
## 1of5_1 383 0.305 0.461 0.331 0.319
## 1of5_2 383 0.303 0.460 0.222 0.209
## 1of5_3 383 0.245 0.431 0.237 0.225
## 1of5_4 383 0.431 0.496 0.255 0.242
## 2of5_1 383 0.475 0.500 0.345 0.332
## 2of5_2 383 0.269 0.444 0.416 0.406
## 2of5_3 383 0.465 0.499 0.487 0.476
## 2of5_4 383 0.266 0.443 0.432 0.422
## 2of5_5 383 0.554 0.498 0.426 0.414
## 2of5_6 383 0.713 0.453 0.524 0.515
## 2of5_7 383 0.313 0.464 0.248 0.235
## 2of5_8 383 0.245 0.431 0.406 0.395
## 2of5_9 383 0.436 0.497 0.435 0.423
## 2of5_10 383 0.423 0.495 0.324 0.311
## 2of5_11 383 0.527 0.500 0.306 0.292
## 2of5_12 383 0.232 0.423 0.315 0.304
## 2of5_13 383 0.326 0.469 0.389 0.377
## 2of5_14 383 0.136 0.343 0.244 0.235
## 2of5_15 383 0.721 0.449 0.493 0.483
## 2of5_16 383 0.493 0.501 0.469 0.457
## 2of5_17 383 0.569 0.496 0.572 0.562
## 2of5_18 383 0.402 0.491 0.582 0.573
## 2of5_19 383 0.522 0.500 0.370 0.357
## 2of5_20 383 0.559 0.497 0.305 0.291
## 2of5_21 383 0.266 0.443 0.425 0.414
## 2of5_22 383 0.567 0.496 0.725 0.718
## 2of5_23 383 0.282 0.451 0.257 0.245
## 2of5_25 383 0.543 0.499 0.599 0.589
## 2of5_26 383 0.467 0.500 0.573 0.563
## 2of5_27 383 0.256 0.437 0.443 0.432
## 2of5_28 383 0.554 0.498 0.256 0.242
## 2of5_29 383 0.420 0.494 0.457 0.445
## 2of5_30 383 0.580 0.494 0.443 0.431
## 2of5_31 383 0.298 0.458 0.399 0.387
## 2of5_32 383 0.117 0.322 0.334 0.326
## 2of5_33 383 0.272 0.445 0.250 0.238
## 2of5_34 383 0.509 0.501 0.380 0.368
## 2of5_35 383 0.433 0.496 0.241 0.227
## 2of5_36 383 0.990 0.102 0.151 0.148
## 2of5_37 383 0.997 0.051 0.103 0.101
## 3of5_1 383 0.407 0.492 0.234 0.220
## 3of5_2 383 0.157 0.364 0.291 0.281
## 3of5_3 383 0.185 0.389 0.323 0.313
## 3of5_4 383 0.480 0.500 0.576 0.566
## 3of5_5 383 0.394 0.489 0.310 0.297
## 3of5_6 383 0.475 0.500 0.599 0.590
## 3of5_7 383 0.230 0.421 0.444 0.434
## 3of5_8 383 0.099 0.299 0.204 0.196
## 3of5_10 383 0.794 0.405 0.578 0.570
## 3of5_11 383 0.311 0.463 0.538 0.529
## 3of5_12 383 0.499 0.501 0.460 0.449
## 3of5_13 383 0.180 0.385 0.226 0.215
## 3of5_14 383 0.587 0.493 0.410 0.398
## 3of5_16 383 0.467 0.500 0.278 0.264
## 3of5_17 383 0.368 0.483 0.325 0.312
## 3of5_18 383 0.428 0.495 0.273 0.259
## 3of5_20 383 0.339 0.474 0.440 0.429
## 3of5_21 383 0.601 0.490 0.344 0.331
## 3of5_22 383 0.540 0.499 0.405 0.393
## 3of5_23 383 0.898 0.303 0.462 0.455
## 3of5_24 383 0.637 0.481 0.457 0.446
## 3of5_25 383 0.379 0.486 0.416 0.404
## 3of5_26 383 0.373 0.484 0.564 0.554
## 3of5_27 383 0.178 0.383 0.379 0.369
## 3of5_28 383 0.815 0.389 0.275 0.264
## 3of5_29 383 0.825 0.380 0.347 0.337
## 3of5_30 383 0.433 0.496 0.423 0.411
## 3of5_31 383 0.702 0.458 0.329 0.317
## 3of5_32 383 0.705 0.457 0.436 0.425
## alpha_if_rm loading discrim difficulty
## a_specific_number 0.975 0.456 0.873 -1.901
## a_type_of_brass_instrument 0.975 0.877 3.113 -4.945
## a_type_of_drapery 0.975 0.652 1.465 -2.098
## a_type_of_fabric_101 0.975 0.744 1.894 -3.742
## a_type_of_fabric_98 0.975 0.700 1.667 -1.707
## a_type_of_grasshopper 0.975 0.803 2.295 -2.683
## a_type_of_hat 0.975 0.574 1.192 0.723
## a_type_of_heating_unit 0.975 0.498 0.977 -2.215
## a_type_of_magistrate_position 0.975 0.746 1.907 -3.199
