Implements the set of fixed-item calibration methods described by Kim (2006). The initial
calibrated model must be fitted via mirt, is currently limited to
unidimensional models only, and should only be utilized when the new set of responses
are obtained from a population with similar distributional characteristics in the latent traits.
For more flexible calibration of items, including a fixed-item calibration variant involving
anchor items for equating, see multipleGroup.
Usage
fixedCalib(
data,
model = 1,
old_mod,
PAU = "MWU",
NEMC = "MEM",
technical = list(),
...
)Arguments
- data
new data to be used for calibration. Note that to be consistent with the
modobject, observed responses/NA placeholders must be included to link the item names used in the originalmoddefinition (i.e.,extract.mirt(mod, what = 'itemnames'))- model
type of model to fit for the complete dataset (not that for the fixed items in
old_modthe factor loadings/constraints specified by the potentialmirt.modelspecification is not relevant)- old_mod
a model of class SingleGroupClass fitted using
mirt- PAU
prior ability update (PAU) approach. Supports none (
"NWU"), one ("OWU"), and many ("MWU")- NEMC
number of EM cycles (NEMC) to use for the to-be-estimated parameters. Supports one (
"OEM") and many ("MEM")- technical
list of technical estimation arguments (see
mirtfor details)- ...
additional arguments to pass to
mirt
References
Kim, S. (2006). A comparative study of IRT fixed parameter calibration methods. Journal of Educational Measurement, 4(43), 355-381.
Examples
# \donttest{
# single factor
set.seed(12345)
J <- 50
a <- matrix(abs(rnorm(J,1,.3)), ncol=1)
d <- matrix(rnorm(J,0,.7),ncol=1)
itemtype <- rep('2PL', nrow(a))
# calibration data theta ~ N(0,1)
N <- 3000
dataset1 <- simdata(a, d, N = N, itemtype=itemtype)
# new data (again, theta ~ N(0,1))
dataset2 <- simdata(a, d, N = 1000, itemtype=itemtype)
# last 40% of experimental items not given to calibration group
# (unobserved; hence removed)
dataset1 <- dataset1[,-c(J:(J*.6))]
head(dataset1)
#> Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9 Item_10
#> [1,] 0 0 0 0 0 0 1 1 1 0
#> [2,] 0 0 0 1 0 1 0 0 0 0
#> [3,] 0 1 0 1 1 1 1 1 1 1
#> [4,] 0 1 1 0 1 0 0 0 1 0
#> [5,] 1 0 1 1 1 0 1 0 1 0
#> [6,] 1 1 0 1 0 1 0 1 1 0
#> Item_11 Item_12 Item_13 Item_14 Item_15 Item_16 Item_17 Item_18 Item_19
#> [1,] 1 1 1 1 1 0 0 0 1
#> [2,] 0 0 1 0 0 0 1 1 0
#> [3,] 1 1 0 1 0 1 0 0 0
#> [4,] 0 0 1 1 0 0 1 1 0
#> [5,] 0 0 0 1 0 0 1 1 1
#> [6,] 1 0 1 1 0 0 1 0 1
#> Item_20 Item_21 Item_22 Item_23 Item_24 Item_25 Item_26 Item_27 Item_28
#> [1,] 0 0 0 0 1 0 0 1 0
#> [2,] 0 1 0 0 1 0 0 1 1
#> [3,] 0 1 0 1 1 1 1 0 0
#> [4,] 0 0 0 0 0 1 0 1 0
#> [5,] 0 1 1 1 1 1 1 1 1
#> [6,] 0 0 0 1 1 1 0 0 0
#> Item_29
#> [1,] 1
#> [2,] 1
#> [3,] 1
#> [4,] 1
#> [5,] 1
#> [6,] 1
#--------------------------------------
# calibrated model from dataset1 only
mod <- mirt(dataset1, model = 1)
#>
Iteration: 1, Log-Lik: -51018.249, Max-Change: 0.45064
Iteration: 2, Log-Lik: -50605.130, Max-Change: 0.15434
Iteration: 3, Log-Lik: -50572.394, Max-Change: 0.06416
Iteration: 4, Log-Lik: -50564.557, Max-Change: 0.03545
Iteration: 5, Log-Lik: -50561.298, Max-Change: 0.02162
Iteration: 6, Log-Lik: -50559.809, Max-Change: 0.01402
Iteration: 7, Log-Lik: -50558.612, Max-Change: 0.00415
Iteration: 8, Log-Lik: -50558.533, Max-Change: 0.00311
Iteration: 9, Log-Lik: -50558.493, Max-Change: 0.00204
Iteration: 10, Log-Lik: -50558.461, Max-Change: 0.00106
Iteration: 11, Log-Lik: -50558.456, Max-Change: 0.00079
Iteration: 12, Log-Lik: -50558.453, Max-Change: 0.00058
Iteration: 13, Log-Lik: -50558.450, Max-Change: 0.00015
Iteration: 14, Log-Lik: -50558.450, Max-Change: 0.00013
Iteration: 15, Log-Lik: -50558.450, Max-Change: 0.00012
Iteration: 16, Log-Lik: -50558.450, Max-Change: 0.00005
coef(mod, simplify=TRUE)
#> $items
#> a1 d g u
#> Item_1 1.196 -0.366 0 1
#> Item_2 1.218 1.345 0 1
#> Item_3 1.029 -0.017 0 1
#> Item_4 0.817 0.230 0 1
#> Item_5 1.148 -0.462 0 1
#> Item_6 0.473 0.157 0 1
#> Item_7 1.172 0.491 0 1
#> Item_8 0.882 0.599 0 1
#> Item_9 0.732 1.367 0 1
#> Item_10 0.737 -1.703 0 1
#> Item_11 0.988 0.057 0 1
#> Item_12 1.621 -0.888 0 1
#> Item_13 1.211 0.362 0 1
#> Item_14 1.261 1.101 0 1
#> Item_15 0.748 -0.319 0 1
#> Item_16 1.171 -1.247 0 1
#> Item_17 0.742 0.637 0 1
#> Item_18 0.925 1.128 0 1
#> Item_19 1.477 0.395 0 1
#> Item_20 1.037 -0.993 0 1
#> Item_21 1.136 0.068 0 1
#> Item_22 1.402 -0.513 0 1
#> Item_23 0.679 -0.684 0 1
#> Item_24 0.483 1.690 0 1
#> Item_25 0.501 1.048 0 1
#> Item_26 1.604 0.636 0 1
#> Item_27 0.833 0.559 0 1
#> Item_28 1.100 -0.493 0 1
#> Item_29 1.200 0.354 0 1
#>
#> $means
#> F1
#> 0
#>
#> $cov
#> F1
#> F1 1
#>
# No Prior Weights Updating and One EM Cycle (NWU-OEM)
NWU_OEM <- fixedCalib(dataset2, model=1, old_mod=mod, PAU='NWU', NEMC='OEM')
#>
Iteration: 1, Log-Lik: -86075.672, Max-Change: 2.54541
coef(NWU_OEM, simplify=TRUE)
#> $items
#> a1 d g u
#> Item_1 1.196 -0.366 0 1
#> Item_2 1.218 1.345 0 1
#> Item_3 1.029 -0.017 0 1
