Assessing item parameter drift (IPD) in the Transition Diagnostic Classification Model (TDCM)
Source:R/tdcm.ipd.R
tdcm.ipd.RdThe tdcm.ipd() function assesses item parameter drift (IPD) in the TDCM (e.g., Madison & Bradshaw, 2018) by applying the Wald test
for differential item functioning (de la Torre, 2011; Hou, de la Torre & Nandakumar, 2014).
The p-values are also calculated by a Holm adjustment for multiple comparisons. In the case of two time
points, an effect size of item parameter drift (labeled as UA in the ipd.stats value)
is defined as the weighted absolute difference of item response functions.
Arguments
- model
A
tdcmobject returned from thetdcmfunction.
Value
A list with the following items:
$ipd.stats: Data frame containing results of item-wise Wald tests.$coef: Data frame containing item parameter estimates for each time point.$estimates: List of \(\lambda\) vectors containing all item parameter estimates.$item.probs.time: List with predicted item response probabilities for each time point.
#' @references de la Torre, J. (2011). The Generalized DINA model framework. Psychometrika, 76, 179–199. https://doi.org/10.1007/s11336-011-9207-7.
Hou, L., de la Torre, J., & Nandakumar, R. (2014). Differential item functioning assessment in cognitive diagnostic modeling: Application of the Wald test to investigate DIF in the DINA model. Journal of Educational Measurement, 51, 98-125. https://doi.org/10.1111/jedm.12036.
Madison, M. J., & Bradshaw, L. (2018a). Assessing growth in a diagnostic classification model framework. Psychometrika, 83(4), 963-990. https://doi.org/10.1007/s11336-018-9638-5.
Examples
# \donttest{
############################################################################
# Example 1: TDCM with full measurement invariance
############################################################################
# Load dataset: T=2, A=4
data(data.tdcm01, package = "TDCM")
data <- data.tdcm01$data
q.matrix <- data.tdcm01$q.matrix
# Estimate model
model1 <- TDCM::tdcm(data, q.matrix, num.time.points = 2, invariance = TRUE,
rule = "LCDM", num.q.matrix = 1)
#> [1] Preparing data for tdcm()...
#> [1] Estimating the TDCM in tdcm()...
#> [1] Depending on model complexity, estimation time may vary...
#> [1] TDCM estimation complete.
#> [1] Use tdcm.summary() to display results.
# Run IPD analysis
ipd = tdcm.ipd(model1)
ipd$ipd.stats
#> item X2 df p p.holm UA
#> 1 Item1 0.22156469 2 0.8951336 1 0.008980171
#> 2 Item2 0.07761982 2 0.9619335 1 0.005209066
#> 3 Item3 0.88000141 2 0.6440360 1 0.011576302
#> 4 Item4 3.53498844 4 0.4725783 1 0.040003125
#> 5 Item5 0.46599238 4 0.9767261 1 0.018472372
#> 6 Item6 0.82278150 2 0.6627279 1 0.015561819
#> 7 Item7 0.38751170 2 0.8238590 1 0.010677069
#> 8 Item8 0.33877604 2 0.8441813 1 0.009624126
#> 9 Item9 4.81487276 4 0.3068255 1 0.029992050
#> 10 Item10 0.34295555 4 0.9868751 1 0.017882758
#> 11 Item11 1.62618390 2 0.4434847 1 0.013465488
#> 12 Item12 0.69515863 2 0.7063960 1 0.012707218
#> 13 Item13 1.76810231 2 0.4131060 1 0.010936366
#> 14 Item14 2.99630231 4 0.5584444 1 0.039664282
#> 15 Item15 1.82736575 4 0.7674720 1 0.021706705
#> 16 Item16 0.92517994 2 0.6296508 1 0.009828840
#> 17 Item17 0.66787532 2 0.7160984 1 0.013790663
#> 18 Item18 0.36405703 2 0.8335776 1 0.010721126
