README.md
In woshikaqia/MIRTutils: MIRT Utility Package
MIRTutils package
Overview
This package provides a set of functions to calculate some commonly used
values when doing IRT analysis, especially with new item types such as
item bundles (testlets).
IRT model currently supported are 1-3 PL, GPCM, Rasch Testlet Model, and
a mix of these models. Values that can be computed include the
probability of correct response, item information, item score residuals,
person scores, person fit index, etc. It also provides a function for
multidimensional IRT data simulation.
In the context of the current package, test items can be either
standalone items (SA) or cluster items (Cluster). Both SA and
cluster items consist of assertions. An assertion is the smallest
item scoring unit in the test. You can think of assertion as the same as
a traditional item that is typically modeled by a unidimensional IRT
model. An SA item typically includes 1 to a handful of assertions,
whereas a cluster item typically includes 6 or more assertions. An SA
item is more like a small set of traditional items assuming local
dependence among assertions, whereas a cluster is essentially a testlet.
The IRT model used is a special model similar to a Rasch Testlet model
but allows for SA items to load only on the overall dimension. When
there are only SA items, the model reduces to a regular unidimensional
IRT model, and all the values computed in this package fits to the
traditional unidimensional IRT paradigm. When there are only cluster
items, the model reduces to a Rasch testlet model. Unlike the
unidimensional model where theta is usually estimated by the univariate
MLE, EAP or MAP, and the multidimensional model where theta is usually
estimated by the multivarite MLE or EAP, most of the values computed by
this package involving testlets is based on the marginal maximum
likelihood estimation (MMLE) of theta. MMLE is a hybrid of MLE and EAP,
where the nuisance dimension of a testlet (cluster) is first integrated
out, and the resulting marginal likelihood is then maximized to find the
theta estimate.
Installation
devtools::install_github("woshikaqia/MIRTutils")
Github Repo
https://github.com/woshikaqia/MIRTutils/
Examples
Simulate Data
Simulate 7 examniees’ item responses to a test consist of 20 SA items
(each with only 1 assertion; 17 of them are dichotomous and 3 are
polytomous) and 7 Cluster items (with a total of 81 assertions).
library(MIRTutils)
data(example_SA_parm)
data(example_Cluster_parm)
sigma <- diag(c(1, sqrt(unique(example_Cluster_parm$cluster_var))))
mu <- rep(0, nrow(sigma))
thetas <- MASS::mvrnorm(7,mu,sigma)
thetas[,1] <- seq(-3,3,1) #overall dimension theta values
itmDat <- sim_data(thetas = thetas, SA_parm = example_SA_parm, Cluster_parm = example_Cluster_parm)
library(dplyr)
as_tibble(example_SA_parm)