#> Item_4 0.817 0.230 0 1
#> Item_5 1.148 -0.462 0 1
#> Item_6 0.473 0.157 0 1
#> Item_7 1.172 0.491 0 1
#> Item_8 0.882 0.599 0 1
#> Item_9 0.732 1.367 0 1
#> Item_10 0.737 -1.703 0 1
#> Item_11 0.988 0.057 0 1
#> Item_12 1.621 -0.888 0 1
#> Item_13 1.211 0.362 0 1
#> Item_14 1.261 1.101 0 1
#> Item_15 0.748 -0.319 0 1
#> Item_16 1.171 -1.247 0 1
#> Item_17 0.742 0.637 0 1
#> Item_18 0.925 1.128 0 1
#> Item_19 1.477 0.395 0 1
#> Item_20 1.037 -0.993 0 1
#> Item_21 1.136 0.068 0 1
#> Item_22 1.402 -0.513 0 1
#> Item_23 0.679 -0.684 0 1
#> Item_24 0.483 1.690 0 1
#> Item_25 0.501 1.048 0 1
#> Item_26 1.604 0.636 0 1
#> Item_27 0.833 0.559 0 1
#> Item_28 1.100 -0.493 0 1
#> Item_29 1.200 0.354 0 1
#> Item_30 0.750 1.329 0 1
#> Item_31 1.093 1.235 0 1
#> Item_32 1.380 1.740 0 1
#> Item_33 1.112 0.441 0 1
#> Item_34 1.164 2.443 0 1
#> Item_35 1.054 1.361 0 1
#> Item_36 0.863 1.818 0 1
#> Item_37 0.717 0.865 0 1
#> Item_38 0.379 0.044 0 1
#> Item_39 1.180 1.336 0 1
#> Item_40 0.713 0.967 0 1
#> Item_41 0.865 0.150 0 1
#> Item_42 0.205 -0.581 0 1
#> Item_43 0.587 1.914 0 1
#> Item_44 0.977 0.509 0 1
#> Item_45 0.944 -0.151 0 1
#> Item_46 1.239 1.288 0 1
#> Item_47 0.547 0.176 0 1
#> Item_48 0.811 2.059 0 1
#> Item_49 0.841 0.169 0 1
#> Item_50 0.631 -0.103 0 1
#>
#> $means
#> F1
#> 0
#>
#> $cov
#> F1
#> F1 1
#>
data.frame(coef(NWU_OEM, simplify=TRUE)$items[,c('a1','d')],
pop_a1=a, pop_d=d)
#> a1 d pop_a1 pop_d
#> Item_1 1.1961890 -0.36582599 1.1756586 -0.37827025
#> Item_2 1.2180200 1.34513036 1.2128398 1.36338487
#> Item_3 1.0287076 -0.01749165 0.9672090 0.03751319
#> Item_4 0.8169838 0.22955350 0.8639508 0.24616399
#> Item_5 1.1477420 -0.46213650 1.1817662 -0.46968358
#> Item_6 0.4734409 0.15748181 0.4546132 0.19456759
#> Item_7 1.1723767 0.49084966 1.1890296 0.48381989
#> Item_8 0.8823964 0.59861143 0.9171448 0.57665673
#> Item_9 0.7320060 1.36669674 0.9147521 1.50154551
#> Item_10 0.7374958 -1.70288028 0.7242034 -1.64286078
#> Item_11 0.9877230 0.05684034 0.9651257 0.10471439
#> Item_12 1.6208445 -0.88830542 1.5451936 -0.93977204
#> Item_13 1.2113938 0.36247319 1.1111884 0.38731215
#> Item_14 1.2608594 1.10068854 1.1560649 1.11297399
#> Item_15 0.7483149 -0.31912299 0.7748404 -0.41081572
#> Item_16 1.1708992 -1.24683338 1.2450700 -1.28266411
#> Item_17 0.7422645 0.63674114 0.7340927 0.62169760
#> Item_18 0.9248296 1.12848731 0.9005267 1.11544193
#> Item_19 1.4767582 0.39539515 1.3362138 0.36179827
#> Item_20 1.0368814 -0.99330414 1.0896171 -0.90697018
#> Item_21 1.1357543 0.06752098 1.2338866 0.03823090
#> Item_22 1.4021119 -0.51282038 1.4367355 -0.54925456
#> Item_23 0.6786602 -0.68438097 0.8067015 -0.73454697
#> Item_24 0.4828002 1.68992778 0.5340588 1.63135837
#> Item_25 0.5011412 1.04812815 0.5206871 0.98189377
#> Item_26 1.6039924 0.63625385 1.5415293 0.65982060
#> Item_27 0.8328685 0.55938549 0.8555058 0.57838080
#> Item_28 1.1001393 -0.49299690 1.1861139 -0.56807834
#> Item_29 1.1996287 0.35417420 1.1836370 0.33337380
#> Item_30 0.7503191 1.32941502 0.9513067 0.71488089
#> Item_31 1.0934852 1.23450251 1.2435620 0.45176815
#> Item_32 1.3797225 1.73968930 1.6590501 0.73020049
#> Item_33 1.1122063 0.44125253 1.6147571 -0.21305838
#> Item_34 1.1635528 2.44296521 1.4897337 1.73397764
#> Item_35 1.0542788 1.36075678 1.0762814 0.67985447
#> Item_36 0.8625460 1.81754474 1.1473565 1.30696943
#> Item_37 0.7169594 0.86486730 0.9027740 0.47042973
#> Item_38 0.3789943 0.04394555 0.5013849 -0.21556737
#> Item_39 1.1801729 1.33626718 1.5303202 0.37556660
#> Item_40 0.7130625 0.96707202 1.0077403 0.57740905
#> Item_41 0.8654027 0.14975466 1.3385533 -0.67473104
#> Item_42 0.2054520 -0.58087717 0.2858926 -0.59855776
#> Item_43 0.5870526 1.91384494 0.6819203 1.32086286
#> Item_44 0.9773758 0.50918361 1.2811422 -0.27427356
#> Item_45 0.9438821 -0.15062731 1.2563355 -0.68644306
#> Item_46 1.2394331 1.28838231 1.4382188 0.48113247
#> Item_47 0.5466966 0.17590264 0.5760704 -0.35353046
#> Item_48 0.8112318 2.05870733 1.1702210 1.51040387
#> Item_49 0.8414788 0.16883149 1.1749563 -0.41985829
#> Item_50 0.6307197 -0.10310709 0.6079603 -0.48618269
plot(NWU_OEM, type = 'empiricalhist')
# No Prior Weights Updating and Multiple EM Cycles (NWU-MEM)
NWU_MEM <- fixedCalib(dataset2, model = 1, old_mod = mod, PAU = 'NWU')
#>
Iteration: 1, Log-Lik: -86075.672, Max-Change: 2.54541
Iteration: 2, Log-Lik: -79793.751, Max-Change: 0.81033
Iteration: 3, Log-Lik: -79268.889, Max-Change: 0.33784
Iteration: 4, Log-Lik: -79189.031, Max-Change: 0.11718
Iteration: 5, Log-Lik: -79179.523, Max-Change: 0.03455
Iteration: 6, Log-Lik: -79177.827, Max-Change: 0.01404
Iteration: 7, Log-Lik: -79177.564, Max-Change: 0.00859
Iteration: 8, Log-Lik: -79177.457, Max-Change: 0.00417
Iteration: 9, Log-Lik: -79177.433, Max-Change: 0.00419
Iteration: 10, Log-Lik: -79177.426, Max-Change: 0.00091
Iteration: 11, Log-Lik: -79177.426, Max-Change: 0.00077
Iteration: 12, Log-Lik: -79177.425, Max-Change: 0.00074
Iteration: 13, Log-Lik: -79177.425, Max-Change: 0.00019
