infutil (version 1.0)

nmru: Normalized Minimum Reduction in Uncertainty

Description

This function calculates the normalized minimum reduction in uncertainty (NMRU) for a test, given an item response model.

Usage

nmru(ltm.obj, range.int = c(-Inf, Inf))

Arguments

ltm.obj

An object representing an IRT model of a set of items, from the ltm package (e.g., using the ltm, grm, or gpcm functions).

range.int

the range of integration; defaults to c(-Inf, Inf).

Value

val

the NMRU value.

iota.l

the information utility lower bound.

iota.u

the information utility upper bound.

Details

This function calculates the normalized minimum reduction in uncertainty (NMRU) for a test, given an item response model. It is equal to the information utility lower bound divided by the upper bound (which are returned by iota.l and iota.u, respectively. The NMRU is a normalized mutual information index, where the mutual information between the data and trait estimate is normalized by the entropy of the prior.

Note that the range of integration may have to be changed; the integration function sometimes throws an error with infinite limits.

References

Markon, K. E. (2013). Information utility: Quantifying the total psychometric information provided by a measure. Psychological Methods, 18, 15-35. doi: 10.1037/a0030638..

See Also

iota.l, iota.u, ltm, grm, gpcm

Examples

# five items
ltm.lsat <- ltm(LSAT~z1, IRT=FALSE)

nmru(ltm.lsat)
nmru(ltm.lsat, range.int=c(-20,20))

# seven items
ltm.lsat <- ltm(cbind(LSAT, LSAT[,1:2])~z1, IRT=FALSE)

nmru(ltm.lsat)

# ten items
ltm.lsat <- ltm(cbind(LSAT, LSAT)~z1, IRT=FALSE)

nmru(ltm.lsat)