check.ca {mokken}

Check conditional association to indentify local dependence.

Description

The function uses three special cases of conditional association (CA; Holland & Rosenbaum, 1986) to identify positive and negative local dependence in the monotone homogeneity model. Straat, Van der Ark, and Sijtsma (2016; also, see Sijtsma, Van der Ark, & Straat, 2015) described the procedure.

Usage

check.ca(X, Windex = FALSE, MINSIZE = 4, NWEIGHTOPTION = "noweight", 
            COVWEIGHTOPTION = "pnorm", MINGROUP = 4)

Arguments

X

Matrix of integers, missing values are not allowed

Windex

Boolean. Should output contain indices W1, W2, and W3?

MINSIZE

Minimum sample size of a rest-score group

NWEIGHTOPTION

Weight of sample size on each conditional covariance. Options: "noweight" (each covariance has weight 1, default in Straat et al., 2016) and "sqrt" (each covariance has weight sqrt(N_k(x)), this option was used in an older, decrepit, version of Straat et al., 2016)

COVWEIGHTOPTION

Weight of each conditional covariance on the computation of W1, W2, and W3. Options: "pnorm" (weight equals P[cov < 0], default in Straat et al., 2014) and "noweight" (if cov < 0, then weight = 1, and weight = 0, otherwise; this option was used in a previous version of Straat et al., 2014)

MINGROUP

Minimum sample size of the conditioning variable to compute a covariance. Since the term N-3 is used in the computation of the standard error, N = 4 is the default.

Value

list of three components:

(1) InScale (vector of booleans with length equal to the number of items): indicates whether an item is still in the scale.

(2) Index (list): Numerical values of indices W1, W2, and W3 (shown only if Windex = TRUE). Index has three subcomponents: W1, W2, and W3.

(3) Flagged (list): Boolean indicating whether a value of W1, W2, and W3 is flagged (1) or not (0) (shown only if Windex = TRUE) Index has three subcomponents: F1, F2, and F3, corresponding to the flagging of indices W1, W2, and W3, respectively.

Subcomponents correspond to the iteration. The first subcomponent refers to the situation with all items in the test, the second subcomponent refers to the sitution with the worst item deleted, the third subcomponent refers to the sitution with the two worst items deleted, etc.

Author(s)

L. A. van der Ark [e-mail] and J. H. Straat

References

Straat, J. H., Van der Ark, L. A., & Sijtsma, K. (2016). Using conditional association to identify locally Independent item sets. Methodology, 12, 117-123. doi:10.1027/1614-2241/a000115

Sijtsma, K., van der Ark, L. A., & Straat, J. H. (2015) Goodness of fit methods for nonparametric IRT models. In L. A. van der Ark, D. M. Bolt, W.-C. Wang, J. Douglas, & S.-M. Chow (Eds.), Quantitative psychology research: The 79th Annual Meeting of the Psychometric Society, Madison, Wisconsin, 2014. (pp. 109 - 120) Springer. doi:10.1007/978-3-319-19977-1_9

See Also

DS14, recode, twoway

Examples

  data(DS14)

  # Handle missing data nand recode negatively worded items
  X <- DS14[, 3 : 16]
  X <- twoway(X)
  X <- recode(X, c(1, 3))
  
  # Negative affectivity
  Na <- X[, c(1, 3, 6, 8, 10, 11, 14)] 
  
  # Social inhibition
  Si <- X[, c(2, 4, 5, 7, 9, 12, 13)] 
  
  check.ca(Na, TRUE)