Iteration: 14, Log-Lik: -79177.425, Max-Change: 0.00013
Iteration: 15, Log-Lik: -79177.425, Max-Change: 0.00009
coef(NWU_MEM, simplify=TRUE)
#> $items
#> a1 d g u
#> Item_1 1.196 -0.366 0 1
#> Item_2 1.218 1.345 0 1
#> Item_3 1.029 -0.017 0 1
#> Item_4 0.817 0.230 0 1
#> Item_5 1.148 -0.462 0 1
#> Item_6 0.473 0.157 0 1
#> Item_7 1.172 0.491 0 1
#> Item_8 0.882 0.599 0 1
#> Item_9 0.732 1.367 0 1
#> Item_10 0.737 -1.703 0 1
#> Item_11 0.988 0.057 0 1
#> Item_12 1.621 -0.888 0 1
#> Item_13 1.211 0.362 0 1
#> Item_14 1.261 1.101 0 1
#> Item_15 0.748 -0.319 0 1
#> Item_16 1.171 -1.247 0 1
#> Item_17 0.742 0.637 0 1
#> Item_18 0.925 1.128 0 1
#> Item_19 1.477 0.395 0 1
#> Item_20 1.037 -0.993 0 1
#> Item_21 1.136 0.068 0 1
#> Item_22 1.402 -0.513 0 1
#> Item_23 0.679 -0.684 0 1
#> Item_24 0.483 1.690 0 1
#> Item_25 0.501 1.048 0 1
#> Item_26 1.604 0.636 0 1
#> Item_27 0.833 0.559 0 1
#> Item_28 1.100 -0.493 0 1
#> Item_29 1.200 0.354 0 1
#> Item_30 0.976 0.738 0 1
#> Item_31 1.355 0.436 0 1
#> Item_32 1.896 0.751 0 1
#> Item_33 1.483 -0.136 0 1
#> Item_34 1.566 1.615 0 1
#> Item_35 1.108 0.689 0 1
#> Item_36 1.027 1.297 0 1
#> Item_37 0.950 0.485 0 1
#> Item_38 0.636 -0.358 0 1
#> Item_39 1.561 0.369 0 1
#> Item_40 1.002 0.572 0 1
#> Item_41 1.293 -0.537 0 1
#> Item_42 0.237 -0.569 0 1
#> Item_43 0.759 1.528 0 1
#> Item_44 1.267 -0.198 0 1
#> Item_45 1.179 -0.719 0 1
#> Item_46 1.484 0.418 0 1
#> Item_47 0.517 -0.350 0 1
#> Item_48 1.204 1.560 0 1
#> Item_49 1.178 -0.381 0 1
#> Item_50 0.611 -0.485 0 1
#>
#> $means
#> F1
#> 0
#>
#> $cov
#> F1
#> F1 1
#>
data.frame(coef(NWU_MEM, simplify=TRUE)$items[,c('a1','d')],
pop_a1=a, pop_d=d)
#> a1 d pop_a1 pop_d
#> Item_1 1.1961890 -0.36582599 1.1756586 -0.37827025
#> Item_2 1.2180200 1.34513036 1.2128398 1.36338487
#> Item_3 1.0287076 -0.01749165 0.9672090 0.03751319
#> Item_4 0.8169838 0.22955350 0.8639508 0.24616399
#> Item_5 1.1477420 -0.46213650 1.1817662 -0.46968358
#> Item_6 0.4734409 0.15748181 0.4546132 0.19456759
#> Item_7 1.1723767 0.49084966 1.1890296 0.48381989
#> Item_8 0.8823964 0.59861143 0.9171448 0.57665673
#> Item_9 0.7320060 1.36669674 0.9147521 1.50154551
#> Item_10 0.7374958 -1.70288028 0.7242034 -1.64286078
#> Item_11 0.9877230 0.05684034 0.9651257 0.10471439
#> Item_12 1.6208445 -0.88830542 1.5451936 -0.93977204
#> Item_13 1.2113938 0.36247319 1.1111884 0.38731215
#> Item_14 1.2608594 1.10068854 1.1560649 1.11297399
#> Item_15 0.7483149 -0.31912299 0.7748404 -0.41081572
#> Item_16 1.1708992 -1.24683338 1.2450700 -1.28266411
#> Item_17 0.7422645 0.63674114 0.7340927 0.62169760
#> Item_18 0.9248296 1.12848731 0.9005267 1.11544193
#> Item_19 1.4767582 0.39539515 1.3362138 0.36179827
#> Item_20 1.0368814 -0.99330414 1.0896171 -0.90697018
#> Item_21 1.1357543 0.06752098 1.2338866 0.03823090
#> Item_22 1.4021119 -0.51282038 1.4367355 -0.54925456
#> Item_23 0.6786602 -0.68438097 0.8067015 -0.73454697
#> Item_24 0.4828002 1.68992778 0.5340588 1.63135837
#> Item_25 0.5011412 1.04812815 0.5206871 0.98189377
#> Item_26 1.6039924 0.63625385 1.5415293 0.65982060
#> Item_27 0.8328685 0.55938549 0.8555058 0.57838080
#> Item_28 1.1001393 -0.49299690 1.1861139 -0.56807834
#> Item_29 1.1996287 0.35417420 1.1836370 0.33337380
#> Item_30 0.9762030 0.73762603 0.9513067 0.71488089
#> Item_31 1.3546278 0.43608060 1.2435620 0.45176815
#> Item_32 1.8963614 0.75072559 1.6590501 0.73020049
#> Item_33 1.4833684 -0.13615393 1.6147571 -0.21305838
#> Item_34 1.5661380 1.61503162 1.4897337 1.73397764
#> Item_35 1.1080231 0.68889209 1.0762814 0.67985447
#> Item_36 1.0265916 1.29656964 1.1473565 1.30696943
#> Item_37 0.9495227 0.48504809 0.9027740 0.47042973
#> Item_38 0.6357917 -0.35821345 0.5013849 -0.21556737
#> Item_39 1.5609002 0.36934080 1.5303202 0.37556660
#> Item_40 1.0017413 0.57214795 1.0077403 0.57740905
#> Item_41 1.2934463 -0.53663846 1.3385533 -0.67473104
#> Item_42 0.2365342 -0.56867576 0.2858926 -0.59855776
#> Item_43 0.7585749 1.52822491 0.6819203 1.32086286
#> Item_44 1.2665593 -0.19834384 1.2811422 -0.27427356
#> Item_45 1.1786531 -0.71904132 1.2563355 -0.68644306
#> Item_46 1.4839823 0.41813815 1.4382188 0.48113247
#> Item_47 0.5165255 -0.35006720 0.5760704 -0.35353046
#> Item_48 1.2040324 1.55971466 1.1702210 1.51040387
#> Item_49 1.1779999 -0.38145049 1.1749563 -0.41985829
#> Item_50 0.6105721 -0.48525352 0.6079603 -0.48618269
plot(NWU_MEM, type = 'empiricalhist')
# One Prior Weights Updating and One EM Cycle (OWU-OEM)
OWU_OEM <- fixedCalib(dataset2, model=1, old_mod=mod, PAU='OWU', NEMC="OEM")
#>
Iteration: 1, Log-Lik: -86077.528, Max-Change: 2.55772
coef(OWU_OEM, simplify=TRUE)
#> $items
#> a1 d g u
#> Item_1 1.196 -0.366 0 1
#> Item_2 1.218 1.345 0 1
#> Item_3 1.029 -0.017 0 1
#> Item_4 0.817 0.230 0 1
#> Item_5 1.148 -0.462 0 1
#> Item_6 0.473 0.157 0 1
#> Item_7 1.172 0.491 0 1
#> Item_8 0.882 0.599 0 1
#> Item_9 0.732 1.367 0 1
#> Item_10 0.737 -1.703 0 1
#> Item_11 0.988 0.057 0 1
#> Item_12 1.621 -0.888 0 1
#> Item_13 1.211 0.362 0 1
#> Item_14 1.261 1.101 0 1
