| lazy.irt {lazy.irt} | R Documentation |
The following are the description of the item parameter data frame and
the item weight data frame, and the list of functions.
Japanese help file: (lazy.irt_JPH)
Structure of Item Parameter Data Frame
Each row of the Item Parameter Data Frame corresponds to an item.
The data frame must have the following variables.
name item name type item type B | B3 | Bn | Bn3 | G | Gn | P ncat # of categories p1 item parameter 1 (discrimination) p2 item parameter 2 (difficulty) p3 item parameter 3 (diffuculty or asymptote) :: ::
For type = "B" or "B2" or "B3" or "Bn" or "Bn3" items:
p1 discrimination \eqn{a_j}
p2 difficulty \eqn{b_j}
p3 lower asymptote \eqn{c_j} or 0
For type = "B" or "B2" or "B3" or "Bn" or "Bn3" items:
p1 discrimination \eqn{a_j}
p2 difficulty \eqn{b_j}
p3 lower asymptote \eqn{c_j} or 0
For type = "G" or "Gn" items:
p1 discrimination \eqn{a_j}
p2 threshold 1 \eqn{b_{j1}}
p3 threshold 2 \eqn{b_{j2}}
:: ::
p_ncat thresold ncat-1 \eqn{b_{j,[ncat-1]}}
For type = "P" items:
p1 discrimination \eqn{a_j}
p2 step 1 \qen{b_{j1}}
p3 step 2 \qen{b_{j2}}
:: ::
p_ncat step ncat-1 \eqn{b_{j,[ncat-1]}}
For type = "PN" items:
p1 slope \eqn{a_j}
p2 intercept 1 \eqn{b_{j1}}
p3 intercept 2 \eqn{b_{j2}}
:: ::
p_ncat intercept ncat-1 \eqn{b_{j,[ncat-1]}}
For type = "N" items:
p1through p_(ncat[j]-1) slope parameters
p_ncat[j] through p_2*(ncat[j]-1) intercept parameters
Binary items have three parameters, namely, discrimination, difficulty
and asymptote which is set equal to 0 for B or Bn items.
Ordered polytomous items (P, G, Gn) have ncat[j] parameters, and,
Nomimal Response itms (N) have 2*(ncat[j]-1) parameters.
See the test data section below.
Structure of Item Weight Data Frame
Each row of the Item Weight Data Frame corresponds to an item.
The data frame must have the following variables.
name item name type item type B | B3 | Bn | Bn3 | G | Gn | P ncat # of categories w weight to the item v0 category weight 0 p1 category weight 1 p2 category weight 2 :: ::
See the test data section below.
uIRT: Item Parameter Estimation of Unidimensional IRT
est_theta: Estimation of Theta
cala: Calibration of Independently Estimated Sets of Item Parameters by Minimizing the LS Criterion Defined in terms of Parameter Values
calr: Calibration of Independently Estimated Sets of Item Parameters
by Minimizing the LS Criterion Defined in terms of Probability Values
tseq: IRT True Score Equating
oseq: IRT Observed Score Equating
coseq: Classical Observed Score Equating
ordinal_reg: Oridinal Regression (used in the m-step of uIRT.)
smn: Parameter Estimation of Parametric (Normal pdf) Scored Multinomial Distributions
invtrf: The inverse function of trf (used in tseq.)
irf: Calculation of Item Response Function
icrfB: Calculation of Item Response Function of Binary Logistic items
icrfG: Calculation of Item Response Function of Graded Response items
icrfN: Calculation of Item Response Function of Nominal items (N.A.)
icrfP: Calculation of Item Response Function of Partial Credit items
icrfPN: Calculation of Item Response Function of Partial Credit items in Nominal Model Format
icrfPN0: Calculation of Partial Credit ICRF in Nominal format
dirf: Calculation of Derivative of Item Response Function
dicrfB: Calculation of the Derivative of Item Response Function of Binary Logistic Items
dicrfG: Calculation of the Derivative of Item Response Function of Graded Response Items
dicrfN: Calculation of the Derivative of Item Response Function of Nominal Items (N.A.)
dicrfP: Calculation of the Derivative of Item Response Function of Partial Credit Items
dicrfPN: Calculation of the Derivative of Item Response Function of Partial Credit Items in Nominal Format
dicrfPN0: Calculation of the Derivative of
Partial Credit ICRF in Nominal format
dicrf_num: Numerical Derivative of Item Response Function
using JacobianMat
dirf_p: Calculation of the Derivative of Item Response Function with respect to Item Parameters
obscore: Calculation of Observed Score Distribution and Posterior Distribution of Theta with Various Information Functions
obscore_s: Calculation of Observed Score Distribution
(simple version of obscore.)
