person_fit: Person fit index computation

In woshikaqia/MIRTutils: MIRT Utility Package

Person fit index computation

Description

Calculates person fit statistics. Models currently supported are 1-3 PL, GPCM, Rasch Testlet, and a mix of these models.

• For traditional test (i.e., standalone items only), this is lz* described in Snijders (2001).

• 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, .

Usage

person_fit(
  theta,
  SA_dat = NULL,
  Cluster_dat = NULL,
  SA_parm = NULL,
  Cluster_parm = NULL,
  Dv = 1,
  Alpha = 0.05,
  n.nodes = 21
)

Arguments

theta	a scalar or a vector of examinee ability
SA_dat	For one examinee, a vector of response to standalone items. For more than one examinee, a matrix or dataframe of response to standalone items. One assertion per column. Column order must match row order in SA_parm. Use NA for missing responses
Cluster_dat	For one examinee, a vector of response to cluster items. For more than one examinee, a matrix or dataframe of response to cluster items. One assertion per column. Column order must match row order in Cluster_parm. Use NA for missing responses.
SA_parm	a matrix or dataframe of item parameters for standalone items, where columns are a (slope), b1, b2, ..., b_k (difficulty or step difficulty), g (guessing), ItemID, and AssertionID. Columns must follow the above order. See example_SA_parm for an example. Use ?example_SA_parm for detailed column descriptions
Cluster_parm	a matrix or dataframe of item parameters for cluster items, where columns are a (slope), b (difficulty), cluster variance, cluster position, ItemID, and AssertionID. Columns must follow the above order. See example_Cluster_parm for an example. Use ?example_Cluster_parm for detailed column descriptions
Dv	scaling factor for IRT model (usually 1 or 1.7)
Alpha	a numeric vector for one or more nominal type I error rates for flagging aberrant responses. For example, c(0.01,0.05)
n.nodes	number of nodes used when integrating out the nuisance dimension

Value

a one-row dataframe with the following columns:

• theta: theta score user supplied
  

• raw: raw score
  

• ll: observed data loglikelihood based on MMLE
  

• exp_ll: expected value of the data loglikelihood
  

• var_ll_org: variance of the data loglikelihood before correction
  

• correction: correction of the variance of the data loglikelihood
  

• var_ll: variance of the data loglikelihood after correction
  

• lz: lz* or lzt* person fit index
  

• flag_[Alpha]: one or more columns of flags for aberrant responses based on lz and the type I error rates specified in Alpha

Note

This function should be run for one examinee at a time. Use parallel processing for higher processing speed.

If the test does not have SA items or Cluster items, use default (NULL) for the corresponding data and parameter arguments

If one prefer, Rasch SA items can be treated as clusters. To do so, store SA item parameters in the Cluster_parm argument with 0 variances, and store all examinee responses in Cluster_dat

Author(s)

Zhongtian Lin [e-mail]

References

Snijders, T. A. (2001). Asymptotic null distribution of person fit statistics with estimated person parameter. Psychometrika, 66(3), 331-342.

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_SA_parm)
data(example_Cluster_parm)
sigma <- diag(c(1, sqrt(unique(example_Cluster_parm$cluster_var))))
mu <- rep(0, nrow(sigma))
thetas <- MASS::mvrnorm(7,mu,sigma)
thetas[,1] <- seq(-3,3,1) #overall dimension theta values
itmDat <- sim_data(thetas = thetas, SA_parm = example_SA_parm, Cluster_parm = example_Cluster_parm)
SA_dat <- itmDat[,1:20]
Cluster_dat <- itmDat[,-1:-20]
# Scoring for the first examinee
out_scoring <- scoring(SA_dat[1,], Cluster_dat[1,], example_SA_parm, example_Cluster_parm, n.nodes = 11, SE=TRUE)
est_theta <- out_scoring$par
# 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))

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