#> Item_15 0.748 -0.319 0 1
#> Item_16 1.171 -1.247 0 1
#> Item_17 0.742 0.637 0 1
#> Item_18 0.925 1.128 0 1
#> Item_19 1.477 0.395 0 1
#> Item_20 1.037 -0.993 0 1
#> Item_21 1.136 0.068 0 1
#> Item_22 1.402 -0.513 0 1
#> Item_23 0.679 -0.684 0 1
#> Item_24 0.483 1.690 0 1
#> Item_25 0.501 1.048 0 1
#> Item_26 1.604 0.636 0 1
#> Item_27 0.833 0.559 0 1
#> Item_28 1.100 -0.493 0 1
#> Item_29 1.200 0.354 0 1
#> Item_30 0.734 1.342 0 1
#> Item_31 1.081 1.235 0 1
#> Item_32 1.354 1.740 0 1
#> Item_33 1.087 0.449 0 1
#> Item_34 1.180 2.469 0 1
#> Item_35 1.080 1.352 0 1
#> Item_36 0.867 1.826 0 1
#> Item_37 0.736 0.845 0 1
#> Item_38 0.407 0.018 0 1
#> Item_39 1.192 1.330 0 1
#> Item_40 0.694 0.970 0 1
#> Item_41 0.876 0.141 0 1
#> Item_42 0.207 -0.593 0 1
#> Item_43 0.608 1.915 0 1
#> Item_44 0.948 0.525 0 1
#> Item_45 0.918 -0.150 0 1
#> Item_46 1.246 1.287 0 1
#> Item_47 0.541 0.194 0 1
#> Item_48 0.824 2.052 0 1
#> Item_49 0.881 0.150 0 1
#> Item_50 0.643 -0.109 0 1
#>
#> $means
#> F1
#> 0
#>
#> $cov
#> F1
#> F1 1
#>
data.frame(coef(OWU_OEM, simplify=TRUE)$items[,c('a1','d')], pop_a1=a, pop_d=d)
#> a1 d pop_a1 pop_d
#> Item_1 1.1961890 -0.36582599 1.1756586 -0.37827025
#> Item_2 1.2180200 1.34513036 1.2128398 1.36338487
#> Item_3 1.0287076 -0.01749165 0.9672090 0.03751319
#> Item_4 0.8169838 0.22955350 0.8639508 0.24616399
#> Item_5 1.1477420 -0.46213650 1.1817662 -0.46968358
#> Item_6 0.4734409 0.15748181 0.4546132 0.19456759
#> Item_7 1.1723767 0.49084966 1.1890296 0.48381989
#> Item_8 0.8823964 0.59861143 0.9171448 0.57665673
#> Item_9 0.7320060 1.36669674 0.9147521 1.50154551
#> Item_10 0.7374958 -1.70288028 0.7242034 -1.64286078
#> Item_11 0.9877230 0.05684034 0.9651257 0.10471439
#> Item_12 1.6208445 -0.88830542 1.5451936 -0.93977204
#> Item_13 1.2113938 0.36247319 1.1111884 0.38731215
#> Item_14 1.2608594 1.10068854 1.1560649 1.11297399
#> Item_15 0.7483149 -0.31912299 0.7748404 -0.41081572
#> Item_16 1.1708992 -1.24683338 1.2450700 -1.28266411
#> Item_17 0.7422645 0.63674114 0.7340927 0.62169760
#> Item_18 0.9248296 1.12848731 0.9005267 1.11544193
#> Item_19 1.4767582 0.39539515 1.3362138 0.36179827
#> Item_20 1.0368814 -0.99330414 1.0896171 -0.90697018
#> Item_21 1.1357543 0.06752098 1.2338866 0.03823090
#> Item_22 1.4021119 -0.51282038 1.4367355 -0.54925456
#> Item_23 0.6786602 -0.68438097 0.8067015 -0.73454697
#> Item_24 0.4828002 1.68992778 0.5340588 1.63135837
#> Item_25 0.5011412 1.04812815 0.5206871 0.98189377
#> Item_26 1.6039924 0.63625385 1.5415293 0.65982060
#> Item_27 0.8328685 0.55938549 0.8555058 0.57838080
#> Item_28 1.1001393 -0.49299690 1.1861139 -0.56807834
#> Item_29 1.1996287 0.35417420 1.1836370 0.33337380
#> Item_30 0.7338596 1.34171621 0.9513067 0.71488089
#> Item_31 1.0810934 1.23518942 1.2435620 0.45176815
#> Item_32 1.3536031 1.74007904 1.6590501 0.73020049
#> Item_33 1.0871425 0.44941021 1.6147571 -0.21305838
#> Item_34 1.1800858 2.46871234 1.4897337 1.73397764
#> Item_35 1.0803263 1.35175673 1.0762814 0.67985447
#> Item_36 0.8666080 1.82586462 1.1473565 1.30696943
#> Item_37 0.7358795 0.84485396 0.9027740 0.47042973
#> Item_38 0.4070019 0.01833533 0.5013849 -0.21556737
#> Item_39 1.1921382 1.33027311 1.5303202 0.37556660
#> Item_40 0.6941284 0.97027712 1.0077403 0.57740905
#> Item_41 0.8759719 0.14117791 1.3385533 -0.67473104
#> Item_42 0.2070009 -0.59318726 0.2858926 -0.59855776
#> Item_43 0.6082669 1.91531663 0.6819203 1.32086286
#> Item_44 0.9481219 0.52535227 1.2811422 -0.27427356
#> Item_45 0.9181546 -0.15002032 1.2563355 -0.68644306
#> Item_46 1.2461867 1.28672335 1.4382188 0.48113247
#> Item_47 0.5414343 0.19387196 0.5760704 -0.35353046
#> Item_48 0.8238261 2.05156006 1.1702210 1.51040387
#> Item_49 0.8809591 0.15027203 1.1749563 -0.41985829
#> Item_50 0.6425456 -0.10887582 0.6079603 -0.48618269
plot(OWU_OEM, type = 'empiricalhist')
# One Prior Weights Updating and Multiple EM Cycles (OWU-MEM)
OWU_MEM <- fixedCalib(dataset2, model = 1, old_mod = mod, PAU = 'OWU')
#>
Iteration: 1, Log-Lik: -86077.528, Max-Change: 2.55772
Iteration: 2, Log-Lik: -79792.523, Max-Change: 0.91932
Iteration: 3, Log-Lik: -79264.477, Max-Change: 0.42507
Iteration: 4, Log-Lik: -79188.434, Max-Change: 0.10142
Iteration: 5, Log-Lik: -79179.330, Max-Change: 0.03534
Iteration: 6, Log-Lik: -79177.308, Max-Change: 0.01240
Iteration: 7, Log-Lik: -79177.022, Max-Change: 0.01078
Iteration: 8, Log-Lik: -79176.891, Max-Change: 0.00476
Iteration: 9, Log-Lik: -79176.866, Max-Change: 0.00214
Iteration: 10, Log-Lik: -79176.860, Max-Change: 0.00129
Iteration: 11, Log-Lik: -79176.856, Max-Change: 0.00650
Iteration: 12, Log-Lik: -79176.854, Max-Change: 0.00637
Iteration: 13, Log-Lik: -79176.852, Max-Change: 0.00070
Iteration: 14, Log-Lik: -79176.852, Max-Change: 0.00067
Iteration: 15, Log-Lik: -79176.852, Max-Change: 0.00064
Iteration: 16, Log-Lik: -79176.852, Max-Change: 0.00007
coef(OWU_MEM, simplify=TRUE)
#> $items
#> a1 d g u
#> Item_1 1.196 -0.366 0 1
#> Item_2 1.218 1.345 0 1
#> Item_3 1.029 -0.017 0 1