## a_type_of_mathematical_operation 0.975 0.569 1.178 -2.927
## a_type_of_overshoe 0.975 0.495 0.971 -0.690
## a_type_of_plant 0.975 0.734 1.841 -2.726
## a_type_of_religious_teacher 0.975 0.779 2.117 -2.878
## a_type_of_rock 0.975 0.321 0.576 -3.036
## a_type_of_skirts 0.975 0.642 1.426 -2.111
## a_type_of_smokeless_powder 0.975 0.467 0.898 -1.306
## a_type_of_sound 0.975 0.490 0.957 -0.921
## a_type_of_sword 0.975 0.356 0.648 -0.449
## a_type_of_volcanic_crater 0.975 0.666 1.521 -2.417
## a_type_of_wavy_form 0.975 0.706 1.697 -0.806
## actionable_negligence 0.975 0.769 2.048 -2.685
## advisory 0.975 0.723 1.783 -4.193
## advocate 0.975 0.702 1.675 -1.680
## almighty 0.975 0.914 3.839 -6.568
## amazement 0.975 0.661 1.498 -3.137
## amenability 0.975 0.740 1.871 -2.462
## auspices 0.975 0.688 1.611 -0.062
## barely_able_to_read_and_write 0.975 0.841 2.642 -3.630
## because 0.975 0.680 1.580 -3.105
## berate 0.975 0.836 2.596 -3.314
## blade 0.975 0.783 2.142 -4.068
## blend 0.975 0.683 1.590 -3.114
## blunder 0.975 0.860 2.872 -5.416
## bow 0.975 0.751 1.938 -0.774
## brief 0.975 0.432 0.815 -0.350
## bring_about 0.975 0.790 2.192 -3.090
## carelessly_or_hastily_put_together 0.975 0.609 1.308 -2.377
## celebration 0.975 0.719 1.760 -1.779
## cheat 0.975 0.806 2.318 -1.864
## clay_pigeon_shooting 0.975 0.767 2.035 -4.057
## coarse 0.975 0.776 2.097 -4.069
## collect_or_study_insects 0.975 0.626 1.367 -3.247
## colossal 0.975 0.713 1.729 -2.278
## commotion 0.975 0.903 3.572 -4.156
## complainer 0.975 0.795 2.232 -2.810
## confiscate 0.975 0.909 3.718 -4.932
## congratulate 0.975 0.591 1.246 -2.546
## contemplate 0.975 0.468 0.900 -2.509
## convoy 0.975 0.855 2.801 -2.538
## couch 0.975 0.651 1.460 -1.605
## crease 0.975 0.762 2.005 -2.542
## cunning 0.975 0.639 1.414 -1.854
## deceit 0.975 0.575 1.195 -1.395
## deliberately 0.975 0.761 1.996 -2.372
## deprive 0.975 0.636 1.402 -2.171
## detectable 0.975 0.338 0.611 -3.504
## diatribes 0.975 0.579 1.208 -0.699
## disjoined 0.975 0.311 0.558 0.016
## disrupt 0.975 0.791 2.198 -4.609
## distinct 0.975 0.275 0.487 -1.873
## divergence 0.975 0.796 2.237 -1.624
## dome 0.975 0.552 1.126 -1.349
## downfall 0.975 0.775 2.089 -3.359
## drink 0.975 0.851 2.759 -2.550
## elite 0.975 0.700 1.667 -2.501
## embarrassment 0.975 0.602 1.283 -2.451
## emphasize 0.975 0.881 3.161 -5.909
## empire 0.975 0.505 0.997 -1.771
## empty 0.975 0.759 1.985 -2.702
## entanglement 0.975 0.691 1.627 -0.349
## environment 0.975 0.659 1.491 -0.101
## excite 0.975 0.775 2.089 -1.608
## flammable 0.975 0.920 3.999 -8.102
## flatterer 0.975 0.868 2.969 -3.489
## flatteries 0.975 0.646 1.442 -1.430
## forever 0.975 0.799 2.259 -3.096
## gigantic 0.975 0.763 2.011 -4.239
## girl 0.975 0.779 2.113 -3.100
## goo 0.975 0.717 1.753 -4.524
## goodbye 0.975 0.820 2.443 -4.572
## greed 0.975 0.841 2.646 -1.450
## groan 0.975 0.851 2.760 -4.202
## gruesome 0.975 0.666 1.519 -2.230
## guarantee 0.975 0.283 0.502 -2.683
## gutter 0.975 0.658 1.486 -3.509
## harmfulness 0.975 0.523 1.045 -2.233
## hobby 0.975 0.806 2.321 -3.336
## hut 0.975 0.811 2.362 -3.488
## illness 0.975 0.491 0.960 -1.120
## impromptu 