-
Notifications
You must be signed in to change notification settings - Fork 5
Multiple booklets PC items
tmatta edited this page Oct 17, 2017
·
3 revisions
We examined item parameter recovery under the following conditions: 1 (IRT model) x 2 (IRT R packages) x 3 (sample sizes) x 4 (test lengths) x 3 (test booklets).
- One IRT model was included: PC model
- Item parameters were randomly generated
- The bounds of the item difficulty parameter, b, are constrained to
b_bounds = (-2, 2)where -2 is the lowest generating value and 2 is the highest generating value.
- Two IRT R packages were evaluated:
TAM(version 2.4-9) andmirt(version 1.25) - Three sample sizes were used: 500, 1000, and 5000. Simulated samples were based on one ability level from distribution N(0, 1)
- Four test lengths were used: 40, 60, 80, and 100
- Three test booklets were used: 5, 10, and 15 booklets
- One hundred replications were used for each condition for the calibration.
- Summary of item parameter recovery:
-
TAMandmirtdemonstrated a similar level of accuracy - b1-parameter recovered well, with correlation ranging from 0.877 to 0.996, with bias ranging from -0.021 to -0.001, and with RMSE ranging from 0.064 to 0.382
- b2-parameter recovered well, with correlation ranging from 0.889 to 0.997, with bias ranging from -0.007 to 0.015, and with RMSE ranging from 0.063 to 0.383
- For b1- and b2-parameters, sample sizes of 5000 consistently produced the most accurate results
- For b1- and b2-parameters, four levels of test lengths performed very similarly
- For b1- and b2-parameters, , when number of booklets increased, recovery accuracy decreased slightly
-
# Load libraries
if(!require(lsasim)){
install.packages("lsasim")
library(lsasim) #version 1.0.1
}
if(!require(mirt)){
install.packages("mirt")
library(mirt) #version 1.25
}
if(!require(TAM)){
install.packages("TAM")
library(TAM) #version 2.4-9
}# Set up conditions
N.cond <- c(500, 1000, 5000) #number of sample sizes
I.cond <- c(40, 60, 80, 100) #number of items
K.cond <- c(5, 10, 15) #number of booklets
# Set up number of replications
reps <- 100
# Create space for outputs
results <- NULL#==============================================================================#
# START SIMULATION
#==============================================================================#
for (N in N.cond) { #sample size
for (I in I.cond) { #number of items
# generate item parameters for a PC model
set.seed(4366) # fix item parameters across replications
item_pool <- lsasim::item_gen(n_1pl = I,
thresholds = 2,
b_bounds = c(-2, 2))
for (K in K.cond) { #number of booklets
for (r in 1:reps) { #replication
set.seed(8088*(r+4))
# generate thetas
theta <- rnorm(N, mean=0, sd=1)
# assign items to blocks
blocks <- lsasim::block_design(n_blocks = K,
item_parameters = item_pool,
item_block_matrix = NULL)
#assign blocks to booklets
books <- lsasim::booklet_design(item_block_assignment =
blocks$block_assignment,
book_design = NULL)
#assign booklets to subjects
book_samp <- lsasim::booklet_sample(n_subj = N,
book_item_design = books,
book_prob = NULL)
# generate item responses
cog <- lsasim::response_gen(subject = book_samp$subject,
item = book_samp$item,
theta = theta,
b_par = item_pool$b,
d_par = list(item_pool$d1,
item_pool$d2))
# extract item responses (excluding "subject" column)
resp <- cog[, c(1:I)]
#------------------------------------------------------------------------------#
