ConjointChecks: A package to check the cancellation axioms of conjoint measurement.

Description

Implementation of a procedure (Domingue, 2012; see also Karabatsos, 2001 and Kyngdon, 2011) to test the single and double cancellation axioms of conjoint measure in data that is dichotomously coded and measured with error.

Author(s)

Ben Domingue ben.domingue@gmail.com

References

Domingue, B. (2012). Evaluating the Equal-Interval Hypothesis with Test Score Scales. Doctoral Dissertation, University of Colorado Boulder, May 2012.

Karabatsos, G. (2001). The rasch model, additive conjoint measurement, and new models of probabilistic measurement theory. Journal of Applied Measurement, 2(4), 389-423.

Kyngdon, A. (2011). Plausible measurement analogies to some psychometric models of test per- formance. British Journal of Mathematical and Statistical Psychology, 64(3), 478-497.

Perline, R., Wright, B. D., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3(2), 237-255.

Internal Function of Iterations of ConjointChecks

Description

Internal function; should not be used directly.

Usage

CCIterate(nIter, old, old_ll, single, burn, N, n)

Arguments

Author(s)

Ben Domingue ben.domingue@gmail.com

References

Perline, R., Wright, B. D., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3(2), 237-255.

Examples

### INTERNAL FUNCTION ###

Check Single and Double Cancellation in a sample of 3-matrices

Description

Given two matrices, n and N (which contain the number of correct responses and the number of total responses for each cell), a check of single and double cancellation is performed in n.3mat matrices. To check large numbers of 3-matrices (to see why, see Domingue (2012)), parallel options help.

Usage

ConjointChecks(N,n,n.3mat=1,CR=c(.025,.975),single=FALSE,mc.cores=1)

Arguments

Author(s)

Ben Domingue ben.domingue@gmail.com

References

Perline, R., Wright, B. D., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3(2), 237-255.

Examples

######################################################
#parole data
#page 244 (table 2) of Perline, Wright, and Wainer
#about 9% were bad in perline
matrix(c(15,47,61,84,82,86,60,47,8),9,9,byrow=FALSE)->N
per <-structure(c(0, 0.06, 0.07, 0.18, 0.13, 0.13, 0.17, 0.17,
 1, 0, 0.04, 0.15, 0.24, 0.33, 0.28, 0.47, 0.85, 1, 0, 0.04, 0.08,
 0.12, 0.3, 0.64, 0.85, 1, 1, 0, 0.19, 0.39, 0.4, 0.51, 0.58,
 0.82, 0.98, 1, 0, 0.06, 0.18, 0.52, 0.73, 0.95, 1, 1, 1, 0,
 0.23, 0.33, 0.51, 0.68, 0.91, 0.93, 1, 1, 0.27, 0.51, 0.61,
 0.64, 0.68, 0.77, 0.9, 1, 1, 0, 0.21, 0.52, 0.68, 0.84, 0.97,
 0.97, 1, 1, 0.73, 0.64, 0.67, 0.7, 0.78, 0.78, 0.9, 1, 1),
 .Dim = c(9L, 9L) )
round(per*N)->n
ConjointChecks(N,n,n.3mat=1)->out

######################################################
#Data from Rasch (1960) data
#page 250 (table 5) of Perline, Wright, and Wainer
#about 4% showed violations
matrix(c(49,112,32,76,82,102,119,133,123,94,61,17,10),13,7,byrow=FALSE)->N
per <-structure(c(0, 0, 0, 0, 0.02, 0.01, 0.02, 0.03, 0.06, 0.09,
 0.23, 0.35, 0.7, 0.01, 0, 0.04, 0.05, 0.09, 0.09, 0.16, 0.28, 0.39,
 0.66, 0.8, 0.91, 0.85, 0, 0.02, 0.07, 0.07, 0.24, 0.28, 0.45, 0.59,
 0.76, 0.87, 0.9, 1, 0.85, 0.01, 0.04, 0.12, 0.21, 0.42, 0.62, 0.73,
 0.83, 0.9, 0.93, 0.98, 1, 1, 0.06, 0.11, 0.4, 0.7, 0.7, 0.79, 0.84,
 0.88, 0.94, 0.95, 0.98, 1, 1, 0.48, 0.84, 0.84, 0.86, 0.86, 0.9,
 0.95, 0.96, 0.98, 0.99, 0.99, 1, 1, 0.92, 0.98, 0.98, 0.99, 0.98,
 0.99, 0.99, 1, 1, 1, 1, 1, 1), .Dim = c(13L, 7L))
round(per*N)->n
ConjointChecks(N,n,n.3mat=1)->out

###########
#simulated rasch example
n.3mat<-1000
n.items<-20
n.respondents<-2000
#simulate data
rnorm(n.items)->diff
rnorm(n.respondents)->abil
matrix(abil,n.respondents,n.items,byrow=FALSE)->m1
matrix(diff,n.respondents,n.items,byrow=TRUE)->m2
m1-m2 -> kern
exp(kern)/(1+exp(kern))->pv
runif(n.items*n.respondents)->test
ifelse(pv>test,1,0)->resp
##now check
PrepareChecks(resp)->tmp
ConjointChecks(tmp$N,tmp$n,n.3mat=n.3mat,mc.cores=1)->rasch1000

Check Double Cancellation in a sample of 3-matrices

Description

Internal function. Wrapper of the code that checks ONLY the double cancellation bits.