## # A tibble: 20 × 7
## a b1 b2 b3 g ItemID AssertionID
## <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr>
## 1 1 0.588 NA NA 0 SA_i1 SA_i1_AS1
## 2 1 0.423 NA NA 0 SA_i2 SA_i2_AS1
## 3 1 -1.06 NA NA 0 SA_i3 SA_i3_AS1
## 4 1 -0.156 NA NA 0 SA_i4 SA_i4_AS1
## 5 1 -0.416 NA NA 0 SA_i5 SA_i5_AS1
## 6 1 -0.135 NA NA 0 SA_i6 SA_i6_AS1
## 7 1 -1.14 NA NA 0 SA_i7 SA_i7_AS1
## 8 1 -0.573 NA NA 0 SA_i8 SA_i8_AS1
## 9 1 -0.859 NA NA 0 SA_i9 SA_i9_AS1
## 10 1 -0.505 NA NA 0 SA_i10 SA_i10_AS1
## 11 1 0.297 NA NA 0 SA_i11 SA_i11_AS1
## 12 1 0.404 NA NA 0 SA_i12 SA_i12_AS1
## 13 1 -0.386 NA NA 0 SA_i13 SA_i13_AS1
## 14 1 -0.540 NA NA 0 SA_i14 SA_i14_AS1
## 15 1 -1.45 NA NA 0 SA_i15 SA_i15_AS1
## 16 1 0.170 NA NA 0 SA_i16 SA_i16_AS1
## 17 1 0.0839 NA NA 0 SA_i17 SA_i17_AS1
## 18 1 -1 0 0.5 NA CR_i1 CR_i1_AS1
## 19 1.5 0 1 1.5 NA CR_i2 CR_i2_AS1
## 20 2 1 2 NA NA CR_i3 CR_i3_AS1
as_tibble(example_Cluster_parm)
## # A tibble: 81 × 6
## a b cluster_var position ItemID AssertionID
## <dbl> <dbl> <dbl> <dbl> <chr> <chr>
## 1 1 -1.21 0.371 1 CL_i1 CL_i1_AS1
## 2 1 -0.0959 0.371 1 CL_i1 CL_i1_AS2
## 3 1 0.0881 0.371 1 CL_i1 CL_i1_AS3
## 4 1 0.0188 0.371 1 CL_i1 CL_i1_AS4
## 5 1 0.248 0.371 1 CL_i1 CL_i1_AS5
## 6 1 -0.0965 0.371 1 CL_i1 CL_i1_AS6
## 7 1 -0.546 0.371 1 CL_i1 CL_i1_AS7
## 8 1 -0.727 0.371 1 CL_i1 CL_i1_AS8
## 9 1 0.787 0.371 1 CL_i1 CL_i1_AS9
## 10 1 -0.210 0.371 1 CL_i1 CL_i1_AS10
## # ℹ 71 more rows
unique(example_Cluster_parm$ItemID)
## [1] "CL_i1" "CL_i2" "CL_i3" "CL_i4" "CL_i5" "CL_i6" "CL_i7"
as_tibble(itmDat)
## # A tibble: 7 × 101
## SA_i1_AS1 SA_i2_AS1 SA_i3_AS1 SA_i4_AS1 SA_i5_AS1 SA_i6_AS1 SA_i7_AS1
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 0 0 0 0 0 0
## 2 0 0 1 0 1 0 0
## 3 0 0 0 1 0 0 1
## 4 1 1 1 1 0 1 1
## 5 1 0 1 1 1 1 1
## 6 1 1 1 1 1 1 1
## 7 1 1 1 1 1 1 1
## # ℹ 94 more variables: SA_i8_AS1 <dbl>, SA_i9_AS1 <dbl>, SA_i10_AS1 <dbl>,
## # SA_i11_AS1 <dbl>, SA_i12_AS1 <dbl>, SA_i13_AS1 <dbl>, SA_i14_AS1 <dbl>,
## # SA_i15_AS1 <dbl>, SA_i16_AS1 <dbl>, SA_i17_AS1 <dbl>, CR_i1_AS1 <dbl>,
## # CR_i2_AS1 <dbl>, CR_i3_AS1 <dbl>, CL_i1_AS1 <dbl>, CL_i1_AS2 <dbl>,
## # CL_i1_AS3 <dbl>, CL_i1_AS4 <dbl>, CL_i1_AS5 <dbl>, CL_i1_AS6 <dbl>,
## # CL_i1_AS7 <dbl>, CL_i1_AS8 <dbl>, CL_i1_AS9 <dbl>, CL_i1_AS10 <dbl>,
## # CL_i1_AS11 <dbl>, CL_i1_AS12 <dbl>, CL_i1_AS13 <dbl>, CL_i1_AS14 <dbl>, …
Scoring
…continued from the data simulation, this part scores the first
examinee. Note that the scoring function should be run one person at a
time. In general you can construct a loop to score all of the examinees,
or do parallel processing if you are dealing with extremely a large
dataset
SA_dat <- itmDat[,1:20]
Cluster_dat <- itmDat[,-1:-20]
# Score the first examinee
out_scoring <- scoring(SA_dat[1,], Cluster_dat[1,], example_SA_parm, example_Cluster_parm, n.nodes = 11, SE=TRUE)
(est_theta <- out_scoring$par) # estimated theta
## [1] -3.081139
as.vector(out_scoring$SE) # estimated standard error
## [1] 0.4445252
Person Fit
…continued from the data simulation and scoring, this part computes the
person fit statistics for the first examinee.