#> 19 Item19 0.65966825 4 0.9562079 1 0.034882144
#> 20 Item20 4.92455253 4 0.2951269 1 0.096273056
ipd$coef
#> Link Item Item Number Param Type Rule Est SE
#> Item1_0 logit Item1 1 0 LCDM -1.9181441 0.07881600
#> Item1_1 logit Item1 1 1 LCDM 2.6121266 0.11946880
#> Item2_0 logit Item2 2 0 LCDM -2.0705259 0.08351611
#> Item2_1 logit Item2 2 1 LCDM 2.5172348 0.12042195
#> Item3_0 logit Item3 3 0 LCDM -1.9362663 0.07935031
#> Item3_1 logit Item3 3 1 LCDM 2.5263715 0.11875002
#> Item4_0 logit Item4 4 0 LCDM -1.9199198 0.09208705
#> Item4_1 logit Item4 4 1 LCDM 1.0225220 0.22366649
#> Item4_2 logit Item4 4 2 LCDM 1.4950561 0.13917614
#> Item4_1-2 logit Item4 4 1-2 LCDM 1.1698458 0.28125714
#> Item5_0 logit Item5 5 0 LCDM -2.1618846 0.10571189
#> Item5_1 logit Item5 5 1 LCDM 1.6092665 0.28406789
#> Item5_2 logit Item5 5 2 LCDM 1.7547667 0.14124883
#> Item5_1-2 logit Item5 5 1-2 LCDM 0.8682878 0.33125169
#> Item6_0 logit Item6 6 0 LCDM -1.8692012 0.08575761
#> Item6_1 logit Item6 6 1 LCDM 2.1831830 0.11099537
#> Item7_0 logit Item7 7 0 LCDM -1.8581021 0.08541033
#> Item7_1 logit Item7 7 1 LCDM 2.2645963 0.11109938
#> Item8_0 logit Item8 8 0 LCDM -1.9975654 0.08997004
#> Item8_1 logit Item8 8 1 LCDM 2.4915166 0.11507136
#> Item9_0 logit Item9 9 0 LCDM -2.0659941 0.10704271
#> Item9_1 logit Item9 9 1 LCDM 1.2450458 0.20495828
#> Item9_2 logit Item9 9 2 LCDM 1.5332934 0.16050040
#> Item9_1-2 logit Item9 9 1-2 LCDM 1.6512037 0.27433883
#> Item10_0 logit Item10 10 0 LCDM -2.0087885 0.10431434
#> Item10_1 logit Item10 10 1 LCDM 1.7363525 0.18545437
#> Item10_2 logit Item10 10 2 LCDM 1.2912781 0.16233032
#> Item10_1-2 logit Item10 10 1-2 LCDM 1.1061509 0.25679840
#> Item11_0 logit Item11 11 0 LCDM -1.8747240 0.09181673
#> Item11_1 logit Item11 11 1 LCDM 2.3642124 0.11313816
#> Item12_0 logit Item12 12 0 LCDM -2.0744631 0.09901659
#> Item12_1 logit Item12 12 1 LCDM 2.5902837 0.11917466
#> Item13_0 logit Item13 13 0 LCDM -2.0577346 0.09837709
#> Item13_1 logit Item13 13 1 LCDM 2.5397540 0.11849136
#> Item14_0 logit Item14 14 0 LCDM -2.0583473 0.11117160
#> Item14_1 logit Item14 14 1 LCDM 1.6825024 0.17037831
#> Item14_2 logit Item14 14 2 LCDM 2.0351168 0.17411341
#> Item14_1-2 logit Item14 14 1-2 LCDM 0.3926852 0.24636899
#> Item15_0 logit Item15 15 0 LCDM -1.8192094 0.09282435
#> Item15_1 logit Item15 15 1 LCDM 0.7280376 0.30701391
#> Item15_2 logit Item15 15 2 LCDM 1.3301282 0.13248632
#> Item15_1-2 logit Item15 15 1-2 LCDM 1.9201833 0.35342728
#> Item16_0 logit Item16 16 0 LCDM -2.0919725 0.09846987
#> Item16_1 logit Item16 16 1 LCDM 2.6443799 0.11940543
#> Item17_0 logit Item17 17 0 LCDM -2.0909092 0.09842870
#> Item17_1 logit Item17 17 1 LCDM 2.7072410 0.11972119
#> Item18_0 logit Item18 18 0 LCDM -2.0697180 0.09762110
#> Item18_1 logit Item18 18 1 LCDM 2.4378212 0.11792010
#> Item19_0 logit Item19 19 0 LCDM -2.1233179 0.10295081
#> Item19_1 logit Item19 19 1 LCDM 2.4300883 0.26986268
#> Item19_2 logit Item19 19 2 LCDM 1.5012144 0.14252146
#> Item19_1-2 logit Item19 19 1-2 LCDM 0.2183443 0.31979702
#> Item20_0 logit Item20 20 0 LCDM -2.0188010 0.10471455
#> Item20_1 logit Item20 20 1 LCDM 1.7623339 0.18555052
#> Item20_2 logit Item20 20 2 LCDM 1.3839745 0.16132176
#> Item20_1-2 logit Item20 20 1-2 LCDM 0.8721858 0.25315557
