ISO {mudfold}

Iso statistic for a given unfolding scale.

Description

This function calculates the iso statistic based on the conditional adjacency matrix (CAM) of a given scale. In order to quantify if the rows of the CAM show a weakly unimodal pattern, the iso statistic was introduced (Post, 1992). Iso statistic (ISO), is a measure for the degree of unimodality violation in the rows of CAM. ISO can be obtained for each item ({ISO}_j) and their summation results in the total ISO for the scale ({ISO}_{tot}).

To come up with an ISO value for an item j, one should first locate the maximum in each row of the CAM. If we index m^* the maximum in row j of CAM, the ISO measures deviations from unimodality to the left and right of m^*. The function takes as input objects of class "cam.mdf" obtained from the function CAM or objects of class "mdf" obtained from the function mudfold

Usage

ISO(x, type)

Arguments

x

: A matrix of class 'cam.mdf' obtained from the function CAM(). Alternatively, x can be a fitted object of class "mdf" resulted from the mudfold() function.

type

: This argument controls the type of the statistic that is returned. If type="item" (default) then the ISO statisic for each item in the scale. When type="scale" the ISO statistic for the whole scale will be returned.

Details

ISO_j = \sum_{h\leq k \leq m^*} max(0, {CAM}_{jh} - {CAM}_{jk}) + \sum_{m^* \leq h \leq k} max(0,{CAM}_{jk} - {CAM}_{jh} )

Value

A vector with the ISO statistic for each item. The sum of the individual ISO statistics for each of the items yield the ISO statistic for the whole scale.

Author(s)

Spyros E. Balafas ([e-mail])

References

W.J. Post. (1992). Nonparametric Unfolding Models: A Latent Structure Approach. M & T series. DSWO Press.

See Also

CAM

Examples

## load the ANDRICH data
data("ANDRICH")

## Calculate the CAM for the ANDRICH scale
CAM_andrch <- CAM(ANDRICH)

## Use the CAM to calculate the ISO statistic
## for the ANDRICH scale
ISO(CAM_andrch)