- For traditional test (i.e., standalone items only), this is lz*
described in Snijders (2001) or Sinharay (2016).
- For Cluster items, this is lzt* described in Lin et.al (2024), which
extends the lz* to the Rasch testlet model when theta is estimated by
MMLE.
You can specify one ore more alpha levels using the Alpha argument for
flagging.
# Compute person fit for the first examinee
rst <- person_fit(est_theta, SA_dat[1,], Cluster_dat[1,], example_SA_parm, example_Cluster_parm, Alpha=c(0.01,0.05))
rst
## theta raw ll exp_ll var_ll_org correction var_ll lz
## 1 -3.081139 14 -28.48542 -31.13043 46.16721 36.35753 9.809683 0.8445016
## test_info flag_0.01 flag_0.05
## 1 4.265769 0 0
Other Useful Values
You can use the utility() function to compute some useful values if
needed. The example below computes the expected item raw score and
item information.
# Compute person fit for the first examinee
data(example_SA_parm)
data(example_Cluster_parm)
theta <- seq(-3,3,1)
output <- utility(theta, example_SA_parm, example_Cluster_parm, what = c("escore","iteminfo"))
round(output$escore,3)
## theta SA_i1_AS1 SA_i2_AS1 SA_i3_AS1 SA_i4_AS1 SA_i5_AS1 SA_i6_AS1 SA_i7_AS1
## 1 -3 0.027 0.032 0.126 0.055 0.070 0.054 0.134
## 2 -2 0.070 0.081 0.282 0.137 0.170 0.134 0.296
## 3 -1 0.170 0.194 0.516 0.301 0.358 0.296 0.534
## 4 0 0.357 0.396 0.743 0.539 0.603 0.534 0.757
## 5 1 0.602 0.640 0.887 0.761 0.805 0.757 0.894
## 6 2 0.804 0.829 0.955 0.896 0.918 0.894 0.958
## 7 3 0.918 0.929 0.983 0.959 0.968 0.958 0.984
## SA_i8_AS1 SA_i9_AS1 SA_i10_AS1 SA_i11_AS1 SA_i12_AS1 SA_i13_AS1 SA_i14_AS1
## 1 0.081 0.105 0.076 0.036 0.032 0.068 0.079
## 2 0.194 0.242 0.183 0.091 0.083 0.166 0.188
## 3 0.395 0.465 0.379 0.215 0.197 0.351 0.387
## 4 0.639 0.702 0.624 0.426 0.400 0.595 0.632
## 5 0.828 0.865 0.818 0.669 0.645 0.800 0.823
## 6 0.929 0.946 0.924 0.846 0.831 0.916 0.927
## 7 0.973 0.979 0.971 0.937 0.931 0.967 0.972
## SA_i15_AS1 SA_i16_AS1 SA_i17_AS1 CR_i1_AS1 CR_i2_AS1 CR_i3_AS1 CL_i1 CL_i2
## 1 0.175 0.040 0.044 0.131 0.011 0.000 1.105 2.008
## 2 0.365 0.102 0.111 0.337 0.048 0.002 2.582 3.446
## 3 0.610 0.237 0.253 0.809 0.199 0.018 5.271 5.085
## 4 0.810 0.458 0.479 1.620 0.675 0.123 8.998 6.574
## 5 0.920 0.696 0.714 2.385 1.639 0.595 12.731 7.678
## 6 0.969 0.862 0.872 2.770 2.558 1.405 15.427 8.361
## 7 0.988 0.944 0.949 2.917 2.895 1.877 16.904 8.722
## CL_i3 CL_i4 CL_i5 CL_i6 CL_i7
## 1 2.887 0.369 1.401 0.705 4.796
## 2 4.677 0.877 2.754 1.507 6.571
## 3 6.689 1.820 4.773 2.732 8.160
## 4 8.601 3.182 7.294 4.148 9.366
## 5 10.177 4.714 9.895 5.387 10.152
## 6 11.336 6.088 12.077 6.224 10.598
## 7 12.103 7.059 13.552 6.671 10.824
round(output$iteminfo,4)