#> Attr Est_Time1 SE_Time1 Est_Time2 SE_Time2
#> Item1_0 -1.9394905 0.1060563 -1.8913855 0.1178005
#> Item1_1 Att1 2.6786282 0.1875512 2.5621712 0.1613610
#> Item2_0 -2.0655097 0.1112725 -2.0770304 0.1263879
#> Item2_1 Att1 2.5448357 0.1858570 2.5068802 0.1654496
#> Item3_0 -2.0018560 0.1085837 -1.8568750 0.1163185
#> Item3_1 Att1 2.5647227 0.1855489 2.4612483 0.1595113
#> Item4_0 -2.0317093 0.1245540 -1.7710159 0.1370468
#> Item4_1 Att1 1.3941485 0.3583598 0.7317442 0.2921050
#> Item4_2 Att2 1.6181206 0.1967423 1.3361739 0.1982667
#> Item4_1-2 Att1-Att2 0.6447309 0.4466662 1.5514364 0.3677453
#> Item5_0 -2.1385808 0.1348117 -2.1983409 0.1703671
#> Item5_1 Att1 1.6948946 0.4603497 1.5857696 0.3710749
#> Item5_2 Att3 1.7263355 0.1915294 1.7958340 0.2138092
#> Item5_1-2 Att1-Att3 0.8998252 0.5433736 0.8328820 0.4288022
#> Item6_0 -1.8847639 0.1143494 -1.8489924 0.1296533
#> Item6_1 Att2 2.2751615 0.1599827 2.1121368 0.1582813
#> Item7_0 -1.8656031 0.1135484 -1.8483267 0.1296218
#> Item7_1 Att2 2.3256498 0.1599874 2.2191586 0.1586993
#> Item8_0 -1.9959266 0.1192080 -1.9998027 0.1371460
#> Item8_1 Att2 2.5411135 0.1648703 2.4596833 0.1653690
#> Item9_0 -2.2623561 0.1497788 -1.8209200 0.1538178
#> Item9_1 Att2 1.5535282 0.2771132 0.8618754 0.3065097
#> Item9_2 Att3 1.7528186 0.2271841 1.2660390 0.2274215
#> Item9_1-2 Att2-Att3 1.2804863 0.3943612 2.0802684 0.3907802
#> Item10_0 -2.0286783 0.1265802 -1.9657871 0.1841945
#> Item10_1 Att2 1.7437274 0.2088202 1.7660030 0.4399032
#> Item10_2 Att4 1.2483235 0.3044172 1.2643659 0.2309030
#> Item10_1-2 Att2-Att4 1.0831072 0.4170480 1.0926936 0.4856761
#> Item11_0 -1.9752677 0.1242769 -1.7428452 0.1364784
#> Item11_1 Att3 2.4809023 0.1619812 2.2213207 0.1611512
#> Item12_0 -2.1318363 0.1320243 -1.9967551 0.1497770
#> Item12_1 Att3 2.6869122 0.1684125 2.4859254 0.1726130
#> Item13_0 -1.9527347 0.1232259 -2.2245165 0.1637565
#> Item13_1 Att3 2.4425194 0.1610470 2.7012347 0.1848149
#> Item14_0 -1.9917488 0.1298363 -2.2259973 0.2156643
#> Item14_1 Att3 1.6523938 0.1950924 1.7176166 0.3534159
#> Item14_2 Att4 1.9845776 0.3290908 2.1988416 0.2624030
#> Item14_1-2 Att3-Att4 0.6946480 0.4378059 0.2661592 0.4060766
#> Item15_0 -1.9183836 0.1238926 -1.6806192 0.1404227
#> Item15_1 Att1 0.6719940 0.5303650 0.6677128 0.3827256
#> Item15_2 Att3 1.4251722 0.1849191 1.1952457 0.1916060
#> Item15_1-2 Att1-Att3 1.9256480 0.6009015 2.0062347 0.4440953
#> Item16_0 -2.0338403 0.1137357 -2.2521703 0.1971267
#> Item16_1 Att4 2.5942329 0.1749861 2.8018064 0.2121456
#> Item17_0 -2.0855375 0.1160334 -2.1047261 0.1858854
#> Item17_1 Att4 2.6092859 0.1760042 2.7539344 0.2021908
#> Item18_0 -2.0489588 0.1143995 -2.1238839 0.1872869
#> Item18_1 Att4 2.4731057 0.1737813 2.4725936 0.2023773
#> Item19_0 -2.1278381 0.1227006 -2.1126437 0.1892351
#> Item19_1 Att1 2.4743809 0.2953007 2.1626656 0.7048039
#> Item19_2 Att4 1.4714515 0.2351649 1.5015040 0.2204878
#> Item19_1-2 Att1-Att4 0.3732437 0.4582551 0.4183436 0.7317910
#> Item20_0 -2.0985278 0.1300515 -1.8574051 0.1769300
#> Item20_1 Att2 1.7255098 0.2118868 2.2725733 0.4429452
#> Item20_2 Att4 1.6061008 0.2950766 1.1845196 0.2247439
#> Item20_1-2 Att2-Att4 0.8391367 0.4120808 0.3726742 0.4850887
ipd$parameters
#> NULL
# }