deriv_nu {cogirt} | R Documentation |
Derivatives and Information for Nu
Description
This function calculates the matrix of first partial derivatives, the matrix of second partial derivatives, and matrix of posterior and Fisher information for the posterior distribution with respect to nu (easiness) based on the slope-intercept form of the 1-, 2-, or 3-P item response theory model.
Usage
deriv_nu(
y = NULL,
omega = NULL,
gamma = NULL,
lambda = NULL,
zeta = NULL,
nu = NULL,
kappa = NULL,
nu_mu = NULL,
nu_sigma2 = NULL,
link = NULL
)
Arguments
y |
Item response matrix (K by IJ). |
omega |
Contrast effects matrix (K by MN). |
gamma |
Contrast codes matrix (JM by MN). |
lambda |
Item slope matrix (IJ by JM). |
zeta |
Specific effects matrix (K by JM). |
nu |
Item intercept matrix (IJ by 1). |
kappa |
Item guessing matrix (IJ by 1). Defaults to 0. |
nu_mu |
Mean prior for nu (1 by 1) |
nu_sigma2 |
Covariance prior for nu (1 by 1) |
link |
Choose between "logit" or "probit" link functions. |
Value
List with elements fpd (1 by 1 vector of first partial derivatives for nu), spd (1 by 1 matrix of second partial derivatives for nu), post_info (1 by 1 posterior information matrix for nu), and fisher_info (1 by 1) Fisher information matrix for nu). Within each of these elements, there are sub-elements for all IJ items.
Dimensions
I = Number of items per condition; J = Number of conditions; K = Number of examinees; M Number of ability (or trait) dimensions; N Number of contrasts (should include intercept).
A Note About Model Notation
The function converts GLLVM notation to the more typical IRT notation used by Segall (1996) for ease of referencing formulas (with the exception of using the slope-intercept form of the item response model).
References
Carlson, J. E. (1987). Multidimensional Item Response Theory Estimation: A computer program (Reprot No. ONR87-2). The American College Testing Program. https://apps.dtic.mil/sti/pdfs/ADA197160.pdf
Segall, D. O. (1996). Multidimensional adaptive testing. Psychometrika, 61(2), 331-354. https://doi.org/10.1007/BF02294343
Segall, D. O. (2009). Principles of Multidimensional Adaptive Testing. In W. J. van der Linden & C. A. W. Glas (Eds.), Elements of Adaptive Testing (pp. 57-75). https://doi.org/10.1007/978-0-387-85461-8_3