MAX | R Documentation |
This function calculates the max statistic based on the conditional adjacency matrix (CAM) of a given scale. This statistic quantifies violations of the moving maxima property for the item response functions (Post,1992) and it can be calculated for each item and the whole scale. For each row of the CAM, the max statistic is calculated using both a top-down and a bottom-up method.
Both methods yield the same max statistic value for the scale, however, the number of items with non-zero max statistisc may change. In this case, the method that yields the smaller number of items with zero max statististic will be prefered.
MAX(X, type)
X |
: A matrix of class 'cam.mdf' obtained from the function |
type |
: This argument controls the type of the statistic that is returned. If |
To come up with a value of the max statistic for each item in a scale with N items in total, we need first to locate the maximum position in each row of the CAM m_i^*. Then the max statistic for the item i is calculated using a top-down method according to which,
MAX_i = ∑_{k = i+1}^{N} max(0, m_i^* - m_k^*)
and a bottom-up method according to which,
MAX_i = ∑_{k = 1}^{i-1} max(0, m_k^* - m_i^*).
A vector with the MAX statistic for each item. The sum of the individual MAX statistics for each of the items yields the MAX statistic for the whole scale.
Spyros E. Balafas (s.balafas@rug.nl)
W.J. Post. (1992). Nonparametric Unfolding Models: A Latent Structure Approach. M & T series. DSWO Press.
CAM
## load the ANDRICH data data("ANDRICH") ## Calculate the CAM for the ANDRICH scale CAM_andrch <- CAM(ANDRICH) ## Use the CAM to calculate the MAX statistic ## for each item in the ANDRICH scale MAX(CAM_andrch) ## and the whole scale MAX(CAM_andrch, type="scale")
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.