Usage

DoubleCancel(N,n,n.3mat=1,CR=c(.025,.975),mc.cores=1)

Arguments

Author(s)

Ben Domingue ben.domingue@gmail.com

References

Perline, R., Wright, B. D., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3(2), 237-255.

Examples

### INTERNAL FUNCTION ###

Check What Ordering to Use

Description

Internal funcion. This checks to see whether the p-value (rasch difficulty) ordering should be used or if ordering should be 'as is'.

Usage

ManyBands(th, se, cc.type, resp, bands=seq(10,50,by=10), uniform.bands=TRUE,
           trim.window=NULL, pv.order=TRUE,mc.cores=1)

Arguments

Author(s)

Ben Domingue ben.domingue@gmail.com

References

Perline, R., Wright, B. D., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3(2), 237-255.

Examples

### INTERNAL FUNCTION ###

Prepare raw response data for ConjointChecks.

Description

Takes output from ConjointChecks and produces a matrix showing the percentage of reported violations at each cell.

Usage

PrepareChecks(resp,ss.lower=10, collapse.columns = FALSE) 

Arguments

Value

Returns n and N, respectively, containing the number of correct responses and the number of total responses for each cell.

Examples

#simulated Rasch example
n.items<-20
n.respondents<-2000
#simulate data
rnorm(n.items)->diff
rnorm(n.respondents)->abil
matrix(abil,n.respondents,n.items,byrow=FALSE)->m1
matrix(diff,n.respondents,n.items,byrow=TRUE)->m2
m1-m2 -> kern
exp(kern)/(1+exp(kern))->pv
runif(n.items*n.respondents)->test
ifelse(pv>test,1,0)->resp
#now check
PrepareChecks(resp)->obj

Check Single Cancellation in a sample

Description

Internal function. Wrapper of the code that checks ONLY the single cancellation bits.

Usage

SingleCancel(N,n,CR=c(.025,.975),single,mc.cores=1)

Arguments

Author(s)

Ben Domingue ben.domingue@gmail.com

References

Perline, R., Wright, B. D., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3(2), 237-255.

Examples

### INTERNAL FUNCTION ###

Class "checks"

Description

The formal S4 class for checks. This class contains transformed version of the raw response data as well as summaries of the checks.

Details

Objects of class checks contains all information returned by ConjointChecks.

Objects from the Class

Object created by a call to function ConjointChecks.

Slots

N:

matrix containing the number of respondents at each item/ability intersection

n:

matrix containing the number of correct responses at each item/ability intersection

Checks:

List containing information about each checked 3-matrix

tab:

matrix containing information about the detected violations at each item/ability intersection

means:

vector containing weighted and unweighted means for the detected violations (where weights are the number of individuals at each ability level)

check.counts:

matrix giving the number of times a item/ability cell was sampled

Author(s)

Ben Domingue ben.domingue@gmail.com

See Also

ConjointChecks, summary.checks, plot.checks

Class "list.null"

Description

The formal S4 class for list.null. This class contains a null list.

Details

Objects of class are used internally.

Objects from the Class

Object used internally.

Author(s)

Ben Domingue ben.domingue@gmail.com

See Also

ConjointChecks, summary.checks, plot.checks

Check Single and Double Cancellation in a sample of 3-matrices

Description

Internal function. This checks both single and double cancellation.

Usage

omni.check(N,n,n.iter,burn=1000,thin=4,CR,single)

Arguments

Author(s)

Ben Domingue ben.domingue@gmail.com

References

Perline, R., Wright, B. D., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3(2), 237-255.

Examples

### INTERNAL FUNCTION ###

Check Double Cancellation in a sample of 3-matrices

Description

Internal function. Checks ONLY the double cancellation bits.

Usage

omni.check_double(N,n,n.iter,burn=1000,thin=4,CR)

Arguments

Author(s)

Ben Domingue ben.domingue@gmail.com

References

Perline, R., Wright, B. D., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3(2), 237-255.

Examples

### INTERNAL FUNCTION ###

Check Single Cancellation in a sample

Description

Internal function. Code that checks ONLY the single cancellation bits.

Usage

omni.check_single(N,n,n.iter,burn=1000,thin=4,CR,single)

Arguments

Author(s)

Ben Domingue ben.domingue@gmail.com

References

Perline, R., Wright, B. D., & Wainer, H. (1979). The Rasch model as additive conjoint measurement. Applied Psychological Measurement, 3(2), 237-255.

Examples

### INTERNAL FUNCTION ###

Plot checks produced by ConjointChecks.

Description

Takes output from ConjointChecks and produces a matplot showing the percentage of reported violations at each cell.

Usage

## S3 method for class 'checks'
plot(x,items=NULL,item.labels=TRUE,...)

Arguments

Value

No return value, called for side effects

References

Tufte, E. R. (2001). The visual display of quantitative information (2nd ed.). Chesire, CT: Graphics Press.

Examples

opar <- par()
par(mfrow=c(3,2))
plot(rasch1000)
plot(rasch1000,items=c(5,10,15))
for (i in c(3,9,13,18)) plot(rasch1000,items=i)
par(opar)

1000 sampled 3-matrices from simulated Rasch data.

Description

Object created by first generating Rasch data and then running ConjointChecks on 1000 sampled 3 matrices

Usage

rasch1000

Format

An object of class checks.

Source

Simulated via Rasch model.

Summarize checks produced by ConjointChecks.

Description

Takes output from ConjointChecks and produces a matrix showing the percentage of reported violations at each cell.

Usage

## S3 method for class 'checks'
summary(object, ...)

Arguments

Value

No return value, called for side effects

Examples

summary(rasch1000)