ConjointChecks (version 0.0.9)

ConjointChecks: 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,par.options=NULL,CR=c(.025,.975),seed=NULL)

Arguments

N

Matrix containing the total number of responses.

n

Matrix containing the number of correct responses.

n.3mat

Number of 3-matrices to sample or the string "adjacent" if all adjacently formed 3-matrices are to be checked.

par.options

A named list indicating "n.workers" and "type". The first defaults to unity and the latter to PSOCK.

seed

Random number seed.

CR

Width of the credible region taken from the posterior. Defaults to a 95% credible region (c(.025,.975)).

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<-5000
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
#not run
#detectCores()->n.workers
#ConjointChecks(tmp$N,tmp$n,n.3mat=5000,
#  par.options=list(n.workers=n.workers,type="PSOCK"))->rasch5000