## theta SA_i1_AS1 SA_i2_AS1 SA_i3_AS1 SA_i4_AS1 SA_i5_AS1 SA_i6_AS1 SA_i7_AS1
## 1 -3 0.0262 0.0306 0.1102 0.0520 0.0653 0.0510 0.1162
## 2 -2 0.0650 0.0748 0.2023 0.1179 0.1413 0.1161 0.2086
## 3 -1 0.1409 0.1565 0.2497 0.2103 0.2299 0.2085 0.2488
## 4 0 0.2296 0.2392 0.1908 0.2485 0.2395 0.2489 0.1840
## 5 1 0.2397 0.2303 0.1000 0.1821 0.1571 0.1841 0.0945
## 6 2 0.1575 0.1419 0.0426 0.0930 0.0752 0.0946 0.0399
## 7 3 0.0755 0.0656 0.0166 0.0392 0.0308 0.0399 0.0155
## SA_i8_AS1 SA_i9_AS1 SA_i10_AS1 SA_i11_AS1 SA_i12_AS1 SA_i13_AS1 SA_i14_AS1
## 1 0.0745 0.0941 0.0704 0.0344 0.0311 0.0636 0.0725
## 2 0.1561 0.1835 0.1496 0.0830 0.0760 0.1385 0.1529
## 3 0.2389 0.2488 0.2353 0.1686 0.1583 0.2279 0.2372
## 4 0.2306 0.2090 0.2347 0.2446 0.2401 0.2409 0.2326
## 5 0.1423 0.1166 0.1487 0.2215 0.2291 0.1600 0.1454
## 6 0.0659 0.0513 0.0698 0.1303 0.1401 0.0771 0.0678
## 7 0.0266 0.0202 0.0283 0.0588 0.0646 0.0317 0.0274
## SA_i15_AS1 SA_i16_AS1 SA_i17_AS1 CR_i1_AS1 CR_i2_AS1 CR_i3_AS1 CL_i1 CL_i2
## 1 0.1442 0.0387 0.0419 0.1266 0.0247 0.0013 0.7032 0.5083
## 2 0.2319 0.0920 0.0984 0.3108 0.1062 0.0099 1.1321 0.5761
## 3 0.2379 0.1807 0.1889 0.6559 0.4025 0.0713 1.4725 0.5808
## 4 0.1541 0.2482 0.2496 0.8907 1.0817 0.4498 1.5988 0.5277
## 5 0.0732 0.2115 0.2041 0.5742 1.6803 1.4709 1.4745 0.4279
## 6 0.0299 0.1191 0.1118 0.2322 0.8992 1.4709 1.1328 0.3010
## 7 0.0114 0.0526 0.0487 0.0843 0.2325 0.4498 0.7012 0.1788
## CL_i3 CL_i4 CL_i5 CL_i6 CL_i7
## 1 0.3958 0.3106 0.4971 0.4624 0.3013
## 2 0.4296 0.6040 0.6373 0.7147 0.2991
## 3 0.4355 0.9235 0.7278 0.8775 0.2787
## 4 0.4191 1.1144 0.7640 0.8799 0.2415
## 5 0.3841 1.1173 0.7434 0.7283 0.1913
## 6 0.3316 0.9363 0.6588 0.4871 0.1358
## 7 0.2631 0.6274 0.5125 0.2611 0.0848
References
- Lin, Z., Jiang, T., Rijmen, F., & Van Wamelen, P. (2024). Asymptotically Correct Person Fit z-Statistics For the Rasch Testlet Model. Psychometrika, https://doi.org/10.1007/s11336-024-09997-y
- Sinharay, S. (2016). Asymptotically correct standardization of person-fit statistics beyond dichotomous items. Psychometrika, 81(4), 992-1013.