0.975 0.660 1.496 -0.804
## indescribable 0.975 0.762 2.001 -4.286
## intellectual 0.975 0.711 1.720 -3.759
## jargon 0.975 0.926 4.172 -6.900
## knowledgeable 0.975 0.817 2.415 -2.800
## lackadaisical 0.975 0.606 1.298 -1.416
## manager 0.975 0.868 2.971 -6.748
## meal 0.975 0.792 2.210 -0.965
## melodic 0.975 0.729 1.812 -2.823
## mutually 0.975 0.873 3.054 -5.781
## nonsense 0.975 0.861 2.879 -3.766
## nonsensical 0.975 0.872 3.029 -6.021
## not_coveted 0.975 0.664 1.511 -2.388
## pamper 0.975 0.590 1.245 0.118
## penitentiary 0.975 0.528 1.057 -2.811
## perplexing 0.975 0.691 1.625 -3.050
## persistence 0.975 0.638 1.412 -2.405
## predetermine 0.975 0.542 1.098 -2.807
## pretender 0.975 0.857 2.833 -7.019
## questioning 0.975 0.662 1.502 -2.894
## quickly 0.975 0.657 1.485 -1.845
## rebellious 0.975 0.803 2.295 -2.793
## referee 0.975 0.772 2.068 -3.340
## referendum 0.975 0.525 1.051 0.482
## relating_to_the_right 0.975 0.350 0.637 -0.922
## relevant 0.975 0.699 1.665 -1.366
## respectful 0.975 0.771 2.058 -2.877
## retailer 0.975 0.601 1.280 -1.792
## retract 0.975 0.524 1.048 -2.301
## ropes 0.975 0.799 2.260 -3.022
## sag 0.975 0.596 1.262 -1.258
## schemer 0.975 0.669 1.533 -0.578
## seize 0.975 0.793 2.219 -3.061
## sensitivity 0.975 0.717 1.752 -1.565
## shadows 0.975 0.658 1.488 -1.153
## sketch 0.975 0.655 1.473 -1.373
## slang 0.975 0.803 2.290 -2.679
## slave 0.975 0.481 0.934 -1.462
## sluggish 0.975 0.634 1.395 -1.495
## somber 0.975 0.606 1.296 -0.940
## spinelessness 0.975 0.632 1.390 -2.106
## sporadic 0.975 0.832 2.549 -1.474
## squad 0.975 0.975 7.487 -14.285
## stagger 0.975 0.652 1.465 -1.687
## stinking 0.975 0.877 3.102 -3.831
## stroll 0.975 0.872 3.034 -2.092
## stubborn_100 0.975 0.552 1.128 -2.239
## stubborn_143 0.975 0.654 1.473 -2.539
## stylish 0.975 0.693 1.634 0.086
## summit 0.975 0.756 1.965 -2.801
## terminology 0.975 0.830 2.528 -2.128
## the_science_of_speech_sounds 0.975 0.751 1.938 -4.477
## transportation 0.975 0.298 0.532 -0.711
## tyrant 0.975 0.439 0.833 0.781
## unhealthful 0.975 0.419 0.785 0.278
## vile 0.975 0.881 3.177 -5.378
## vulgar 0.975 0.720 1.765 -0.802
## wandering 0.975 0.415 0.777 -0.313
## warning 0.975 0.637 1.408 -2.739
## wave 0.975 0.721 1.771 -2.288
## weaponry 0.975 0.676 1.562 -2.259
## 1of5_1 0.975 0.440 0.834 0.977
## 1of5_2 0.975 0.289 0.515 0.908
## 1of5_3 0.975 0.378 0.695 1.271
## 1of5_4 0.975 0.311 0.557 0.322
## 2of5_1 0.975 0.411 0.766 0.139
## 2of5_2 0.975 0.536 1.080 1.274
## 2of5_3 0.975 0.581 1.215 0.204
## 2of5_4 0.975 0.619 1.341 1.403
## 2of5_5 0.975 0.521 1.039 -0.239
## 2of5_6 0.975 0.736 1.849 -1.406
## 2of5_7 0.975 0.375 0.688 0.896
## 2of5_8 0.975 0.585 1.229 1.496
## 2of5_9 0.975 0.554 1.134 0.350
## 2of5_10 0.975 0.378 0.695 0.371
## 2of5_11 0.975 0.371 0.679 -0.096
## 2of5_12 0.975 0.418 0.784 1.384
## 2of5_13 0.975 0.491 0.959 0.898
## 2of5_14 0.975 0.402 0.746 2.089
## 2of5_15 0.975 0.677 1.564 -1.325
## 2of5_16 0.975 0.574 1.194 0.054
## 2of5_17 0.975 0.679 1.576 -0.402
## 2of5_18 0.975 0.735 1.844 0.638
## 2of5_19 0.975 0.447 0.850 -0.077
## 2of5_20 0.975 0.384 0.709 -0.237
## 2of5_21 0.975 0.514 1.021 