#> Item_4 0.817 0.230 0 1
#> Item_5 1.148 -0.462 0 1
#> Item_6 0.473 0.157 0 1
#> Item_7 1.172 0.491 0 1
#> Item_8 0.882 0.599 0 1
#> Item_9 0.732 1.367 0 1
#> Item_10 0.737 -1.703 0 1
#> Item_11 0.988 0.057 0 1
#> Item_12 1.621 -0.888 0 1
#> Item_13 1.211 0.362 0 1
#> Item_14 1.261 1.101 0 1
#> Item_15 0.748 -0.319 0 1
#> Item_16 1.171 -1.247 0 1
#> Item_17 0.742 0.637 0 1
#> Item_18 0.925 1.128 0 1
#> Item_19 1.477 0.395 0 1
#> Item_20 1.037 -0.993 0 1
#> Item_21 1.136 0.068 0 1
#> Item_22 1.402 -0.513 0 1
#> Item_23 0.679 -0.684 0 1
#> Item_24 0.483 1.690 0 1
#> Item_25 0.501 1.048 0 1
#> Item_26 1.604 0.636 0 1
#> Item_27 0.833 0.559 0 1
#> Item_28 1.100 -0.493 0 1
#> Item_29 1.200 0.354 0 1
#> Item_30 0.975 0.738 0 1
#> Item_31 1.353 0.436 0 1
#> Item_32 1.892 0.749 0 1
#> Item_33 1.482 -0.137 0 1
#> Item_34 1.563 1.614 0 1
#> Item_35 1.107 0.689 0 1
#> Item_36 1.026 1.297 0 1
#> Item_37 0.949 0.485 0 1
#> Item_38 0.637 -0.358 0 1
#> Item_39 1.559 0.369 0 1
#> Item_40 1.001 0.572 0 1
#> Item_41 1.294 -0.537 0 1
#> Item_42 0.237 -0.569 0 1
#> Item_43 0.758 1.528 0 1
#> Item_44 1.266 -0.199 0 1
#> Item_45 1.179 -0.719 0 1
#> Item_46 1.482 0.418 0 1
#> Item_47 0.517 -0.350 0 1
#> Item_48 1.203 1.560 0 1
#> Item_49 1.178 -0.382 0 1
#> Item_50 0.611 -0.485 0 1
#>
#> $means
#> F1
#> 0
#>
#> $cov
#> F1
#> F1 1
#>
data.frame(coef(OWU_MEM, simplify=TRUE)$items[,c('a1','d')],
pop_a1=a, pop_d=d)
#> a1 d pop_a1 pop_d
#> Item_1 1.1961890 -0.36582599 1.1756586 -0.37827025
#> Item_2 1.2180200 1.34513036 1.2128398 1.36338487
#> Item_3 1.0287076 -0.01749165 0.9672090 0.03751319
#> Item_4 0.8169838 0.22955350 0.8639508 0.24616399
#> Item_5 1.1477420 -0.46213650 1.1817662 -0.46968358
#> Item_6 0.4734409 0.15748181 0.4546132 0.19456759
#> Item_7 1.1723767 0.49084966 1.1890296 0.48381989
#> Item_8 0.8823964 0.59861143 0.9171448 0.57665673
#> Item_9 0.7320060 1.36669674 0.9147521 1.50154551
#> Item_10 0.7374958 -1.70288028 0.7242034 -1.64286078
#> Item_11 0.9877230 0.05684034 0.9651257 0.10471439
#> Item_12 1.6208445 -0.88830542 1.5451936 -0.93977204
#> Item_13 1.2113938 0.36247319 1.1111884 0.38731215
#> Item_14 1.2608594 1.10068854 1.1560649 1.11297399
#> Item_15 0.7483149 -0.31912299 0.7748404 -0.41081572
#> Item_16 1.1708992 -1.24683338 1.2450700 -1.28266411
#> Item_17 0.7422645 0.63674114 0.7340927 0.62169760
#> Item_18 0.9248296 1.12848731 0.9005267 1.11544193
#> Item_19 1.4767582 0.39539515 1.3362138 0.36179827
#> Item_20 1.0368814 -0.99330414 1.0896171 -0.90697018
#> Item_21 1.1357543 0.06752098 1.2338866 0.03823090
#> Item_22 1.4021119 -0.51282038 1.4367355 -0.54925456
#> Item_23 0.6786602 -0.68438097 0.8067015 -0.73454697
#> Item_24 0.4828002 1.68992778 0.5340588 1.63135837
#> Item_25 0.5011412 1.04812815 0.5206871 0.98189377
#> Item_26 1.6039924 0.63625385 1.5415293 0.65982060
#> Item_27 0.8328685 0.55938549 0.8555058 0.57838080
#> Item_28 1.1001393 -0.49299690 1.1861139 -0.56807834
#> Item_29 1.1996287 0.35417420 1.1836370 0.33337380
#> Item_30 0.9754835 0.73759996 0.9513067 0.71488089
#> Item_31 1.3529960 0.43565857 1.2435620 0.45176815
#> Item_32 1.8920655 0.74941926 1.6590501 0.73020049
#> Item_33 1.4823957 -0.13676561 1.6147571 -0.21305838
#> Item_34 1.5632963 1.61443582 1.4897337 1.73397764
#> Item_35 1.1070549 0.68876441 1.0762814 0.67985447
#> Item_36 1.0257494 1.29658002 1.1473565 1.30696943
#> Item_37 0.9487642 0.48500521 0.9027740 0.47042973
#> Item_38 0.6365371 -0.35814281 0.5013849 -0.21556737
#> Item_39 1.5587391 0.36866684 1.5303202 0.37556660
#> Item_40 1.0011701 0.57211468 1.0077403 0.57740905
#> Item_41 1.2936486 -0.53716279 1.3385533 -0.67473104
#> Item_42 0.2372635 -0.56862885 0.2858926 -0.59855776
#> Item_43 0.7581178 1.52829512 0.6819203 1.32086286
#> Item_44 1.2655570 -0.19867816 1.2811422 -0.27427356
#> Item_45 1.1789916 -0.71942555 1.2563355 -0.68644306
#> Item_46 1.4820218 0.41756426 1.4382188 0.48113247
#> Item_47 0.5174459 -0.34998852 0.5760704 -0.35353046
#> Item_48 1.2029294 1.55973508 1.1702210 1.51040387
#> Item_49 1.1780664 -0.38178278 1.1749563 -0.41985829
#> Item_50 0.6113326 -0.48518034 0.6079603 -0.48618269
plot(OWU_MEM, type = 'empiricalhist')
# Multiple Prior Weights Updating and Multiple EM Cycles (MWU-MEM)
MWU_MEM <- fixedCalib(dataset2, model = 1, old_mod = mod)
#>
Iteration: 1, Log-Lik: -86077.528, Max-Change: 2.55772
Iteration: 2, Log-Lik: -79814.110, Max-Change: 0.67910
Iteration: 3, Log-Lik: -79284.126, Max-Change: 0.31053
Iteration: 4, Log-Lik: -79193.135, Max-Change: 0.09811
Iteration: 5, Log-Lik: -79179.638, Max-Change: 0.04404
Iteration: 6, Log-Lik: -79176.503, Max-Change: 0.02529
Iteration: 7, Log-Lik: -79175.604, Max-Change: 0.01231
Iteration: 8, Log-Lik: -79175.209, Max-Change: 0.00629
Iteration: 9, Log-Lik: -79174.990, Max-Change: 0.00297
Iteration: 10, Log-Lik: -79174.844, Max-Change: 0.00121
Iteration: 11, Log-Lik: -79174.733, Max-Change: 0.00082
Iteration: 12, Log-Lik: -79174.641, Max-Change: 0.00054
Iteration: 13, Log-Lik: -79174.563, Max-Change: 0.00038