- Snijders, T. A. (2001). Asymptotic null distribution of person fit statistics with estimated person parameter. Psychometrika, 66, 331-342.
woshikaqia/MIRTutils documentation built on Aug. 21, 2024, 4:30 p.m.
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MIRTutils package
Overview
This package provides a set of functions to calculate some commonly used values when doing IRT analysis, especially with new item types such as item bundles (testlets).
IRT model currently supported are 1-3 PL, GPCM, Rasch Testlet Model, and a mix of these models. Values that can be computed include the probability of correct response, item information, item score residuals, person scores, person fit index, etc. It also provides a function for multidimensional IRT data simulation.
In the context of the current package, test items can be either standalone items (SA) or cluster items (Cluster). Both SA and cluster items consist of assertions. An assertion is the smallest item scoring unit in the test. You can think of assertion as the same as a traditional item that is typically modeled by a unidimensional IRT model. An SA item typically includes 1 to a handful of assertions, whereas a cluster item typically includes 6 or more assertions. An SA item is more like a small set of traditional items assuming local dependence among assertions, whereas a cluster is essentially a testlet.
The IRT model used is a special model similar to a Rasch Testlet model but allows for SA items to load only on the overall dimension. When there are only SA items, the model reduces to a regular unidimensional IRT model, and all the values computed in this package fits to the traditional unidimensional IRT paradigm. When there are only cluster items, the model reduces to a Rasch testlet model. Unlike the unidimensional model where theta is usually estimated by the univariate MLE, EAP or MAP, and the multidimensional model where theta is usually estimated by the multivarite MLE or EAP, most of the values computed by this package involving testlets is based on the marginal maximum likelihood estimation (MMLE) of theta. MMLE is a hybrid of MLE and EAP, where the nuisance dimension of a testlet (cluster) is first integrated out, and the resulting marginal likelihood is then maximized to find the theta estimate.
Installation
devtools::install_github("woshikaqia/MIRTutils")
Github Repo
https://github.com/woshikaqia/MIRTutils/
Examples
Simulate Data
Simulate 7 examniees’ item responses to a test consist of 20 SA items (each with only 1 assertion; 17 of them are dichotomous and 3 are polytomous) and 7 Cluster items (with a total of 81 assertions).
library(MIRTutils)
data(example_SA_parm)
data(example_Cluster_parm)
sigma <- diag(c(1, sqrt(unique(example_Cluster_parm$cluster_var))))
mu <- rep(0, nrow(sigma))
thetas <- MASS::mvrnorm(7,mu,sigma)
thetas[,1] <- seq(-3,3,1) #overall dimension theta values
itmDat <- sim_data(thetas = thetas, SA_parm = example_SA_parm, Cluster_parm = example_Cluster_parm)
library(dplyr)
as_tibble(example_SA_parm)
