PerFit (version 1.2)

lzpoly: lzpoly person-fit statistic

Description

Compute the lzpoly (Drasgow, Levine, and Williams, 1985) person-fit statistic.

Usage

lzpoly(matrix,Ncat,ip = NA, model = "GRM", ability = NA, method = "EAP")

Arguments

matrix

A data matrix of polytomous item scores: Persons as rows, items as columns, item scores are integers between 0 and (Ncat-1), no missing data.

Ncat

Number of answer options for each item.

ip

Matrix with previously estimated item parameters: One row per item. The first (Ncat-1) columns contain the between-categories threshold parameters (for the GRM) or the item step difficulties (for the PCM and the GPCM). The last, Ncat-th, column has the sl

model

Specify the IRT model to use in order to estimate the item parameters. The options available are "PCM", "GPCM", and "GRM" (default).

ability

Vector with previoulsy estimated latent ability parameters, one per respondent, following the order of the row index of matrix. In case no ability parameters are available then ability=NA.

method

Specify the method to use in order to estimate the latent ability parameters. The options available are "EB", "EAP" (default), and "MI".

Value

• An object of class "PerFit", which is a list with elements:
• PFscores
  A vector of length $N$ (number of respondents) with the values of the person-fit statistic.
• PFstatistic
  The name of the person-fit statistic used.

Details

Statistic lzpoly is the natural extension of lz to polytomously scores items. In this case the user can choose one from three possible IRT models to fit the data: The partial credit model (model="PCM"), the generalized partial credit model (model="GPCM"), or the graded response model (model="GRM"). Ability parameters can be estimated by means of one of three methods: Empirical Bayes ("EB"), expected a posteriori ("EAP"), or multiple imputation ("MI"). Both item and ability parameters may be provided as function parameters (ip and ability, respectively). If ip is provided then ability must also be provided. The reason is that the estimation of the ability parameters is done via the function factor.scores from the ltm package, and this procedure requires an object of a specific class (gpcm or grm) containing the estimated item parameters (i.e., providing a matrix of item parameters to ip is not sufficient). Aberrant response behavior is (potentially) indicated by small values of lzpoly (i.e., in the left tail of the sampling distribution).

References

Drasgow, F., Levine, M. V., and Williams, E. A. (1985) Appropriateness measurement with polychotomous item response models and standardized indices. British Journal of Mathematical and Statistical Psychology, 38(1), 67--86. Karabatsos, G. (2003) Comparing the Aberrant Response Detection Performance of Thirty-Six Person-Fit Statistics. Applied Measurement In Education, 16(4), 277--298. Magis, D., Raiche, G., and Beland, S. (2012) A didactic presentation of Snijders's l[sub]z[/sub] index of person fit with emphasis on response model selection and ability estimation. Journal of Educational and Behavioral Statistics, 37(1), 57--81. Meijer, R. R., and Sijtsma, K. (2001) Methodology review: Evaluating person fit. Applied Psychological Measurement, 25(2), 107--135. Molenaar, I. W., and Hoijtink, H. (1990) The many null distributions of person fit indices. Psychometrika, 55(1), 75--106. Snijders, T. B. (2001) Asymptotic null distribution of person fit statistics with estimated person parameter. Psychometrika, 66(3), 331--342.

See Also

lz,lzstar

Examples

# Load the physical functioning data (polytomous item scores):
data(PhysFuncData);

# Compute the lzpoly scores:
lzpoly(PhysFuncData,Ncat=3);