CDM (version 1.4-16)

fraction.subtraction.data: Fraction Subtraction Data

Description

Tatsuoka's (1984) fraction subtraction data set is comprised of responses to $J=20$ fraction subtraction test items from $N=536$ middle school students.

Usage

data(fraction.subtraction.data)

format

The fraction.subtraction.data data frame consists of 536 rows and 20 columns, representing the responses of the $N=536$ students to each of the $J=20$ test items. Each row in the data set corresponds to the responses of a particular student. Thereby a "1" denotes that a correct response was recorded, while "0" denotes an incorrect response. The other way round, each column corresponds to all responses to a particular item.

source

The Royal Statistical Society Datasets Website, Series C, Applied Statistics, Data analytic methods for latent partially ordered classification models: URL: http://www.blackwellpublishing.com/rss/Volumes/Cv51p2_read2.htm

Details

The items used for the fraction subtraction test originally appeared in Tatsuoka (1984) and are published in Tatsuoka (2002). They can also be found in DeCarlo (2011). All test items are based on 8 attributes (e.g. convert a whole number to a fraction, separate a whole number from a fraction or simplify before subtracting). The complete list of skills can be found in fraction.subtraction.qmatrix.

References

DeCarlo, L. T. (2011) On the Analysis of Fraction Subtraction Data: The DINA Model, Classification, Latent Class Sizes, and the Q-Matrix. Applied Psychological Measurement, 35, 8--26. Tatsuoka, C. (2002) Data analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society, Series C, Applied Statistics, 51, 337--350. Tatsuoka, K. (1984) Analysis of errors in fraction addition and subtraction problems. Final Report for NIE-G-81-0002, University of Illinois, Urbana-Champaign.

See Also

fraction.subtraction.qmatrix for the corresponding Q-matrix.

Examples

##
## (1) examples based on dataset fractions.subtraction.data
##

## dataset fractions.subtraction.data and corresponding Q-Matrix
head(fraction.subtraction.data)
fraction.subtraction.qmatrix

## Misspecification in parameter specification for method din()
## leads to warnings and terminates estimation procedure. E.g.,

# See Q-Matrix specification
fractions.dina.warning1 <- din(data = fraction.subtraction.data,
  q.matrix = t(fraction.subtraction.qmatrix)) 
  
# See guess.init specification
fractions.dina.warning2 <- din(data = fraction.subtraction.data,
  q.matrix = fraction.subtraction.qmatrix, guess.init = rep(1.2,
  ncol(fraction.subtraction.data)))
  
# See rule specification   
fractions.dina.warning3 <- din(data = fraction.subtraction.data,
  q.matrix = fraction.subtraction.qmatrix, rule = c(rep("DINA",
  10), rep("DINO", 9)))

## Parameter estimation of DINA model
# rule = "DINA" is default
fractions.dina <- din(data = fraction.subtraction.data,
  q.matrix = fraction.subtraction.qmatrix, rule = "DINA")
attributes(fractions.dina)
str(fractions.dina)	  

## For instance accessing the guessing parameters through
## assignment
fractions.dina$guess

## corresponding summaries, including diagnostic accuracies,
## most frequent skill classes and information 
## criteria AIC and BIC
summary(fractions.dina)

## In particular, accessing detailed summary through assignment
detailed.summary.fs <- summary(fractions.dina)
str(detailed.summary.fs)


## Item discrimination index of item 8 is too low. This is also
## visualized in the first plot 
plot(fractions.dina)

## The reason therefore is a high guessing parameter
round(fractions.dina$guess[,1], 2)

## Fix the guessing parameters of items 5, 8 and 9 equal to .20
# define a constraint.guess matrix
constraint.guess <-  matrix(c(5,8,9, rep(0.2, 3)), ncol = 2)
fractions.dina.fixed <- din(data = fraction.subtraction.data, 
  q.matrix = fraction.subtraction.qmatrix, 
  constraint.guess=constraint.guess)

## The second plot shows the expected (MAP) and observed skill 
## probabilities. The third plot visualizes the skill classes
## occurrence probabilities; Only the 'top.n.skill.classes' most frequent 
## skill classes are labeled; it
## is obvious that the skill class '11111111' (all skills are
## mastered) is the most probable in this population. The fourth
## plot shows the skill probabilities conditional on response
## patterns; in this population the skills 3 and 6 seem to be
## mastered easier than the others. The fifth plot shows the
## skill probabilities conditional on a specified response
## pattern; it is shown whether a skill is mastered (above 
## .5+'uncertainty') unclassifiable (within the boundaries) or
## not mastered (below .5-'uncertainty'). In this case, the
## 527th respondent was chosen; if no response pattern is 
## specified, the plot will not be shown (of course)
pattern <- paste(fraction.subtraction.data[527, ], collapse = "")
plot(fractions.dina, pattern = pattern, display.nr = 5)

#uncertainty = 0.1, top.n.skill.classes = 6 are default
plot(fractions.dina.fixed, uncertainty = 0.1, top.n.skill.classes = 6, 
  pattern = pattern)