## # A tibble: 20 × 7
## a b1 b2 b3 g ItemID AssertionID
## <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr>
## 1 1 0.588 NA NA 0 SA_i1 SA_i1_AS1
## 2 1 0.423 NA NA 0 SA_i2 SA_i2_AS1
## 3 1 -1.06 NA NA 0 SA_i3 SA_i3_AS1
## 4 1 -0.156 NA NA 0 SA_i4 SA_i4_AS1
## 5 1 -0.416 NA NA 0 SA_i5 SA_i5_AS1
## 6 1 -0.135 NA NA 0 SA_i6 SA_i6_AS1
## 7 1 -1.14 NA NA 0 SA_i7 SA_i7_AS1
## 8 1 -0.573 NA NA 0 SA_i8 SA_i8_AS1
## 9 1 -0.859 NA NA 0 SA_i9 SA_i9_AS1
## 10 1 -0.505 NA NA 0 SA_i10 SA_i10_AS1
## 11 1 0.297 NA NA 0 SA_i11 SA_i11_AS1
## 12 1 0.404 NA NA 0 SA_i12 SA_i12_AS1
## 13 1 -0.386 NA NA 0 SA_i13 SA_i13_AS1
## 14 1 -0.540 NA NA 0 SA_i14 SA_i14_AS1
## 15 1 -1.45 NA NA 0 SA_i15 SA_i15_AS1
## 16 1 0.170 NA NA 0 SA_i16 SA_i16_AS1
## 17 1 0.0839 NA NA 0 SA_i17 SA_i17_AS1
## 18 1 -1 0 0.5 NA CR_i1 CR_i1_AS1
## 19 1.5 0 1 1.5 NA CR_i2 CR_i2_AS1
## 20 2 1 2 NA NA CR_i3 CR_i3_AS1
as_tibble(example_Cluster_parm)
## # A tibble: 81 × 6
## a b cluster_var position ItemID AssertionID
## <dbl> <dbl> <dbl> <dbl> <chr> <chr>
## 1 1 -1.21 0.371 1 CL_i1 CL_i1_AS1
## 2 1 -0.0959 0.371 1 CL_i1 CL_i1_AS2
## 3 1 0.0881 0.371 1 CL_i1 CL_i1_AS3
## 4 1 0.0188 0.371 1 CL_i1 CL_i1_AS4
## 5 1 0.248 0.371 1 CL_i1 CL_i1_AS5
## 6 1 -0.0965 0.371 1 CL_i1 CL_i1_AS6
## 7 1 -0.546 0.371 1 CL_i1 CL_i1_AS7
## 8 1 -0.727 0.371 1 CL_i1 CL_i1_AS8
## 9 1 0.787 0.371 1 CL_i1 CL_i1_AS9
## 10 1 -0.210 0.371 1 CL_i1 CL_i1_AS10
## # ℹ 71 more rows
unique(example_Cluster_parm$ItemID)
## [1] "CL_i1" "CL_i2" "CL_i3" "CL_i4" "CL_i5" "CL_i6" "CL_i7"
as_tibble(itmDat)
## # A tibble: 7 × 101
## SA_i1_AS1 SA_i2_AS1 SA_i3_AS1 SA_i4_AS1 SA_i5_AS1 SA_i6_AS1 SA_i7_AS1
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 0 0 0 0 0 0 0
## 2 0 0 1 0 1 0 0
## 3 0 0 0 1 0 0 1
## 4 1 1 1 1 0 1 1
## 5 1 0 1 1 1 1 1
## 6 1 1 1 1 1 1 1
## 7 1 1 1 1 1 1 1
## # ℹ 94 more variables: SA_i8_AS1 <dbl>, SA_i9_AS1 <dbl>, SA_i10_AS1 <dbl>,
## # SA_i11_AS1 <dbl>, SA_i12_AS1 <dbl>, SA_i13_AS1 <dbl>, SA_i14_AS1 <dbl>,
## # SA_i15_AS1 <dbl>, SA_i16_AS1 <dbl>, SA_i17_AS1 <dbl>, CR_i1_AS1 <dbl>,
## # CR_i2_AS1 <dbl>, CR_i3_AS1 <dbl>, CL_i1_AS1 <dbl>, CL_i1_AS2 <dbl>,
## # CL_i1_AS3 <dbl>, CL_i1_AS4 <dbl>, CL_i1_AS5 <dbl>, CL_i1_AS6 <dbl>,
## # CL_i1_AS7 <dbl>, CL_i1_AS8 <dbl>, CL_i1_AS9 <dbl>, CL_i1_AS10 <dbl>,
## # CL_i1_AS11 <dbl>, CL_i1_AS12 <dbl>, CL_i1_AS13 <dbl>, CL_i1_AS14 <dbl>, …
Scoring
…continued from the data simulation, this part scores the first
examinee. Note that the scoring function should be run one person at a
time. In general you can construct a loop to score all of the examinees,
or do parallel processing if you are dealing with extremely a large
dataset
SA_dat <- itmDat[,1:20]
Cluster_dat <- itmDat[,-1:-20]
# Score the first examinee
out_scoring <- scoring(SA_dat[1,], Cluster_dat[1,], example_SA_parm, example_Cluster_parm, n.nodes = 11, SE=TRUE)
(est_theta <- out_scoring$par) # estimated theta
## [1] -3.081139
as.vector(out_scoring$SE) # estimated standard error
## [1] 0.4445252
Person Fit
…continued from the data simulation and scoring, this part computes the person fit statistics for the first examinee.