Iteration: 14, Log-Lik: -79174.495, Max-Change: 0.00032
Iteration: 15, Log-Lik: -79174.436, Max-Change: 0.00024
Iteration: 16, Log-Lik: -79174.382, Max-Change: 0.00017
Iteration: 17, Log-Lik: -79174.334, Max-Change: 0.00017
Iteration: 18, Log-Lik: -79174.290, Max-Change: 0.00015
Iteration: 19, Log-Lik: -79174.250, Max-Change: 0.00016
Iteration: 20, Log-Lik: -79174.212, Max-Change: 0.00013
Iteration: 21, Log-Lik: -79174.177, Max-Change: 0.00012
Iteration: 22, Log-Lik: -79174.144, Max-Change: 0.00010
coef(MWU_MEM, simplify=TRUE)
#> $items
#> a1 d g u
#> Item_1 1.196 -0.366 0 1
#> Item_2 1.218 1.345 0 1
#> Item_3 1.029 -0.017 0 1
#> Item_4 0.817 0.230 0 1
#> Item_5 1.148 -0.462 0 1
#> Item_6 0.473 0.157 0 1
#> Item_7 1.172 0.491 0 1
#> Item_8 0.882 0.599 0 1
#> Item_9 0.732 1.367 0 1
#> Item_10 0.737 -1.703 0 1
#> Item_11 0.988 0.057 0 1
#> Item_12 1.621 -0.888 0 1
#> Item_13 1.211 0.362 0 1
#> Item_14 1.261 1.101 0 1
#> Item_15 0.748 -0.319 0 1
#> Item_16 1.171 -1.247 0 1
#> Item_17 0.742 0.637 0 1
#> Item_18 0.925 1.128 0 1
#> Item_19 1.477 0.395 0 1
#> Item_20 1.037 -0.993 0 1
#> Item_21 1.136 0.068 0 1
#> Item_22 1.402 -0.513 0 1
#> Item_23 0.679 -0.684 0 1
#> Item_24 0.483 1.690 0 1
#> Item_25 0.501 1.048 0 1
#> Item_26 1.604 0.636 0 1
#> Item_27 0.833 0.559 0 1
#> Item_28 1.100 -0.493 0 1
#> Item_29 1.200 0.354 0 1
#> Item_30 0.979 0.736 0 1
#> Item_31 1.356 0.434 0 1
#> Item_32 1.901 0.748 0 1
#> Item_33 1.486 -0.138 0 1
#> Item_34 1.571 1.614 0 1
#> Item_35 1.110 0.687 0 1
#> Item_36 1.033 1.297 0 1
#> Item_37 0.952 0.484 0 1
#> Item_38 0.642 -0.359 0 1
#> Item_39 1.565 0.367 0 1
#> Item_40 1.006 0.571 0 1
#> Item_41 1.299 -0.539 0 1
#> Item_42 0.241 -0.569 0 1
#> Item_43 0.763 1.528 0 1
#> Item_44 1.269 -0.200 0 1
#> Item_45 1.180 -0.720 0 1
#> Item_46 1.488 0.416 0 1
#> Item_47 0.523 -0.351 0 1
#> Item_48 1.209 1.559 0 1
#> Item_49 1.182 -0.383 0 1
#> Item_50 0.616 -0.486 0 1
#>
#> $means
#> F1
#> 0
#>
#> $cov
#> F1
#> F1 1
#>
data.frame(coef(MWU_MEM, simplify=TRUE)$items[,c('a1','d')],
pop_a1=a, pop_d=d)
#> a1 d pop_a1 pop_d
#> Item_1 1.1961890 -0.36582599 1.1756586 -0.37827025
#> Item_2 1.2180200 1.34513036 1.2128398 1.36338487
#> Item_3 1.0287076 -0.01749165 0.9672090 0.03751319
#> Item_4 0.8169838 0.22955350 0.8639508 0.24616399
#> Item_5 1.1477420 -0.46213650 1.1817662 -0.46968358
#> Item_6 0.4734409 0.15748181 0.4546132 0.19456759
#> Item_7 1.1723767 0.49084966 1.1890296 0.48381989
#> Item_8 0.8823964 0.59861143 0.9171448 0.57665673
#> Item_9 0.7320060 1.36669674 0.9147521 1.50154551
#> Item_10 0.7374958 -1.70288028 0.7242034 -1.64286078
#> Item_11 0.9877230 0.05684034 0.9651257 0.10471439
#> Item_12 1.6208445 -0.88830542 1.5451936 -0.93977204
#> Item_13 1.2113938 0.36247319 1.1111884 0.38731215
#> Item_14 1.2608594 1.10068854 1.1560649 1.11297399
#> Item_15 0.7483149 -0.31912299 0.7748404 -0.41081572
#> Item_16 1.1708992 -1.24683338 1.2450700 -1.28266411
#> Item_17 0.7422645 0.63674114 0.7340927 0.62169760
#> Item_18 0.9248296 1.12848731 0.9005267 1.11544193
#> Item_19 1.4767582 0.39539515 1.3362138 0.36179827
#> Item_20 1.0368814 -0.99330414 1.0896171 -0.90697018
#> Item_21 1.1357543 0.06752098 1.2338866 0.03823090
#> Item_22 1.4021119 -0.51282038 1.4367355 -0.54925456
#> Item_23 0.6786602 -0.68438097 0.8067015 -0.73454697
#> Item_24 0.4828002 1.68992778 0.5340588 1.63135837
#> Item_25 0.5011412 1.04812815 0.5206871 0.98189377
#> Item_26 1.6039924 0.63625385 1.5415293 0.65982060
#> Item_27 0.8328685 0.55938549 0.8555058 0.57838080
#> Item_28 1.1001393 -0.49299690 1.1861139 -0.56807834
#> Item_29 1.1996287 0.35417420 1.1836370 0.33337380
#> Item_30 0.9791660 0.73649261 0.9513067 0.71488089
#> Item_31 1.3557620 0.43401149 1.2435620 0.45176815
#> Item_32 1.9007882 0.74806045 1.6590501 0.73020049
#> Item_33 1.4862529 -0.13819824 1.6147571 -0.21305838
#> Item_34 1.5713559 1.61388772 1.4897337 1.73397764
#> Item_35 1.1101719 0.68737052 1.0762814 0.67985447
#> Item_36 1.0330416 1.29655187 1.1473565 1.30696943
#> Item_37 0.9517934 0.48386436 0.9027740 0.47042973
#> Item_38 0.6415895 -0.35896158 0.5013849 -0.21556737
#> Item_39 1.5653049 0.36728263 1.5303202 0.37556660
#> Item_40 1.0055938 0.57108702 1.0077403 0.57740905
#> Item_41 1.2988445 -0.53887261 1.3385533 -0.67473104
#> Item_42 0.2407043 -0.56898111 0.2858926 -0.59855776
#> Item_43 0.7634191 1.52801497 0.6819203 1.32086286
#> Item_44 1.2688454 -0.20002553 1.2811422 -0.27427356
#> Item_45 1.1799250 -0.72019334 1.2563355 -0.68644306
#> Item_46 1.4880374 0.41618563 1.4382188 0.48113247
#> Item_47 0.5228163 -0.35071973 0.5760704 -0.35353046
#> Item_48 1.2091851 1.55916704 1.1702210 1.51040387
#> Item_49 1.1823034 -0.38320022 1.1749563 -0.41985829
#> Item_50 0.6156231 -0.48588671 0.6079603 -0.48618269
plot(MWU_MEM, type = 'empiricalhist')
# factor scores distribution check
fs <- fscores(MWU_MEM)
hist(fs)
c(mean_calib=mean(fs[1:N, ]), sd_calib=sd(fs[1:N, ]))
#> mean_calib sd_calib
#> -0.0001434688 0.9215504578
c(mean_exper=mean(fs[-c(1:N), ]), sd_exper=sd(fs[-c(1:N), ]))
