ChenThissen1997() R function from [rpf]

Computes local dependence indices for all pairs of items

Item Factor Analysis makes two assumptions: (1) that the latent distribution is reasonably approximated by the multivariate Normal and (2) that items are conditionally independent. This test examines the second assumption. The presence of locally dependent items can inflate the precision of estimates causing a test to seem more accurate than it really is.


ChenThissen1997(
  grp,
  ...,
  data = NULL,
  inames = NULL,
  qwidth = 6,
  qpoints = 49,
  method = "pearson",
  .twotier = TRUE,
  .parallel = TRUE
)

Arguments

grp: a list containing the model and data. See the details section.
...: Not used. Forces remaining arguments to be specified by name.
data: data lifecycle::badge("deprecated")
inames: a subset of items to examine
qwidth: lifecycle::badge("deprecated")
qpoints: lifecycle::badge("deprecated")
method: method to use to calculate P values. The default is the Pearson X^2 statistic. Use "lr" for the similar likelihood ratio statistic.
.twotier: whether to enable the two-tier optimization
.parallel: whether to take advantage of multiple CPUs (default TRUE)

Returns

a list with raw, pval and detail. The pval matrix is a lower triangular matrix of log P values with the sign determined by relative association between the observed and expected tables (see ordinal.gamma)

Details

Statically significant entries suggest that the item pair has local dependence. Since log(.01)=-4.6, an absolute magitude of 5 is a reasonable cut-off. Positive entries indicate that the two item residuals are more correlated than expected. These items may share an unaccounted for latent dimension. Consider a redesign of the items or the use of testlets for scoring. Negative entries indicate that the two item residuals are less correlated than expected.

Format of a group

A model, or group within a model, is represented as a named list.

spec: list of response model objects
param: numeric matrix of item parameters
free: logical matrix of indicating which parameters are free (TRUE) or fixed (FALSE)
mean: numeric vector giving the mean of the latent distribution
cov: numeric matrix giving the covariance of the latent distribution
data: data.frame containing observed item responses, and optionally, weights and frequencies
score: factors scores with response patterns in rows
weightColumn: name of the data column containing the numeric row weights (optional)
freqColumn: name of the data column containing the integral row frequencies (optional)
qwidth: width of the quadrature expressed in Z units
qpoints: number of quadrature points
minItemsPerScore: minimum number of non-missing items when estimating factor scores

The param matrix stores items parameters by column. If a column has more rows than are required to fully specify a model then the extra rows are ignored. The order of the items in spec and order of columns in param are assumed to match. All items should have the same number of latent dimensions. Loadings on latent dimensions are given in the first few rows and can be named by setting rownames. Item names are assigned by param colnames.

Currently only a multivariate normal distribution is available, parameterized by the mean and cov. If mean and cov are not specified then a standard normal distribution is assumed. The quadrature consists of equally spaced points. For example, qwidth=2 and qpoints=5 would produce points -2, -1, 0, 1, and 2. The quadrature specification is part of the group and not passed as extra arguments for the sake of consistency. As currently implemented, OpenMx uses EAP scores to estimate latent distribution parameters. By default, the exact same EAP scores should be produced by EAPscores .

References

Chen, W.-H. & Thissen, D. (1997). Local dependence indexes for item pairs using Item Response Theory. Journal of Educational and Behavioral Statistics, 22(3), 265-289.

Thissen, D., Steinberg, L., & Mooney, J. A. (1989). Trace lines for testlets: A use of multiple-categorical-response models. Journal of Educational Measurement, 26 (3), 247--260.

Wainer, H. & Kiely, G. L. (1987). Item clusters and computerized adaptive testing: A case for testlets. Journal of Educational measurement, 24(3), 185--201.

ChenThissen1997 function