PerFit (version 1.2)

PRFplot: Person response function (PRF)

Description

Plot the nonparametric person response function with variability bands.

Usage

PRFplot(matrix, respID, h = 0.09, N.FPts = 101, VarBands = FALSE,
 VarBands.area = FALSE, alpha = 0.05,
 Xlabel=NA,Xcex=1.5,Ylabel=NA,Ycex=1.5,title=NA,Tcex=1.5)

Arguments

matrix

A data matrix of dichotomous item scores: Persons as rows, items as columns, item scores are either 0 or 1, no missing data.

respID

Row index identifiying the respondent for whom the PRF is to be computed.

h

Bandwidth value. Default is 0.09.

N.FPts

Number of (equidistant) focal points in the [0,1] interval. Default is 101.

VarBands

Logical: Draw the (1-alpha) variability bands? Default is FALSE.

VarBands.area

Logical: Draw the area between the (1-alpha) variability bands? Default is FALSE.

alpha

Significance level for the variability bands. Default is 0.05.

Xlabel

Define label of x-axis, otherwise a default label is shown.

Xcex

Font size of the label of x-axis.

Ylabel

Define label of y-axis, otherwise a default label is shown.

Ycex

Font size of the label of y-axis.

title

Define the title of the plot, otherwise a default title is shown.

Tcex

Font size of the title of the plot.

Details

This function plots the so-called nonparametric person response function (PRF; Emons, Sijtsma, and Meijer, 2004; Sijtsma and Meijer, 2001) for respondent respID. The PRF relates item difficulty (0-1 range on the x-axis) with the associated probability of correct response (on the y-axis). The PRF is typically nonincreasing, implying that the probability of answering increasingly difficult items should (at least) not increase. The code is based on nonparametric kernel smoothing (Emons et al., 2004). The value of the PRF at each focal point (representing a difficulty parameter between 0 and 1) is estimated as a weighted sum score, where scores pertaining to items with difficulty close to the focal point are given the largest weights. The weights are functions of the Gaussian kernel function. It is necessary to specify a bandwidth value (h) in order to compute the weights. The h value controls the trade-off between bias and sampling variation (Emons et al., 2004). Small h values reduce bias but increase variance, leading to PRFs that capture too much measurement error. Large h values, on the other hand, increase bias which renders PRFs that are often too flat, thus missing potentially relevant misfitting response behavior. Therefore, it is important to carefuly specify the value h. Emons et al. (2004, pp. 10-13), after a simulation study, advised that "h values between 0.07 and 0.11 are reasonable choices". Variability bands of level alpha (0.05 by default) can also be added to the plot. These bands are computed following the jackknife procedure explained in Emons et al. (2004).

References

Emons, W. M., Sijtsma, K., and Meijer, R. R. (2004) Testing hypotheses about the person-response function in person-fit analysis. Multivariate Behavioral Research, 39(1), 1--35. Sijtsma, K., and Meijer, R. R. (2001) The person response function as a tool in person-fit research. Psychometrika, 66(2), 191--207.

See Also

cutoff, plot.PerFit, flagged.resp

Examples

# Load the inadequacy scale data (dichotomous item scores):
data(InadequacyData);

# As an example, compute the Ht person-fit scores:
Ht.PF <- Ht(InadequacyData);
Ht.PF$PFscores

# Determine which respondents were flagged by Ht at 1%:
flagged.resp(InadequacyData,x=Ht.PF,Qlvl=.01);
# Flagged respondents: 30, 37, 46, 49,...

# Plot the person response function of respondent 30 (flagged as aberrant):
PRFplot(InadequacyData,respID=30);
# Plot the person response function of respondent 35 (not flagged as aberrant):
PRFplot(InadequacyData,respID=35);