#> mean_exper sd_exper
#> 0.03352674 0.93335579
############################
## Item length constraint example for each participant in the experimental
## items group. In this example, all participants were forced to have a test
## length of J=30, though the item pool had J=50 total items.
# new experimental data (relatively extreme, theta ~ N(.5,1.5))
dataset2 <- simdata(a, d, N = 1000, itemtype=itemtype,
mu=.5, sigma=matrix(1.5))
# Add missing values to each participant in new dataset where individuals
# were randomly administered 10 experimental items, subject to the constraint
# that each participant received a test with J=30 items.
dataset2 <- t(apply(dataset2, 1, function(x){
NA_precalib <- sample(1:30, 10)
NA_experimental <- sample(31:50, 10)
x[c(NA_precalib, NA_experimental)] <- NA
x
}))
head(dataset2)
#> Item_1 Item_2 Item_3 Item_4 Item_5 Item_6 Item_7 Item_8 Item_9 Item_10
#> [1,] NA 1 0 0 NA NA 0 NA 1 0
#> [2,] NA NA NA 1 1 1 NA 0 1 NA
#> [3,] NA NA 0 1 1 1 1 NA 1 0
#> [4,] NA 1 1 NA 0 NA 1 1 1 1
#> [5,] 1 1 1 1 NA NA 0 1 NA NA
#> [6,] 1 0 0 1 1 1 NA NA NA 0
#> Item_11 Item_12 Item_13 Item_14 Item_15 Item_16 Item_17 Item_18 Item_19
#> [1,] 1 0 NA 0 NA 0 0 1 0
#> [2,] 1 1 1 NA 0 0 1 NA 1
#> [3,] 1 1 0 1 1 1 NA NA NA
#> [4,] NA NA 1 NA 0 0 1 0 0
#> [5,] 1 NA 0 1 1 0 1 1 NA
#> [6,] 0 1 1 1 0 0 NA 1 NA
#> Item_20 Item_21 Item_22 Item_23 Item_24 Item_25 Item_26 Item_27 Item_28
#> [1,] 0 0 NA 0 1 NA 0 1 0
#> [2,] NA 0 1 NA 1 1 1 1 0
#> [3,] 1 1 NA 0 NA NA 1 NA 1
#> [4,] 1 1 1 NA NA 1 1 1 1
#> [5,] 1 NA 1 NA 1 NA NA 0 1
#> [6,] 1 1 0 0 0 NA NA NA 0
#> Item_29 Item_30 Item_31 Item_32 Item_33 Item_34 Item_35 Item_36 Item_37
#> [1,] NA NA 0 1 1 NA 0 NA 0
#> [2,] NA 1 1 NA NA 1 NA 1 1
#> [3,] 1 1 1 NA NA NA NA 1 NA
#> [4,] NA NA NA NA NA NA 0 NA 1
#> [5,] 1 1 NA 1 NA 1 1 NA NA
#> [6,] NA NA NA 1 NA NA 1 1 0
#> Item_38 Item_39 Item_40 Item_41 Item_42 Item_43 Item_44 Item_45 Item_46
#> [1,] 0 NA NA NA NA 1 0 NA 0
#> [2,] NA NA NA 1 NA 1 1 1 1
#> [3,] 1 NA NA NA 1 0 1 NA NA
#> [4,] 0 1 NA NA NA NA 1 1 0
#> [5,] NA 1 1 NA NA 1 NA NA 1
#> [6,] 1 NA NA NA NA 1 NA NA 1
#> Item_47 Item_48 Item_49 Item_50
#> [1,] NA NA 0 NA
#> [2,] NA 1 NA NA
#> [3,] 0 0 1 1
#> [4,] NA 1 0 1
#> [5,] NA 1 1 1
#> [6,] 0 1 NA 1
# check that all individuals had 30 items
all(rowSums(!is.na(dataset2)) == 30)
#> [1] TRUE
# Multiple Prior Weights Updating and Multiple EM Cycles (MWU-MEM)
MWU_MEM <- fixedCalib(dataset2, model = 1, old_mod = mod)
#>
Iteration: 1, Log-Lik: -72283.605, Max-Change: 3.24082
Iteration: 2, Log-Lik: -67005.537, Max-Change: 0.59290
Iteration: 3, Log-Lik: -66785.257, Max-Change: 0.19125
Iteration: 4, Log-Lik: -66755.474, Max-Change: 0.09878
Iteration: 5, Log-Lik: -66749.767, Max-Change: 0.04483
Iteration: 6, Log-Lik: -66748.297, Max-Change: 0.01797
Iteration: 7, Log-Lik: -66747.840, Max-Change: 0.01108
Iteration: 8, Log-Lik: -66747.599, Max-Change: 0.00459
Iteration: 9, Log-Lik: -66747.470, Max-Change: 0.00264
Iteration: 10, Log-Lik: -66747.385, Max-Change: 0.00082
Iteration: 11, Log-Lik: -66747.327, Max-Change: 0.00076
Iteration: 12, Log-Lik: -66747.284, Max-Change: 0.00072
Iteration: 13, Log-Lik: -66747.249, Max-Change: 0.00044
Iteration: 14, Log-Lik: -66747.220, Max-Change: 0.00026
Iteration: 15, Log-Lik: -66747.195, Max-Change: 0.00030
Iteration: 16, Log-Lik: -66747.174, Max-Change: 0.00031
Iteration: 17, Log-Lik: -66747.155, Max-Change: 0.00032
Iteration: 18, Log-Lik: -66747.137, Max-Change: 0.00031
Iteration: 19, Log-Lik: -66747.121, Max-Change: 0.00026
Iteration: 20, Log-Lik: -66747.106, Max-Change: 0.00013
Iteration: 21, Log-Lik: -66747.092, Max-Change: 0.00008
coef(MWU_MEM, simplify=TRUE)
#> $items
#> a1 d g u
#> Item_1 1.196 -0.366 0 1
#> Item_2 1.218 1.345 0 1
#> Item_3 1.029 -0.017 0 1
#> Item_4 0.817 0.230 0 1
#> Item_5 1.148 -0.462 0 1
#> Item_6 0.473 0.157 0 1
#> Item_7 1.172 0.491 0 1
#> Item_8 0.882 0.599 0 1
#> Item_9 0.732 1.367 0 1
#> Item_10 0.737 -1.703 0 1
#> Item_11 0.988 0.057 0 1
#> Item_12 1.621 -0.888 0 1
#> Item_13 1.211 0.362 0 1
#> Item_14 1.261 1.101 0 1
#> Item_15 0.748 -0.319 0 1
#> Item_16 1.171 -1.247 0 1
#> Item_17 0.742 0.637 0 1