# Item calibration
#------------------------------------------------------------------------------#
# fit PC model using mirt package
mirt.mod <- NULL
mirt.mod <- mirt::mirt(resp, 1, itemtype = 'Rasch', verbose = F,
technical = list( NCYCLES = 500))
# fit PC model using TAM package
tam.mod <- NULL
tam.mod <- TAM::tam.mml(resp, irtmodel = "PCM2", control = list(maxiter = 200))
#------------------------------------------------------------------------------#
# Item parameter extraction
#------------------------------------------------------------------------------#
# extract b1, b2 in mirt package
mirt_b1 <- coef(mirt.mod, IRTpars = TRUE, simplify=TRUE)$items[,"b1"]
mirt_b2 <- coef(mirt.mod, IRTpars = TRUE, simplify=TRUE)$items[,"b2"]
# convert TAM output into PCM parametrization
tam_b1 <- tam.mod$item$AXsi_.Cat1
tam_b2 <- (tam.mod$item$AXsi_.Cat2) - (tam.mod$item$AXsi_.Cat1)
#------------------------------------------------------------------------------#
# Item parameter recovery
#------------------------------------------------------------------------------#
# summarize results
itempars <- data.frame(matrix(c(N, I, K, r), nrow=1))
colnames(itempars) <- c("N", "I", "K", "rep")
# retrieve generated item parameters
genPC.b1 <- item_pool$b + item_pool$d1
genPC.b2 <- item_pool$b + item_pool$d2
# calculate corr, bias, RMSE for item parameters in mirt pacakge
itempars$corr_mirt_b1 <- cor( genPC.b1, mirt_b1)
itempars$bias_mirt_b1 <- mean( mirt_b1 - genPC.b1 )
itempars$RMSE_mirt_b1 <- sqrt(mean( ( mirt_b1 - genPC.b1 )^2 ))
itempars$corr_mirt_b2 <- cor( genPC.b2, mirt_b2)
itempars$bias_mirt_b2 <- mean( mirt_b2 - genPC.b2 )
itempars$RMSE_mirt_b2 <- sqrt(mean( ( mirt_b2 - genPC.b2 )^2 ))
# calculate corr, bias, RMSE for item parameters in TAM pacakge
itempars$corr_tam_b1 <- cor( genPC.b1, tam_b1)
itempars$bias_tam_b1 <- mean( tam_b1 - genPC.b1 )
itempars$RMSE_tam_b1 <- sqrt(mean( ( tam_b1 - genPC.b1 )^2 ))
itempars$corr_tam_b2 <- cor( genPC.b2, tam_b2)
itempars$bias_tam_b2 <- mean( tam_b2 - genPC.b2 )
itempars$RMSE_tam_b2 <- sqrt(mean( ( tam_b2 - genPC.b2 )^2 ))
# combine results
results <- rbind(results, itempars)
}
}
}
}
- Correlation, bias, and RMSE for item parameter recovery in
mirtpackage
mirt_recovery <- aggregate(cbind(corr_mirt_b1, bias_mirt_b1, RMSE_mirt_b1,
corr_mirt_b2, bias_mirt_b2, RMSE_mirt_b2) ~ N + I + K,
data=results, mean, na.rm=TRUE)
names(mirt_recovery) <- c("N", "I", "K",
"corr_b1", "bias_b1", "RMSE_b1",
"corr_b2", "bias_b2", "RMSE_b2")
round(mirt_recovery, 3)## N I K corr_b1 bias_b1 RMSE_b1 corr_b2 bias_b2 RMSE_b2
## 1 500 40 5 0.961 -0.004 0.200 0.966 -0.006 0.203
## 2 1000 40 5 0.979 -0.007 0.144 0.983 -0.001 0.144
## 3 5000 40 5 0.996 -0.003 0.065 0.997 -0.003 0.063
## 4 500 60 5 0.958 -0.016 0.208 0.962 0.004 0.208
## 5 1000 60 5 0.979 -0.008 0.143 0.981 -0.006 0.144
## 6 5000 60 5 0.996 -0.002 0.064 0.996 -0.001 0.064
## 7 500 80 5 0.958 -0.009 0.205 0.965 0.003 0.203
## 8 1000 80 5 0.979 -0.010 0.143 0.981 -0.004 0.144
## 9 5000 80 5 0.996 -0.002 0.065 0.996 -0.003 0.064
## 10 500 100 5 0.960 -0.005 0.202 0.966 -0.003 0.206
## 11 1000 100 5 0.979 -0.011 0.144 0.982 -0.003 0.147
## 12 5000 100 5 0.996 -0.002 0.064 0.996 -0.003 0.065
## 13 500 40 10 0.920 -0.009 0.298 0.932 -0.007 0.301
## 14 1000 40 10 0.957 -0.014 0.210 0.964 -0.004 0.207
## 15 5000 40 10 0.991 -0.004 0.092 0.993 0.000 0.092
## 16 500 60 10 0.918 -0.014 0.299 0.927 0.006 0.296
## 17 1000 