- For traditional test (i.e., standalone items only), this is lz* described in Snijders (2001) or Sinharay (2016).
- For Cluster items, this is lzt* described in Lin et.al (2024), which extends the lz* to the Rasch testlet model when theta is estimated by MMLE.
You can specify one ore more alpha levels using the Alpha argument for
flagging.
# Compute person fit for the first examinee
rst <- person_fit(est_theta, SA_dat[1,], Cluster_dat[1,], example_SA_parm, example_Cluster_parm, Alpha=c(0.01,0.05))
rst
## theta raw ll exp_ll var_ll_org correction var_ll lz
## 1 -3.081139 14 -28.48542 -31.13043 46.16721 36.35753 9.809683 0.8445016
## test_info flag_0.01 flag_0.05
## 1 4.265769 0 0
Other Useful Values
You can use the utility() function to compute some useful values if
needed. The example below computes the expected item raw score and
item information.
# Compute person fit for the first examinee
data(example_SA_parm)
data(example_Cluster_parm)
theta <- seq(-3,3,1)
output <- utility(theta, example_SA_parm, example_Cluster_parm, what = c("escore","iteminfo"))
round(output$escore,3)
## theta SA_i1_AS1 SA_i2_AS1 SA_i3_AS1 SA_i4_AS1 SA_i5_AS1 SA_i6_AS1 SA_i7_AS1
## 1 -3 0.027 0.032 0.126 0.055 0.070 0.054 0.134
## 2 -2 0.070 0.081 0.282 0.137 0.170 0.134 0.296
## 3 -1 0.170 0.194 0.516 0.301 0.358 0.296 0.534
## 4 0 0.357 0.396 0.743 0.539 0.603 0.534 0.757
## 5 1 0.602 0.640 0.887 0.761 0.805 0.757 0.894
## 6 2 0.804 0.829 0.955 0.896 0.918 0.894 0.958
## 7 3 0.918 0.929 0.983 0.959 0.968 0.958 0.984
## SA_i8_AS1 SA_i9_AS1 SA_i10_AS1 SA_i11_AS1 SA_i12_AS1 SA_i13_AS1 SA_i14_AS1
## 1 0.081 0.105 0.076 0.036 0.032 0.068 0.079
## 2 0.194 0.242 0.183 0.091 0.083 0.166 0.188
## 3 0.395 0.465 0.379 0.215 0.197 0.351 0.387
## 4 0.639 0.702 0.624 0.426 0.400 0.595 0.632
## 5 0.828 0.865 0.818 0.669 0.645 0.800 0.823
## 6 0.929 0.946 0.924 0.846 0.831 0.916 0.927
## 7 0.973 0.979 0.971 0.937 0.931 0.967 0.972
## SA_i15_AS1 SA_i16_AS1 SA_i17_AS1 CR_i1_AS1 CR_i2_AS1 CR_i3_AS1 CL_i1 CL_i2
## 1 0.175 0.040 0.044 0.131 0.011 0.000 1.105 2.008
## 2 0.365 0.102 0.111 0.337 0.048 0.002 2.582 3.446
## 3 0.610 0.237 0.253 0.809 0.199 0.018 5.271 5.085
## 4 0.810 0.458 0.479 1.620 0.675 0.123 8.998 6.574
## 5 0.920 0.696 0.714 2.385 1.639 0.595 12.731 7.678
## 6 0.969 0.862 0.872 2.770 2.558 1.405 15.427 8.361
## 7 0.988 0.944 0.949 2.917 2.895 1.877 16.904 8.722
## CL_i3 CL_i4 CL_i5 CL_i6 CL_i7
## 1 2.887 0.369 1.401 0.705 4.796
## 2 4.677 0.877 2.754 1.507 6.571
## 3 6.689 1.820 4.773 2.732 8.160
## 4 8.601 3.182 7.294 4.148 9.366
## 5 10.177 4.714 9.895 5.387 10.152
## 6 11.336 6.088 12.077 6.224 10.598
## 7 12.103 7.059 13.552 6.671 10.824
round(output$iteminfo,4)