1.267
## 2of5_22 0.975 0.881 3.162 -0.750
## 2of5_23 0.975 0.310 0.556 1.025
## 2of5_25 0.975 0.734 1.842 -0.288
## 2of5_26 0.975 0.711 1.722 0.200
## 2of5_27 0.975 0.582 1.218 1.418
## 2of5_28 0.975 0.275 0.486 -0.205
## 2of5_29 0.975 0.548 1.116 0.429
## 2of5_30 0.975 0.552 1.127 -0.382
## 2of5_31 0.975 0.538 1.088 1.101
## 2of5_32 0.975 0.627 1.368 2.736
## 2of5_33 0.975 0.333 0.602 1.093
## 2of5_34 0.975 0.453 0.866 -0.017
## 2of5_35 0.975 0.295 0.526 0.308
## 2of5_36 0.975 0.764 2.013 -5.815
## 2of5_37 0.975 0.856 2.824 -8.239
## 3of5_1 0.975 0.271 0.478 0.417
## 3of5_2 0.975 0.494 0.967 2.033
## 3of5_3 0.975 0.476 0.921 1.772
## 3of5_4 0.975 0.707 1.699 0.119
## 3of5_5 0.975 0.329 0.593 0.489
## 3of5_6 0.975 0.750 1.932 0.149
## 3of5_7 0.975 0.594 1.256 1.621
## 3of5_8 0.975 0.411 0.767 2.484
## 3of5_10 0.975 0.850 2.749 -2.626
## 3of5_11 0.975 0.723 1.779 1.270
## 3of5_12 0.975 0.546 1.109 0.029
## 3of5_13 0.975 0.365 0.667 1.686
## 3of5_14 0.975 0.508 1.003 -0.403
## 3of5_16 0.975 0.326 0.587 0.165
## 3of5_17 0.975 0.386 0.711 0.629
## 3of5_18 0.975 0.319 0.573 0.335
## 3of5_20 0.975 0.553 1.129 0.871
## 3of5_21 0.975 0.422 0.792 -0.437
## 3of5_22 0.975 0.443 0.840 -0.161
## 3of5_23 0.975 0.860 2.870 -3.963
## 3of5_24 0.975 0.549 1.119 -0.679
## 3of5_25 0.975 0.526 1.052 0.639
## 3of5_26 0.975 0.709 1.713 0.807
## 3of5_27 0.975 0.596 1.263 2.041
## 3of5_28 0.975 0.413 0.773 -1.612
## 3of5_29 0.975 0.541 1.095 -1.829
## 3of5_30 0.975 0.510 1.010 0.352
## 3of5_31 0.975 0.426 0.801 -0.943
## 3of5_32 0.975 0.576 1.199 -1.079
good_items_stats$itemstats %>%
describe2()
## # A tibble: 9 × 10
## var n mean median sd mad min max skew kurtosis
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 N 219 423. 441 2.70e+1 0 383 441 -0.791 -1.38
## 2 mean 219 0.692 0.757 2.32e-1 2.29e-1 0.0992 0.997 -0.714 -0.618
## 3 sd 219 0.386 0.405 1.04e-1 1.10e-1 0.0511 0.501 -0.892 0.124
## 4 total… 219 0.391 0.396 1.19e-1 1.24e-1 0.0999 0.725 0.0355 -0.280
## 5 total… 219 0.382 0.384 1.19e-1 1.23e-1 0.0942 0.718 0.0607 -0.294
## 6 alpha… 219 0.975 0.975 8.54e-5 8.82e-5 0.975 0.975 -0.498 -0.0909
## 7 loadi… 219 0.634 0.658 1.70e-1 1.80e-1 0.271 0.975 -0.346 -0.798
## 8 discr… 219 1.62 1.49 8.61e-1 7.63e-1 0.478 7.49 1.95 8.85
## 9 diffi… 219 -1.75 -1.71 2.22e+0 2.06e+0 -14.3 2.74 -1.10 3.99
#difficulties
good_items_stats$itemstats$mean %>% GG_denhist() +
scale_x_continuous("Pass rate")
## Input seems like a fraction, set `boundary=0` and `binwidth=1/30` to avoid issues near the limits. Disable this with `auto_fraction_bounary=F`
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
GG_save("figs/good items pass rate.png")
#loadings
good_items_stats$itemstats$loading %>% GG_denhist() +
scale_x_continuous("Factor loading")
## Input seems like a fraction, set `boundary=0` and `binwidth=1/30` to avoid issues near the limits. Disable this with `auto_fraction_bounary=F`
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
GG_save("figs/good items factor loading.png")
#reliability
good_items_fit_scores = fscores(good_items_fit, full.scores.SE = T)
empirical_rxx(good_items_fit_scores)
## F1
## 0.972
#which range has >.90?