60 10 0.957 -0.011 0.208 0.961 -0.005 0.207
## 18 5000 60 10 0.991 -0.001 0.092 0.992 -0.003 0.092
## 19 500 80 10 0.920 -0.018 0.296 0.927 0.008 0.296
## 20 1000 80 10 0.957 -0.010 0.207 0.962 -0.001 0.207
## 21 5000 80 10 0.991 -0.002 0.091 0.992 -0.001 0.092
## 22 500 100 10 0.919 -0.013 0.298 0.930 0.002 0.303
## 23 1000 100 10 0.959 -0.009 0.204 0.965 -0.005 0.205
## 24 5000 100 10 0.991 -0.003 0.092 0.993 0.000 0.092
## 25 500 40 15 0.882 -0.006 0.373 0.898 0.000 0.374
## 26 1000 40 15 0.937 -0.021 0.257 0.946 0.009 0.259
## 27 5000 40 15 0.987 -0.003 0.113 0.989 -0.001 0.112
## 28 500 60 15 0.879 -0.011 0.377 0.893 0.007 0.375
## 29 1000 60 15 0.937 -0.013 0.255 0.944 0.001 0.257
## 30 5000 60 15 0.987 -0.004 0.110 0.988 -0.002 0.112
## 31 500 80 15 0.878 -0.012 0.378 0.889 0.007 0.383
## 32 1000 80 15 0.936 -0.013 0.253 0.942 0.000 0.260
## 33 5000 80 15 0.986 -0.003 0.114 0.988 -0.003 0.114
## 34 500 100 15 0.884 -0.019 0.368 0.899 0.015 0.373
## 35 1000 100 15 0.936 -0.012 0.259 0.946 -0.002 0.258
## 36 5000 100 15 0.987 -0.003 0.112 0.989 -0.002 0.113
- Correlation, bias, and RMSE for item parameter recovery in
TAMpackage
tam_recovery <- aggregate(cbind(corr_tam_b1, bias_tam_b1, RMSE_tam_b1,
corr_tam_b2, bias_tam_b2, RMSE_tam_b2) ~ N + I + K,
data=results, mean, na.rm=TRUE)
names(tam_recovery) <- c("N", "I", "K",
"corr_b1", "bias_b1", "RMSE_b1",
"corr_b2", "bias_b2", "RMSE_b2")
round(tam_recovery, 3)## N I K corr_b1 bias_b1 RMSE_b1 corr_b2 bias_b2 RMSE_b2
## 1 500 40 5 0.961 -0.004 0.200 0.966 -0.006 0.203
## 2 1000 40 5 0.979 -0.007 0.144 0.983 -0.001 0.144
## 3 5000 40 5 0.996 -0.003 0.065 0.997 -0.003 0.063
## 4 500 60 5 0.958 -0.016 0.208 0.962 0.004 0.209
## 5 1000 60 5 0.979 -0.008 0.143 0.981 -0.007 0.144
## 6 5000 60 5 0.996 -0.003 0.064 0.996 -0.002 0.064
## 7 500 80 5 0.958 -0.010 0.205 0.965 0.003 0.203
## 8 1000 80 5 0.979 -0.011 0.143 0.981 -0.003 0.144
## 9 5000 80 5 0.996 -0.002 0.065 0.996 -0.002 0.065
## 10 500 100 5 0.960 -0.010 0.208 0.966 -0.007 0.211
## 11 1000 100 5 0.979 -0.012 0.147 0.982 -0.003 0.149
## 12 5000 100 5 0.996 -0.001 0.065 0.996 0.000 0.066
## 13 500 40 10 0.920 -0.009 0.298 0.932 -0.007 0.301
## 14 1000 40 10 0.957 -0.014 0.210 0.964 -0.004 0.207
## 15 5000 40 10 0.991 -0.004 0.092 0.993 0.000 0.092
## 16 500 60 10 0.918 -0.014 0.299 0.927 0.005 0.296
## 17 1000 60 10 0.957 -0.011 0.208 0.961 -0.005 0.207
## 18 5000 60 10 0.991 -0.001 0.092 0.992 -0.003 0.092
## 19 500 80 10 0.920 -0.017 0.296 0.927 0.009 0.296
## 20 1000 80 10 0.957 -0.010 0.207 0.962 -0.001 0.207
## 21 5000 80 10 0.991 -0.002 0.091 0.992 -0.002 0.092
## 22 500 100 10 0.919 -0.013 0.298 0.930 0.002 0.303
## 23 1000 100 10 0.959 -0.010 0.204 0.965 -0.005 0.205
## 24 5000 100 10 0.991 -0.003 0.092 0.993 0.000 0.092
## 25 500 40 15 0.882 -0.006 0.373 0.898 0.000 0.374
## 26 1000 40 15 0.937 -0.021 0.257 0.946 0.009 0.259
## 27 5000 40 15 0.987 -0.003 0.113 0.989 -0.001 0.112
## 28 500 60 15 0.879 -0.011 0.377 0.893 0.007 0.375
## 29 1000 60 15 0.937 -0.013 0.255 0.944 0.001 0.257
## 30 5000 60 15 0.987 -0.004 0.110 0.988 -0.002 0.112
## 31 500 80 15 0.877 -0.012 0.382 0.889 0.008 0.383
## 32 1000 80 15 0.936 -0.013 0.253 0.942 0.000 0.260
## 33 5000 80 15 0.986 -0.003 0.114 0.988 -0.003 0.114
## 34 500 100 15 0.884 -0.019 0.368 0.899 0.015 0.373
## 35 1000 100 15 0.936 -0.012 0.259 0.946 -0.002 0.258
## 36 5000 100 15 0.987 -0.003 0.112 0.989 -0.002 0.113