lord_wing: Lord-Wingersky algorithm for computing the marginal...

In woshikaqia/MIRTutils: MIRT Utility Package

Lord-Wingersky algorithm for computing the marginal probability of the raw scores

Description

For N persons (theta values), this function makes use of the recursive algorithm by Lord & Wingersky (1984) and its extensions (Lin et.al, 2024) to compute the marginal probability of the raw scores for a cluster item (with J dichotomously scored assertions) modeled by the Rasch testlet model. The word "marginal" here means integrating out the nuisance dimension from the conditional likelihood of the cluster items.

Usage

lord_wing(
  cluster_var,
  a,
  b,
  theta,
  n.nodes = 21,
  return_additional = FALSE,
  Dv = 1
)

Arguments

cluster_var	a vector of of length J with repeated values of the cluster variance (e.g., rep(0.8, 9) for a 9-assertion cluster item). Alternatively, a scalar value of the cluster variance for the item.
a	a vector of length J for the a (slope) parameters
b	a vector of of length J for the b (difficulty) parameters
theta	a vector of length N for the thetas
n.nodes	number of nodes used when integrating out the specific dimension
return_additional	if TRUE, return a list containing the marginal probability as well as some additional by-product of the function such as the conditional probability tables. See Value section for details.
Dv	scaling factor for IRT model (usually 1 or 1.7)

Value

When return_additional = FALSE, returns the marginal probability of raw scores, which is a J+1 by N matrix, where J+1 is the number of possible raw scores

When return_additional = TRUE, returns a list containing

• prk: the marginal probability

• prob: N by n.nodes by J array containing the conditional probability of correct response for each theta at each node of the nuisance dimension for each assertion

• qrob: 1 - prob

• nodes and whts: nodes and weights used in the calculation.

Author(s)

Zhongtian Lin [e-mail]

References

Lord, F. M., & Wingersky, M. S. (1984). Comparison of IRT true-score and equipercentile observed-score "equatings". Applied Psychological Measurement, 8(4), 453-461.

Lin, Z., Jiang, T., Rijmen, F. et al. (2024). Asymptotically Correct Person Fit z-Statistics For the Rasch Testlet Model. Psychometrika, https://doi.org/10.1007/s11336-024-09997-y.

Examples

data(example_Cluster_parm)
# Compute on the first cluster, for 5 students
one_cluster_parm <- example_Cluster_parm[example_Cluster_parm$position == 1,]
rst <- lord_wing(one_cluster_parm$cluster_var , one_cluster_parm$a, one_cluster_parm$b,
theta <- seq(-2,2,1), return_additional = TRUE)

woshikaqia/MIRTutils documentation built on Aug. 21, 2024, 4:30 p.m.