d_rxx_info = rxx_info = get_reliability(good_items_fit)
d_rxx_info %>%
ggplot(aes(z, rel)) +
geom_line() +
scale_y_continuous("Reliability", breaks = seq(0, 1, .05)) +
scale_x_continuous("Ability level (z)") +
coord_cartesian(xlim = c(-4, 4))
#merge g score back to main dataset
d$g = NULL
d = left_join(
d,
tibble(id = itemdata$id,
g = good_items_fit_scores[, 1]),
by = c("Participant_id" = "id")
)
assert_that(!anyDuplicated(d$Participant_id))
## [1] TRUE
Norms
#he age problem
GG_scatter(d, "age", "g") +
geom_smooth()
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
#scores by age group
d$age_group = discretize(d$age, 3)
GG_group_means(d, "g", "age_group", type = "boxplot") +
scale_y_continuous("Vocabulary IRT score") +
scale_x_discrete("Age group")
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
GG_save("figs/good items boxplots by age.png")
describe2(d$g, d$age_group)
## New names:
## • `` -> `...1`
## # A tibble: 3 × 11
## group var n mean median sd mad min max skew kurtosis
## <fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 [18.9,40.3] ...1 176 -0.390 -0.481 0.832 0.841 -2.27 1.81 0.592 -0.194
## 2 (40.3,61.7] ...1 174 0.0964 -0.0615 0.957 1.09 -1.76 2.55 0.460 -0.685
## 3 (61.7,83.1] ...1 91 0.562 0.529 1.02 1.03 -1.50 3.15 0.184 -0.191
#whites differ in age?
describe2(d$age, d$white_only)
## New names:
## • `` -> `...1`
## # A tibble: 2 × 11
## group var n mean median sd mad min max skew kurtosis
## <fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 FALSE ...1 114 41.3 39 14.8 18.5 21 74 0.312 -1.09
## 2 TRUE ...1 327 48.5 51 15.7 17.8 19 83 -0.121 -1.07
#white subset is easier to work with
d_white = d %>% filter(white_only)
(white_ageadj_model = lm(g ~ age, data = d_white))
##
## Call:
## lm(formula = g ~ age, data = d_white)
##
## Coefficients:
## (Intercept) age
## -1.1010 0.0251
#get resids, step 1
d_white$g_ageadj1 = resid(white_ageadj_model)
(ageadj_desc_whites = describe2(d_white$g_ageadj1))
## # A tibble: 1 × 10
## var n mean median sd mad min max skew kurtosis
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 x 327 -2.57e-17 -0.0648 0.901 0.958 -2.26 2.60 0.320 -0.281
#alternative is to just model the absolute resids directly
(absSD_ols_whites = lm(abs(g_ageadj1) ~ age, data = d_white))
##
## Call:
## lm(formula = abs(g_ageadj1) ~ age, data = d_white)
##
## Coefficients:
## (Intercept) age
## 0.46724 0.00544
#get age mean and SD adjusted scores
d_white$g_ageadj2 = d_white$g_ageadj1 / predict(absSD_ols_whites)
#does this work tho?
