yens_q3: Yen's Q_3 statistic for local item dependence

In measr: Bayesian Psychometric Measurement Using 'Stan'

Yen's Q₃ statistic for local item dependence

Description

Calculate the Q₃ statistic to evaluate the assumption of independent items.

Usage

yens_q3(x, ..., crit_value = 0.2, summary = NULL)

Arguments

x	A measrdcm object.
...	Unused.
crit_value	The critical value threshold for flagging the residual correlation of a given item pair. The default is 0.2, as described by Chen and Thissen (1997).
summary	A summary statistic to be returned. Must be one of "q3max" or "q3star" (see Details). If NULL (the default), no summary statistic is return, and all residual correlations are returned.

Details

Psychometric models assume that items are independent of each other, conditional on the latent trait. The Q₃ statistic (Yen, 1984) is used to evaluate this assumption. For each observed item response, we calculate the residual between the model predicted score and the observed score and then estimate correlations between the residuals across items. Each residual correlation is a Q₃ statistic.

Often, a critical values is used to flag a residual correlation above a given threshold (e.g., Chen & Thissen, 1997). Alternatively, we may use a summary statistic such as the maximum Q₃ statistic (Q_3,max; Christensen et al., 2017), or the mean-adjusted maximum Q₃ statistic (Q_3,*; Marais, 2013).

Value

If summary = NULL, a tibble with the residual correlation and flags for all item pairs. Otherwise, a numeric value representing the requested summary statistic.

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), 265-389. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3102/10769986022003265")}

Christensen, K. B., Makransky, G., & Horton, M. (2017). Critical values for Yen's Q3: Identification of local dependence in the Rasch model using residual correlations. Applied Psychological Measurement, 41(3), 178-194. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0146621616677520")}

Marais, I. (2013). Local dependence. In K. B. Christensen, S. Kreiner, & M. Mesbah (Eds.), Rasch models in health (pp. 111-130). Wiley.

Yen, W. M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8(2), 125-145. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/014662168400800201")}

Examples

model_spec <- dcm_specify(
  qmatrix = dcmdata::mdm_qmatrix,
  dentifier = "item"
)
model <- dcm_estimate(
  dcm_spec = model_spec,
  data = dcmdata::mdm_data,
  identifier = "respondent",
  method = "optim",
  seed = 63277
)

yens_q3(model)

measr documentation built on Jan. 14, 2026, 5:08 p.m.