#> Item_18 0.925 1.128 0 1
#> Item_19 1.477 0.395 0 1
#> Item_20 1.037 -0.993 0 1
#> Item_21 1.136 0.068 0 1
#> Item_22 1.402 -0.513 0 1
#> Item_23 0.679 -0.684 0 1
#> Item_24 0.483 1.690 0 1
#> Item_25 0.501 1.048 0 1
#> Item_26 1.604 0.636 0 1
#> Item_27 0.833 0.559 0 1
#> Item_28 1.100 -0.493 0 1
#> Item_29 1.200 0.354 0 1
#> Item_30 1.074 1.010 0 1
#> Item_31 1.416 0.729 0 1
#> Item_32 2.098 0.853 0 1
#> Item_33 1.622 0.025 0 1
#> Item_34 1.242 1.731 0 1
#> Item_35 1.127 0.868 0 1
#> Item_36 1.212 1.155 0 1
#> Item_37 1.022 0.621 0 1
#> Item_38 0.654 -0.203 0 1
#> Item_39 1.333 0.685 0 1
#> Item_40 0.939 0.678 0 1
#> Item_41 1.833 -0.565 0 1
#> Item_42 0.387 -0.631 0 1
#> Item_43 0.691 1.108 0 1
#> Item_44 1.232 -0.054 0 1
#> Item_45 1.105 -0.460 0 1
#> Item_46 1.401 0.694 0 1
#> Item_47 0.532 -0.290 0 1
#> Item_48 1.122 1.509 0 1
#> Item_49 1.158 -0.318 0 1
#> Item_50 0.692 -0.432 0 1
#>
#> $means
#> F1
#> 0
#>
#> $cov
#> F1
#> F1 1
#>
data.frame(coef(MWU_MEM, simplify=TRUE)$items[,c('a1','d')],
pop_a1=a, pop_d=d)
#> a1 d pop_a1 pop_d
#> Item_1 1.1961890 -0.36582599 1.1756586 -0.37827025
#> Item_2 1.2180200 1.34513036 1.2128398 1.36338487
#> Item_3 1.0287076 -0.01749165 0.9672090 0.03751319
#> Item_4 0.8169838 0.22955350 0.8639508 0.24616399
#> Item_5 1.1477420 -0.46213650 1.1817662 -0.46968358
#> Item_6 0.4734409 0.15748181 0.4546132 0.19456759
#> Item_7 1.1723767 0.49084966 1.1890296 0.48381989
#> Item_8 0.8823964 0.59861143 0.9171448 0.57665673
#> Item_9 0.7320060 1.36669674 0.9147521 1.50154551
#> Item_10 0.7374958 -1.70288028 0.7242034 -1.64286078
#> Item_11 0.9877230 0.05684034 0.9651257 0.10471439
#> Item_12 1.6208445 -0.88830542 1.5451936 -0.93977204
#> Item_13 1.2113938 0.36247319 1.1111884 0.38731215
#> Item_14 1.2608594 1.10068854 1.1560649 1.11297399
#> Item_15 0.7483149 -0.31912299 0.7748404 -0.41081572
#> Item_16 1.1708992 -1.24683338 1.2450700 -1.28266411
#> Item_17 0.7422645 0.63674114 0.7340927 0.62169760
#> Item_18 0.9248296 1.12848731 0.9005267 1.11544193
#> Item_19 1.4767582 0.39539515 1.3362138 0.36179827
#> Item_20 1.0368814 -0.99330414 1.0896171 -0.90697018
#> Item_21 1.1357543 0.06752098 1.2338866 0.03823090
#> Item_22 1.4021119 -0.51282038 1.4367355 -0.54925456
#> Item_23 0.6786602 -0.68438097 0.8067015 -0.73454697
#> Item_24 0.4828002 1.68992778 0.5340588 1.63135837
#> Item_25 0.5011412 1.04812815 0.5206871 0.98189377
#> Item_26 1.6039924 0.63625385 1.5415293 0.65982060
#> Item_27 0.8328685 0.55938549 0.8555058 0.57838080
#> Item_28 1.1001393 -0.49299690 1.1861139 -0.56807834
#> Item_29 1.1996287 0.35417420 1.1836370 0.33337380
#> Item_30 1.0736650 1.01026900 0.9513067 0.71488089
#> Item_31 1.4162584 0.72856155 1.2435620 0.45176815
#> Item_32 2.0975461 0.85255109 1.6590501 0.73020049
#> Item_33 1.6216973 0.02486148 1.6147571 -0.21305838
#> Item_34 1.2421629 1.73077613 1.4897337 1.73397764
#> Item_35 1.1268922 0.86756137 1.0762814 0.67985447
#> Item_36 1.2121379 1.15479360 1.1473565 1.30696943
#> Item_37 1.0218142 0.62136695 0.9027740 0.47042973
#> Item_38 0.6544987 -0.20307537 0.5013849 -0.21556737
#> Item_39 1.3326681 0.68465299 1.5303202 0.37556660
#> Item_40 0.9387813 0.67776738 1.0077403 0.57740905
#> Item_41 1.8326249 -0.56461189 1.3385533 -0.67473104
#> Item_42 0.3866839 -0.63085106 0.2858926 -0.59855776
#> Item_43 0.6911816 1.10845312 0.6819203 1.32086286
#> Item_44 1.2321139 -0.05383912 1.2811422 -0.27427356
#> Item_45 1.1045328 -0.45957575 1.2563355 -0.68644306
#> Item_46 1.4012118 0.69353524 1.4382188 0.48113247
#> Item_47 0.5324164 -0.28980316 0.5760704 -0.35353046
#> Item_48 1.1215187 1.50886830 1.1702210 1.51040387
#> Item_49 1.1583841 -0.31781501 1.1749563 -0.41985829
#> Item_50 0.6916807 -0.43180765 0.6079603 -0.48618269
plot(MWU_MEM, type = 'empiricalhist')
## factor scores check
fs <- fscores(MWU_MEM)
hist(fs)
c(mean_calib=mean(fs[1:N, ]), sd_calib=sd(fs[1:N, ]))
#> mean_calib sd_calib
#> -0.0001434688 0.9215504578
## shrinkage, but generally different from calibrated sample
c(mean_exper=mean(fs[-c(1:N), ]), sd_exper=sd(fs[-c(1:N), ]))
#> mean_exper sd_exper
#> 0.3531216 1.0349737
# }