d_white %>%
GG_scatter("age", "g_ageadj2")
## `geom_smooth()` using formula = 'y ~ x'
test_HS(d_white$g_ageadj2, d_white$age)
## number of knots in rcs defaulting to 5
## number of knots in rcs defaulting to 5
## # A tibble: 4 × 5
## test r2adj p fit log10_p
## <chr> <dbl> <dbl> <named list> <dbl>
## 1 linear raw -0.00300 0.872 <ols> 0.0594
## 2 spline raw -0.00246 0.361 <ols> 0.443
## 3 linear rank -0.00305 0.924 <ols> 0.0343
## 4 spline rank 0.00330 0.164 <ols> 0.785
#restore to white z score norms
(white_desc_ageadj2_desc = describe2(d_white$g_ageadj2))
## # A tibble: 1 × 10
## var n mean median sd mad min max skew kurtosis
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 x 327 0.000443 -0.0814 1.22 1.33 -2.59 3.73 0.397 -0.350
d_white$g_ageadj3 = (d_white$g_ageadj2 - white_desc_ageadj2_desc$mean) / white_desc_ageadj2_desc$sd
d_white$g_ageadj3 %>% describe2()
## # A tibble: 1 × 10
## var n mean median sd mad min max skew kurtosis
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 x 327 1.50e-17 -0.0668 1 1.08 -2.12 3.05 0.397 -0.350
#Thus finally, we can make IQs using a function
vocab_to_IQ = function(x, .age) {
#remove age effect first
resid_age = x - predict(white_ageadj_model, newdata = tibble(age = .age, g = x))
#adjust scores as function of their age
SD_factor = predict(absSD_ols_whites, newdata = tibble(
age = .age
))
#adjust SD
resid_age_whitesd_agesd = resid_age / SD_factor
#set to white norms
step3 = (resid_age_whitesd_agesd - white_desc_ageadj2_desc$mean) / white_desc_ageadj2_desc$sd
#output IQ scores
step3 * 15 + 100
}
d$IQ = vocab_to_IQ(d$g, d$age)
#and no heteroscedasticity
test_HS(d$IQ, d$age)
## number of knots in rcs defaulting to 5
## number of knots in rcs defaulting to 5
## # A tibble: 4 × 5
## test r2adj p fit log10_p
## <chr> <dbl> <dbl> <named list> <dbl>
## 1 linear raw -0.00226 0.937 <ols> 0.0282
## 2 spline raw -0.00808 0.925 <ols> 0.0339
## 3 linear rank -0.00211 0.786 <ols> 0.105
## 4 spline rank -0.00674 0.803 <ols> 0.0954
Basic stats
#race gaps
SMD_matrix(d$IQ, d$race_combos_common)
## black east_asian hispanic white white, hispanic Other
## black NA -0.6096 0.306 -0.5590 0.0627 -0.6376
## east_asian -0.6096 NA 0.915 0.0507 0.6723 -0.0279
## hispanic 0.3056 0.9152 NA -0.8646 -0.2429 -0.9432
## white -0.5590 0.0507 -0.865 NA 0.6217 -0.0786
## white, hispanic 0.0627 0.6723 -0.243 0.6217 NA -0.7003
## Other -0.6376 -0.0279 -0.943 -0.0786 -0.7003 NA
describe2(d %>% select(IQ), group = d$race_combos_common) %>% df_round(2)
## # A tibble: 6 × 11
## group var n mean median sd mad min max skew kurtosis
## <chr> <chr> <chr> <chr> <chr> <chr> <chr> <chr> <chr> <chr> <chr>
## 1 black IQ " 47… " 91… " 89.… "14.… "13.… 61.98 120.… 0.34 -0.50
## 2 east_asian IQ " 17… "100… "103.… "16.… "21.… 79.90 134.… 0.30 -1.26
## 3 hispanic IQ " 10… " 86… " 83.… " 9.… " 9.… 74.58 102.… 0.33 -1.61
## 4 white IQ "327… "100… " 99.… "15.… "16.… 68.20 145.… 0.40 -0.35
## 5 white, hispan… IQ " 8… " 90… " 91.… " 9.… "13.… 80.15 107.… 0.37 -1.40
## 6 Other IQ " 32… "101… " 98.… "18.… "18.… 75.66 149.… 0.54 -0.53
SMD_matrix(d$IQ, d$bw)[1, 2]
## [1] -0.568
describe2(d$IQ, d$bw)
## New names:
## • `` -> `...1`
## # A tibble: 3 × 11
## group var n mean median sd mad min max skew kurtosis
## <fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Black ...1 47 91.5 89.5 14.0 13.9 62.0 120. 0.344 -0.500
## 2 White ...1 327 100 99.0 15 16.3 68.2 146. 0.397 -0.350
## 3 <NA> ...1 67 97.7 94.6 17.0 17.8 74.6 149. 0.752 -0.115
#plot results to see if they make sense
d %>%
GG_denhist("IQ", "bw") +
scale_fill_discrete("Race") +
scale_x_continuous("IQ", breaks = seq(0, 200, by = 5))
