plot.irtfit {irtQ}

Draw raw and standardized residual plots

Description

This method function provides graphical displays to look at residuals between the observed data and model-based predictions (Hambleton, Swaminathan, & Rogers, 1991). This function gives two residual plots for each score category of an item: (a) the raw residual plot and (b) the standardized residual plot. Note that for dichotomous items the residual plots are drawn only for the score category of 1.

Usage

## S3 method for class 'irtfit'
plot(
  x,
  item.loc = NULL,
  type = "both",
  ci.method = c("wald", "wilson", "wilson.cr"),
  show.table = TRUE,
  layout.col = 2,
  xlab.text,
  ylab.text,
  main.text,
  lab.size = 15,
  main.size = 15,
  axis.size = 15,
  line.size = 1,
  point.size = 2.5,
  strip.size = 12,
  ylim.icc = c(0, 1),
  ylim.sr.adjust = FALSE,
  ylim.sr = c(-4, 4),
  ...
)

Arguments

x

An object of class irtfit.

item.loc

An integer value indicating that the nth item (or the location of the item) is plotted. See below for details.

type

A character string indicating what type of residual plot is returned. Available options are "icc" for the raw residual plot, "sr" for the standardized residual plot, and "both" for both of them. Default is "both".

ci.method

A character string indicating what method is used to estimate the confidence interval for the raw residual plot. Available options are "wald" for Wald method, "wilson" for Wilson score interval, and "wilson.cr" for Wilson score interval with continuity correction. Default is "wald". See below for details.

show.table

A logical value. If TRUE, a contingency table containing the information used to draw the residual plots for the studied item is returned. This contingency table is the same as one contained in the internal object of contingency.plot in the object of class irtfit. Default is TRUE.

layout.col

An integer value indicating the number of columns in the panel when a polytomous item is used. Default is 2.

xlab.text

A title for the x axis. If missing, the default string is used.

ylab.text

A title for the y axis. If type = "both", two character strings can be specified for the raw residual and standardized residual plots, respectively. If missing, the default strings are used.

main.text

An overall title for the plot. If type = "both", two character strings can be specified for the raw residual and standardized residual plots, respectively. If missing, the default strings are used.

lab.size

The size of xlab and ylab. Default is 15.

main.size

The size of main.text. Default is 15.

axis.size

The size of labels along the x and y axes. Default is 15.

line.size

The size of lines. Default is 1.

point.size

The size of points. Default is 2.5.

strip.size

The size of facet labels. Default is 12.

ylim.icc

A vector of two numeric values specifying the range of y axis for the raw residual plot. Default is c(0, 1).

ylim.sr.adjust

A logical value. If TRUE, the range of y axis for the standardized residual plot is adjusted for each item. If FALSE, the range of y axis for the standardized residual plot is fixed to the values specified in the argument ylim.sr.

ylim.sr

A vector of two numeric values specifying the range of y axis for the standardized residual plot. Default is c(-4, 4).

...

Further arguments passed from the function ggplot() in the ggplot2 package.

Details

All of the plots are drawn using the ggplot2 package.

Once the results of the IRT model fit analysis are obtained from the function irtfit, an object of class irtfit can be used to draw the IRT raw residual and standardized residual plots. Especially, the information contained in an internal object of contingency.plot are mainly used to draw the residual plots.

Because the residual plots are drawn for an item at a time, you have to indicate which item will be evaluated. For this, you should specify an integer value, which is the location of the studied item, in the argument item.loc. For example, if you want to draw the residual plots for the third item, then item.loc = 3.

In terms of the raw residual plot, the argument ci.method is used to select a method to estimate the confidence intervals among four methods. Those methods are "wald" for the Wald interval, which is based on the normal approximation (Laplace, 1812), "wilson" for Wilson score interval (Wilson, 1927), and "wilson.cr" for Wilson score interval with continuity correction (Newcombe, 1998). See https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval for more details about the binomial proportion confidence intervals. Note that the width of confidence interval is determined by the \alpha-level specified in the argument alpha of the function irtfit.

Regarding the standardized residual plot, any standardized residuals greater than the specified criterion value in the argument overSR of the function irtfit are displayed with circles. Otherwise, they are displayed with crosses.

Value

This method function displays the IRT raw residual plot, the standard residual plot, or both of the studied item. when show.table = TRUE, a contingency table used to draw the residual plots is also returned. See irtfit for more detail about the contingency table.

Author(s)

Hwanggyu Lim [e-mail]

References

Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991).Fundamentals of item response theory. Newbury Park, CA: Sage.

Laplace, P. S. (1820).Theorie analytique des probabilites (in French). Courcier.

Newcombe, R. G. (1998). Two-sided confidence intervals for the single proportion: comparison of seven methods. Statistics in medicine, 17(8), 857-872.

Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22(158), 209-212.

See Also

irtfit

Examples

## import the "-prm.txt" output file from flexMIRT
flex_sam <- system.file("extdata", "flexmirt_sample-prm.txt", package = "irtQ")

# select the first two dichotomous items and last polytomous item
x <- bring.flexmirt(file=flex_sam, "par")$Group1$full_df[c(1:2, 55), ]

# generate examinees' abilities from N(0, 1)
set.seed(23)
score <- rnorm(1000, mean=0, sd=1)

# simulate the response data
data <- simdat(x=x, theta=score, D=1)


# compute fit statistics
fit <- irtfit(x=x, score=score, data=data, group.method="equal.freq",
               n.width=11, loc.theta="average", range.score=c(-4, 4), D=1, alpha=0.05, overSR=1.5)

# residual plots for the first item (dichotomous item)
plot(x=fit, item.loc=1, type = "both", ci.method = "wald", show.table=TRUE, ylim.sr.adjust=TRUE)

# residual plots for the third item (polytomous item)
plot(x=fit, item.loc=3, type = "both", ci.method = "wald", show.table=FALSE, ylim.sr.adjust=TRUE)

# raw residual plot for the third item (polytomous item)
plot(x=fit, item.loc=3, type = "icc", ci.method = "wald", show.table=TRUE, ylim.sr.adjust=TRUE)

# standardized residual plot for the third item (polytomous item)
plot(x=fit, item.loc=3, type = "sr", ci.method = "wald", show.table=TRUE, ylim.sr.adjust=TRUE)