aov.rasch {pwrRasch}

Three-Way Analysis of Variance with Mixed Classification for Testing the Rasch Model

Description

This function applies the three-way analysis of variance with mixed classification for testing the Rasch model.

Usage

aov.rasch(data, group = "group", person = "person", item = "item",
  response = "response", output = TRUE)

Arguments

data

A data frame in which the variables specified in the model will be found. Note that data needs to be in 'long' format.

group

Column name of the data frame containing the grouping variable.

person

Column name of the data frame containing the person number variable.

item

Column name of the data frame containing the item number variable.

response

Column name of the data frame containing the response variable.

output

If TRUE, an output will be shown on the console.

Details

The F-test in a three-way analysis of variance design (A > B) x C with mixed classification (fixed factor A = subgroup, random factor B = testees, and fixed factor C = items) is used to test the Rasch model. Rasch model fitting means that there is no interaction A x C. A statistically significant interaction A x C indicates differential item functioning (DIF) of the items with respect of the two groups of testees Note, if a main effect of A (subgroup) exists, an artificially high type I risk of the A x C interaction F-test results - that is, the approach works as long as no statistically significant main effect of A occurs. Note that in case of unbalanced groups computation can take a long time.

Value

Returns an ANOVA table

Author(s)

Takuya Yanagida [e-mail], Jan Steinfeld [e-mail]

References

Kubinger, K. D., Rasch, D., & Yanagida, T. (2009). On designing data-sampling for Rasch model calibrating an achievement test. Psychology Science Quarterly, 51, 370-384.

Kubinger, K. D., Rasch, D., & Yanagida, T. (2011). A new approach for testing the Rasch model. Educational Research and Evaluation, 17, 321-333.

See Also

reshape.rasch, pwr.rasch

Examples

## Not run: 

# simulate Rasch model based data
# 100 persons, 20 items,
dat <- simul.rasch(100, items = seq(-3, 3, length.out = 20))
# reshape simulated data into 'long' format with balanced assignment
# of testees into two subgroups
dat.long <- reshape.rasch(dat, group = rep(0:1, each = nrow(dat) / 2))
# apply three-way analysis of variance with mixed classification for testing the Rasch model
aov.rasch(dat.long)

# extract variable names of items
vnames <- grep("it", names(aid_st2), value = TRUE)
# reshape aid subtest 2 data into 'long' format with split criterium sex
aid_long.sex <- reshape.rasch(aid_st2[, vnames], group = aid_st2[, "sex"])
# apply three-way analysis of variance with mixed classification for testing the Rasch model
aov.rasch(aid_long.sex)

## End(Not run)