## theta SA_i1_AS1 SA_i2_AS1 SA_i3_AS1 SA_i4_AS1 SA_i5_AS1 SA_i6_AS1 SA_i7_AS1
## 1 -3 0.0262 0.0306 0.1102 0.0520 0.0653 0.0510 0.1162
## 2 -2 0.0650 0.0748 0.2023 0.1179 0.1413 0.1161 0.2086
## 3 -1 0.1409 0.1565 0.2497 0.2103 0.2299 0.2085 0.2488
## 4 0 0.2296 0.2392 0.1908 0.2485 0.2395 0.2489 0.1840
## 5 1 0.2397 0.2303 0.1000 0.1821 0.1571 0.1841 0.0945
## 6 2 0.1575 0.1419 0.0426 0.0930 0.0752 0.0946 0.0399
## 7 3 0.0755 0.0656 0.0166 0.0392 0.0308 0.0399 0.0155
## SA_i8_AS1 SA_i9_AS1 SA_i10_AS1 SA_i11_AS1 SA_i12_AS1 SA_i13_AS1 SA_i14_AS1
## 1 0.0745 0.0941 0.0704 0.0344 0.0311 0.0636 0.0725
## 2 0.1561 0.1835 0.1496 0.0830 0.0760 0.1385 0.1529
## 3 0.2389 0.2488 0.2353 0.1686 0.1583 0.2279 0.2372
## 4 0.2306 0.2090 0.2347 0.2446 0.2401 0.2409 0.2326
## 5 0.1423 0.1166 0.1487 0.2215 0.2291 0.1600 0.1454
## 6 0.0659 0.0513 0.0698 0.1303 0.1401 0.0771 0.0678
## 7 0.0266 0.0202 0.0283 0.0588 0.0646 0.0317 0.0274
## SA_i15_AS1 SA_i16_AS1 SA_i17_AS1 CR_i1_AS1 CR_i2_AS1 CR_i3_AS1 CL_i1 CL_i2
## 1 0.1442 0.0387 0.0419 0.1266 0.0247 0.0013 0.7032 0.5083
## 2 0.2319 0.0920 0.0984 0.3108 0.1062 0.0099 1.1321 0.5761
## 3 0.2379 0.1807 0.1889 0.6559 0.4025 0.0713 1.4725 0.5808
## 4 0.1541 0.2482 0.2496 0.8907 1.0817 0.4498 1.5988 0.5277
## 5 0.0732 0.2115 0.2041 0.5742 1.6803 1.4709 1.4745 0.4279
## 6 0.0299 0.1191 0.1118 0.2322 0.8992 1.4709 1.1328 0.3010
## 7 0.0114 0.0526 0.0487 0.0843 0.2325 0.4498 0.7012 0.1788
## CL_i3 CL_i4 CL_i5 CL_i6 CL_i7
## 1 0.3958 0.3106 0.4971 0.4624 0.3013
## 2 0.4296 0.6040 0.6373 0.7147 0.2991
## 3 0.4355 0.9235 0.7278 0.8775 0.2787
## 4 0.4191 1.1144 0.7640 0.8799 0.2415
## 5 0.3841 1.1173 0.7434 0.7283 0.1913
## 6 0.3316 0.9363 0.6588 0.4871 0.1358
## 7 0.2631 0.6274 0.5125 0.2611 0.0848
References
- Lin, Z., Jiang, T., Rijmen, F., & Van Wamelen, P. (2024). Asymptotically Correct Person Fit z-Statistics For the Rasch Testlet Model. Psychometrika, https://doi.org/10.1007/s11336-024-09997-y
- Sinharay, S. (2016). Asymptotically correct standardization of person-fit statistics beyond dichotomous items. Psychometrika, 81(4), 992-1013.
- Snijders, T. A. (2001). Asymptotic null distribution of person fit statistics with estimated person parameter. Psychometrika, 66, 331-342.
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