OscatsAlgMaxFisher

OscatsAlgMaxFisher

Synopsis

struct              OscatsAlgMaxFisher;
void                oscats_alg_max_fisher_resize        (OscatsAlgMaxFisher *alg_data,
                                                         guint num);

Object Hierarchy

  GObject
   +----GInitiallyUnowned
         +----OscatsAlgorithm
               +----OscatsAlgMaxFisher

Properties

  "A-opt"                    gboolean              : Read / Write / Construct Only
  "modelKey"                 gchar*                : Read / Write
  "num"                      guint                 : Read / Write / Construct Only
  "thetaKey"                 gchar*                : Read / Write

Description

Details

struct OscatsAlgMaxFisher

struct OscatsAlgMaxFisher;

Item selection algorithm ("select"). Picks the item with optimal Fisher information. Note: This algorithm may not work correctly if there are multiple items with exactly the same optimality metric.

Fisher Information is: I_j(theta) = -E_{X|theta}[ d^2/dtheta dtheta' log P_j(x|theta) ]

D-optimal Fisher Information minimizes the confidence ellipsoid around theta.hat by maximizing the determinant of the Fisher Information: arg max_j det[ I_j(theta.hat) + sum_k I_k(theta.hat) ], where I_k are the previously administered items. This is equivalent to the traditional Maximum Information Criterion in the unidimensional case.

A-optimal Fisher Information minimizes the trace of the covariance matrix for theta: arg min_j tr{ [ I_j(theta.hat) + sum_k I_k(theta.hat) ]^-1 } This is equivalent to the D-optimal condition in the unidimensional case, but the D-optimal calculation will be slightly faster.

Note for multidimensional tests: These algorithms will not work correctly unless the test information matrix for the items already administered is full rank. If not all of the items in the item bank load onto every dimension, a different item selection mechanism may be needed until the test information achieves full rank.

References:

Joris Mulder and Wim van der Linden (2009). "Multidimensional Adaptive Testing with Optimal Design Criteria for Item Selection." Psychometrika, 74, 273-296.

D.O. Segall (1996). "Multidimensional Adaptive Testing." Psychometrika, 61, 331-354.

Frederick Lord (1980). Applications of Item Response Theory to Practical Testing Problems. p 151.


oscats_alg_max_fisher_resize ()

void                oscats_alg_max_fisher_resize        (OscatsAlgMaxFisher *alg_data,
                                                         guint num);

Set the size of the continuous portion of the test's latent space. This function only needs to be called if the test switches to a set of models from a different latent space (which is not usual).

alg_data :

the OscatsAlgMaxFisher data

num :

the number of continuous dimensions of the test's latent space

Property Details

The "A-opt" property

  "A-opt"                    gboolean              : Read / Write / Construct Only

If true, use the A-optimality critierion. Otherwise, use the D-optimality criterion.

Default value: FALSE


The "modelKey" property

  "modelKey"                 gchar*                : Read / Write

The key indicating which model to use for selection. A NULL value or empty string indicates the item's default model.

Default value: NULL


The "num" property

  "num"                      guint                 : Read / Write / Construct Only

Number of items from which to choose. If one, then the exact optimal item is selected. If greater than one, then a random item is chosen from among the "num" optimal items.

Allowed values: >= 1

Default value: 1


The "thetaKey" property

  "thetaKey"                 gchar*                : Read / Write

The key indicating which latent variable to use for selection. A NULL value or empty string indicates the examinee's default estimation theta.

Default value: NULL