GDINA (version 1.4.2)

designmatrix: Design matrix for parameter transformation

Description

This function calculates the design matrix \(M_j\) in de la Torre (2011), which can be useful for parameter transformation between probability of success and delta.

Usage

designmatrix(Kj, model = "GDINA")

Arguments

Kj

the number of attributes for item j

model

the model fitted to item j; it can be "GDINA","DINA","DINO","ACDM","LLM",or "RRUM". The default is "GDINA".

Value

a design matrix (Mj) which plays a critical role of transforming probability of success with delta parameters. See de la Torre (2011) for details.

References

de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179-199.

Examples

# transform probability of success to delta
# based on saturated GDINA model
# assuming an item with 2 attributes has the following
# probability of success for 00, 10, 01 and 11
pj <- c(0.2,0.4,0.6,0.8)
Mj <- designmatrix(2)
# delta parameters can be calculated in this way:
deltaj <- solve(Mj)%*%pj
# for reduced CDMs, OLS or WLS may be used