mudfold-package {mudfold}

MUDFOLD : A nonparametric unfolding item response theory model for dichotomous preferential-choice data.

Description

This package can be used for the purpose of finding unfolding structures from selected items in tests or questionnaires. Such structures, represent the underlying ordering on a latent scale of those items. The main function of this package is called mudfold and fits the Van Schuur's scaling method to binary valued preference items. The method is called Multiple UniDimensional unFOLDing (MUDFOLD) and is an item selection algorithm belonging in the class of Nonparametric Item Response Theory (IRT) models.

Details

MUDFOLD is a nonparametric probabilistic model for unidimensional unfolding. Originally developed by W. Van Schuur (1984) and further extended following ideas by W.J. Post (1992) who derived testable properties for the model fit. This method can be used to analyse the categorical (binary) responses of individuals to a set of questionnaire items pressumably generated from a nonmonotonic (unimodal) Item Response Function (IRF). The package incorporates the main function mudfold which is used to estimate the MUDFOLD scale from binary valued unfolding items. The output of the main function is a list of S3 class "mdf", for which print(), summary() and plot() generic functions are available to the user. The package provides the user also with the function mudfoldsim that simulates unfolding scales using an item response function (IRF) with flexible parametrization.

The data must be given in an n \times N binary matrix or data.frame with n respondents in the rows and N items in the columns. Each row of the data corresponds to the selections of the i-th individual on a set of N items. Missing values must be coded as NA and the user can choose whether to apply list-wise deletion or impute the missing values using logistic regression multiple imputation by chained equations (logreg MICE).

Ultimate goal for MUDFOLD is to determine a unidimensional rank order of a (sub)set of items such that, they constitute an appropriate scale for measuring a common latent trait of the respondents. The estimation of the item order is done through an heuristic item selection algorithm, which tests iteratively the item fit to the scale with the use of scalability coefficients.

MUDFOLD's H coefficients of scalability are based to Loevinger's coefficient of homogeneity. In MUDFOLD, H coefficients utilize a scalability measure that is used in several criteria in the item selection algorithm. This coefficient in MUDFOLD can be calculated for triples of items, individual items, and the total scale. Diagnostic statistics are used to assess how well the unfolding scale conforms to the assumptions of unfolding response processeses. Uncertainty estimates for the scalability measures and the diagnostic statistics both at the item and scale level are obtained by exploiting nonparametric ordinary bootstrap. A bootstrap estimate of the unfolding scale is also available.

After an unfolding scale is obtained, it can be used to estimate item locations. Two estimators are available to the user of the mudfold package who can choose between an estimator proposed by Van Schuur and an estimator derived by Johnson.

For assessing the unfolding properties of the obtained scale based on the MUDFOLD assumptions, scale diagnostics such as the ISO and MAX statistics, as well as diagnostic matrices for visual inspection of the conditional independence and moving maxima assumptions are available to the user.

Author(s)

Spyros E. Balafas (auth.), Wim P. Krijnen (auth.), Wendy J. Post (contr.), Ernst C. Wit (auth.)

Maintainer: Spyros E. Balafas ([e-mail])

References

W.H. Van Schuur.(1984). Structure in Political Beliefs: A New Model for Stochastic Unfolding with Application to European Party Activists. CT Press.

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

W.J. Post. and T.AB. Snijders (1993). Nonparametric unfolding models for dichotomous data. Methodika.

M.S. Johnson. (2006). Nonparametric Estimation of Item and Respondent Locations from Unfolding-type Items. Psychometrica

Examples

## Not run: 
# Install the R package mudfold
install.packages("mudfold")

# Load the R package mudfold
library(mudfold)


## End(Not run)