## Warning in GG_denhist(., "IQ", "bw"): Grouping variable contained missing
## values. These were removed. If you want an NA group, convert to explicit value.
## Scale for x is already present.
## Adding another scale for x, which will replace the existing scale.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
GG_save("figs/dists for blacks and whites.png")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#adjust for reliability
adj_d_reliability(
SMD_matrix(d$IQ, d$bw)[1, 2],
empirical_rxx(good_items_fit_scores)
)
## F1
## -0.577
Jensen method
#black white gap
good_items_stats$itemstats$bw_gap = map_dbl(itemdata %>% select(-id) %>% names(), function(v) {
#subset to the focus item, and the black and the white pure groups
focus_item = itemdata[[v]]
focus_item_white = focus_item[d$white_only]
focus_item_black = focus_item[d$black_only]
#pass rate to z score
white_z = wtd_mean(focus_item_white) %>% qnorm()
black_z = wtd_mean(focus_item_black) %>% qnorm()
#gap in z
z_gap = white_z - black_z
#Inf to NA
inf_to_NA(z_gap)
})
sum(d$white_only)
## [1] 327
sum(d$black_only)
## [1] 47
#example
itemdata[NA_to_F(d$bw == "White"), 1] %>% mean()
## [1] 0.847
itemdata[NA_to_F(d$bw == "Black"), 1] %>% mean()
## [1] 0.766
itemdata[NA_to_F(d$bw == "White"), 1] %>% mean() %>% qnorm()
## [1] 1.02
itemdata[NA_to_F(d$bw == "Black"), 1] %>% mean() %>% qnorm()
## [1] 0.726
itemdata[NA_to_F(d$bw == "White"), 1] %>% mean() %>% qnorm() - itemdata[NA_to_F(d$bw == "Black"), 1] %>% mean() %>% qnorm()
## [1] 0.298
#spearman jensen method
good_items_stats$itemstats %>%
rownames_to_column() %>%
GG_scatter("loading", "bw_gap", case_names = "rowname") +
scale_x_continuous("Factor loading", breaks = seq(-1, 1, .1)) +
scale_y_continuous("Black-White gap, d")
## `geom_smooth()` using formula = 'y ~ x'
GG_save("figs/Jensen method items.png")
## `geom_smooth()` using formula = 'y ~ x'
#gap at perfect reliability
(jensen_method_ols = ols(bw_gap ~ loading, data = good_items_stats$itemstats))
## Frequencies of Missing Values Due to Each Variable
## bw_gap loading
## 3 0
##
## Linear Regression Model
##
## ols(formula = bw_gap ~ loading, data = good_items_stats$itemstats)
##
##
## Model Likelihood Discrimination
## Ratio Test Indexes
## Obs 216 LR chi2 23.13 R2 0.102
## sigma0.2258 d.f. 1 R2 adj 0.097
## d.f. 214 Pr(> chi2) 0.0000 g 0.087
##
## Residuals
##
## Min 1Q Median 3Q Max
## -0.693528 -0.137776 0.002642 0.135475 0.920415
##
##
## Coef S.E. t Pr(>|t|)
## Intercept 0.1200 0.0594 2.02 0.0447
## loading 0.4470 0.0909 4.92 <0.0001
predict(jensen_method_ols, newdata = tibble(loading = 1))
## 1
## 0.567
lm(bw_gap ~ 0 + loading, data = good_items_stats$itemstats)
##
## Call:
## lm(formula = bw_gap ~ 0 + loading, data = good_items_stats$itemstats)
##
## Coefficients:
## loading
## 0.624
Black-White DIF
#black-white bias
bw_bias_fit = cache_object(
expr = {DIF_test(
items = itemdata %>% select(-id),
model = 1,
group = d$bw,
technical = list(NCYCLES = 2000)
)
}, filename = "DIF_test.rds")
## Cache found, reading object from disk
#DIF items
bw_bias_fit$DIF_stats %>% filter(p < .05)