sumsmnw: Distribution of the Weighted Sum of Several Independent Scored Multinomial Distributions
sumsmnw12: Distribution of the Weighted Sum of
Two Independent Scored Multinomial Distributions
rel_irt: Calculation of Test Reliability and Average SEM under IRT model
iif: Calculation of Information Functions
info_func: Calculation of Various Information Functions
graded_info: Calculation of the Information Function associated with the Graded Observed Score.
flatten_SEM: Find the Transformation of the Observed Score such that the Resulting Score has a Flat SEM almost everywhere.
flatten_SEM_theta: Find the Transformation of
the Thetahat Based Observed Score
such that the Resulting Score has a Flat SEM almost everywhere.
GOptWeight Estimation of the Globally Optimal Item Category Weights
fitG2P: Approximate Conversion of Partial Credit Items to Graded Response Items Using Logit Transformation
fitP2G: Approximate Conversion of Graded Response Items to Partial Credit Items Using Logit Transformation
conv2G: Conversion to Logistic Graded Response Model
conv2Gn: Conversion to Normal Graded Response Model
conv2P: Conversion to Partial Credit Model
conv2Bc: Conversion to 2PLM with fixed c
conv2Bnc: Conversion to 2PNM with fixed c
read.param: Reading Parameter File
read.weight: Reading Weight File
read_blg_par: Read Bilog .par file.
create_weight_df: Creation of Weight Data Frame
find_minmax_score: Find the min and max score from Weight Data Frame
checkparam2: Checking Parameter Data Frame (New Version)
gendataIRT: Generation of Simulated Item Response Data
find_mode: Find the Mode of icrf
find_intersection: Find the Intersection of icrfs
gen_icrfnames: Generate the row names of vec(icrf)
graded_prob; Calculation of Probability Contents
associated with Graded Score
convP2N: Convert Standard Partial Credit Item Parameters (step parameters) to in Nominal Format
convP2PN: Convert Standard Partial Credit Item Parameters (step parameters) to in Nominal Format Standard Format to Partial Credit Parameters in Nominal Format
convPN2P: Convert Partial Credit Item Parameters in Nominal Format to Standard Format (step parameters)
paramA1: Set of All Types of Items # 1. (10 items)
paramB1: Binary Item Parameter Data Frame # 1. (18 2PLM items)
paramB2: Binary Item Parameter Data Frame # 2.
(18 3PLM items)
paramS1: Small Item Parameter Data Frame # 1. (3 mixed type items)
paramS2: Small Item Parameter Data Frame # 2. (8 mixed type items)
paramS3: Small Item Parameter Data Frame # 2.
(20 mixed type items)
weightA1: Item Weight Data Frame for paramA1.
Natural category weight.
weightB1: Item Weight Data Frame for paramB1 or paramB2 1. Natural weight.
weightB11: Item Weight Data Frame for paramB1 or paramB2 2. Large weight for difficult items.
weightB12: Item Weight Data Frame for paramB1 or paramB2 3. Large weight for easy items.
weightB13: Item Weight Data Frame for paramB1 or paramB2 4. Large weight for high discriminative items.
weightB14: Item Weight Data Frame for
paramB1 or paramB2 5. Large weight for low discriminative items.
weightS1: Small Item Weight Data Frame # 1 To be used in conjunction with paramS1.
weightS11: Small Item Weight Data Frame # 2. To be used in conjunction with paramS1.
weightS12: Small Item Weight Data Frame # 3. To be used in conjunction with paramS1.
weightS2: Small Item Weight Data Frame # 4. To be used in conjunction with paramS2.
weightS21: Small Item Weight Data Frame # 5. To be used in conjunction with paramS2.
weightS22: Small Item Weight Data Frame # 6. To be used in conjunction with paramS2.
weightS3: Small Item Weight Data Frame # 7.
To be used in conjunction with paramS3.
paramCal1: Small Item Parameter Data Frame for Testing cala and calr #1.
paramCal2: Small Item Parameter Data Frame for Testing cala and calr #2.
uLRT: Item Parameter Estimation of Unidimensional LRT
with strict monotonicity restrictions.
est_rank: Estmation of LRT latent rank for each person.
fitI2L: Approxiamte Conversion of LRT model to 2PLM IRT model
fitI2L_ls: LS Conversion of LRT model to 2PLM IRT model