## item groups converged AIC SABIC HQ
## 1 a_type_of_mathematical_operation Black,White TRUE -3.63 -2.132 -0.519
## 2 auspices Black,White TRUE -2.94 -1.435 0.178
## 3 berate Black,White TRUE -2.68 -1.176 0.437
## 4 cheat Black,White TRUE -2.38 -0.875 0.739
## 5 embarrassment Black,White TRUE -5.83 -4.328 -2.715
## 6 empire Black,White TRUE -2.57 -1.069 0.544
## 7 gutter Black,White TRUE -2.04 -0.534 1.079
## 8 indescribable Black,White TRUE -5.18 -3.678 -2.065
## 9 meal Black,White TRUE -12.38 -10.872 -9.259
## 10 mutually Black,White TRUE -2.28 -0.780 0.833
## 11 nonsensical Black,White TRUE -4.00 -2.492 -0.878
## 12 referendum Black,White TRUE -2.07 -0.566 1.047
## 13 summit Black,White TRUE -2.83 -1.328 0.285
## 14 2of5_9 Black,White TRUE -3.76 -2.255 -0.642
## 15 2of5_11 Black,White TRUE -5.62 -4.112 -2.498
## 16 2of5_22 Black,White TRUE -2.57 -1.067 0.547
## 17 3of5_5 Black,White TRUE -2.68 -1.177 0.436
## 18 3of5_13 Black,White TRUE -4.92 -3.421 -1.808
## 19 3of5_25 Black,White TRUE -7.46 -5.961 -4.347
## 20 3of5_32 Black,White TRUE -5.55 -4.046 -2.433
## BIC X2 df p number p_adj
## 1 4.213 7.635 2 0.022 10 1.000
## 2 4.910 6.938 2 0.031 27 1.000
## 3 5.169 6.679 2 0.035 30 1.000
## 4 5.471 6.378 2 0.041 39 1.000
## 5 2.017 9.831 2 0.007 66 1.000
## 6 5.277 6.572 2 0.037 68 1.000
## 7 5.812 6.037 2 0.049 85 1.000
## 8 2.667 9.181 2 0.01 91 1.000
## 9 -4.526 16.375 2 0 97 0.061
## 10 5.565 6.284 2 0.043 99 1.000
## 11 3.854 7.995 2 0.018 101 1.000
## 12 5.779 6.069 2 0.048 113 1.000
## 13 5.017 6.831 2 0.033 139 1.000
## 14 4.090 7.758 2 0.021 163 1.000
## 15 2.234 9.615 2 0.008 165 1.000
## 16 5.279 6.57 2 0.037 176 1.000
## 17 5.168 6.68 2 0.035 195 1.000
## 18 2.924 8.924 2 0.012 202 1.000
## 19 0.385 11.464 2 0.003 212 0.707
## 20 2.300 9.549 2 0.008 219 1.000
bw_bias_fit$DIF_stats %>% filter(p_adj < .05)
## [1] item groups converged AIC SABIC HQ BIC
## [8] X2 df p number p_adj
## <0 rows> (or 0-length row.names)
bw_bias_fit$effect_size_test
## $liberal
## Effect Size Value
## 1 STDS 0.6593
## 2 UTDS 2.8640
## 3 UETSDS 0.6699
## 4 ETSSD 0.0206
## 5 Starks.DTFR 0.6294
## 6 UDTFR 2.8953
## 7 UETSDN 0.6364
## 8 theta.of.max.test.D 4.9240
## 9 Test.Dmax 2.1516
##
## $conservative
## Effect Size Value
## 1 STDS 0.000
## 2 UTDS 0.000
## 3 UETSDS 0.000
## 4 ETSSD 0.000
## 5 Starks.DTFR 0.000
## 6 UDTFR 0.000
## 7 UETSDN 0.000
## 8 theta.of.max.test.D 0.971
## 9 Test.Dmax 0.000
bw_bias_fit$DIF_stats$item_number = seq_along_rows(bw_bias_fit$DIF_stats)
#plot items
bw_bias_fit$fits$anchor_conservative %>% plot(type = "trace")
# not working because there is no DIF?
# bw_bias_fit$fits$anchor_conservative %>% plot(type = "trace", which.items = bw_bias_fit$DIF_stats %>% filter(p_adj < .05) %>% pull(item_number))
# this function shows there is no DIF
filtered_items <- bw_bias_fit$DIF_stats %>% filter(p_adj < .05) %>% pull(item_number)
if (length(filtered_items) > 0) {
bw_bias_fit$fits$anchor_conservative %>% plot(type = "trace", which.items = filtered_items)
} else {
message("No items flagged for DIF at p_adj < .05.")
}
## No items flagged for DIF at p_adj < .05.
bw_bias_fit$fits$anchor_liberal %>% plot(type = "trace", which.items = bw_bias_fit$DIF_stats %>% filter(p < .05) %>% pull(item_number))
#plot bias for test
bw_bias_fit$fits$anchor_conservative %>% plot(type = "score")
#bw difference
SMD_matrix(d$IQ, d$bw)
## Black White
## Black NA -0.568
## White -0.568 NA
describe2(d$IQ, d$bw)
## New names:
## • `` -> `...1`
## # A tibble: 3 × 11
## group var n mean median sd mad min max skew kurtosis
## <fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Black ...1 47 91.5 89.5 14.0 13.9 62.0 120. 0.344 -0.500
## 2 White ...1 327 100 99.0 15 16.3 68.2 146. 0.397 -0.350
## 3 <NA> ...1 67 97.7 94.6 17.0 17.8 74.6 149. 0.752 -0.115