modelChoose: Functions For Choosing The m4pl Best Model(s)
In irtProb: Utilities and Probability Distributions Related to Multidimensional Person Item Response Models

Description Usage Arguments Details Value Author(s) References See Also Examples

Functions to help to choose the best models from the m4pl person response models family (Raiche et al., 2013). The function meanModels gives the mean of selected and available statistics from a m4plModelShow result. The function modelChoose shows which model(s) are choosen for each subject, while the function modelChooseAdd adds a supplementary logical variable indicating which model(s) are choosen for each subject to the data.frame returned previously by a m4plModelShow call .

 meanModels(    modelShow, statistics=c("T","S"))

 modelChoose(   modelShow, criteria = "BIC", tol = 0.2)

 modelChooseAdd(modelShow, criteria="LL")

`modelShow`	data.frame: result returned by a `m4plModelShow` call.
`criteria`	character: criteria used to choose between models (LL, AIC or BIC).
`tol`	numeric: tolerance around the choose criteria, so that more models can be considered.
`statistics`	character: a vector of variables for which means of statistics from `m4plModelShow` will be computed.

A tolerance varying between 0.10 and 0.20 is suggested. Lower the value, less models are choosen.

`meanModels`	data.frame: this function return a data.frame of means for each choosen variables.
`modelChoose`	list: return a list of the models(s) choosen for each subject.
`modelChooseAdd`	data.frame: return a data.frame adding a logical indicator of the choosen model(s).

Gilles Raiche, Universite du Quebec a Montreal (UQAM),

Departement d'education et pedagogie

Raiche.Gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/

Blais, J.-G., Raiche, G. and Magis, D. (2009). La detection des patrons de reponses problematiques dans le contexte des tests informatises. In Blais, J.-G. (Ed.): Evaluation des apprentissages et technologies de l'information et de la communication : enjeux, applications et modeles de mesure. Ste-Foy, Quebec: Presses de l'Universite Laval.

Raiche, G., Magis, D. and Beland, S. (2009). La correction du resultat d'un etudiant en presence de tentatives de fraudes. Communication presentee a l'Universite du Quebec a Montreal. Retrieved from http://www.camri.uqam.ca/camri/camriBase/

Raiche, G., Magis, D. and Blais, J.-G. (2008). Multidimensional item response theory models integrating additional inattention, pseudo-guessing, and discrimination person parameters. Communication at the annual international Psychometric Society meeting, Durham, New Hamshire. Retrieved from http://www.camri.uqam.ca/camri/camriBase/

Raiche, G., Magis, D., Blais, J.-G., and Brochu, P. (2013). Taking atypical response patterns into account: a multidimensional measurement model from item response theory. In M. Simon, K. Ercikan, and M. Rousseau (Eds), Improving large-scale assessment in education. New York, New York: Routledge.

m4plModelShow

## Not run: 
## GENERATION OF VECTORS OF RESPONSE
 # NOTE THE USUAL PARAMETRIZATION OF THE ITEM DISCRIMINATION,
 # THE VALUE OF THE PERSONNAL FLUCTUATION FIXED AT 0,
 # AND THE VALUE OF THE PERSONNAL PSEUDO-GUESSING FIXED AT 0.30.
 # IT COULD BE TYPICAL OF PLAGIARISM BEHAVIOR.
 nItems <- 40
 a      <- rep(1.702,nItems); b <- seq(-5,5,length=nItems)
 c      <- rep(0,nItems); d <- rep(1,nItems)
 nSubjects <- 1; rep <- 100
 theta     <- seq(-1,-1,length=nSubjects)
 S         <- runif(n=nSubjects,min=0.0,max=0.0)
 C         <- runif(n=nSubjects,min=0.3,max=0.3)
 D         <- runif(n=nSubjects,min=0,max=0)
 set.seed(seed = 100)
 X         <- ggrm4pl(n=nItems, rep=rep,
                      theta=theta, S=S, C=C, D=D,
                      s=1/a, b=b,c=c,d=d)

## Results for each subjects for each models
 essai <- m4plModelShow(X, b=b, s=1/a, c=c, d=d, m=0, prior="uniform")

## Means of choosen variables from m4plModleShow previous call
 round(meanModels(essai, statistic=c("LL","BIC","T","C")), 2)

## Which model(s) are the best for each subject (LL criteria)
 res <- modelChoose(essai, criteria = "LL", tol = 0.2); res
 
## Which model(s) are the best for each of the first 20 subjects (BIC criteria)
 res <- modelChoose(essai[which(essai$ID < 20) ,], criteria="BIC"); res

## A look at the 15th subject parameters estimation for each models
 essai[which(essai$ID == 15) ,]
 
## Add the logical critLL variable to the data frame
 criteria <- "LL"
 res1    <- modelChooseAdd(essai, criteria=criteria)
 # Create a charcater string composed from "crit" and criteria
 crit    <- paste("crit",criteria,sep="")
 # To Show only the lines where the models is choosen according to critLL
 res2    <- res1[which(res1[crit] == TRUE),]; mean(res2$T);sd(res2$T,na.rm=TRUE);res2
 # Give the mean for choosen variables from m4plModelShow
 meanModels(essai, statistic=c("LL","BIC","T","SeT","S","C","D"))
 # Tabulate only the choosen models
 table(res2$MODEL)
 # Show the information for the subject for which the model TSCD was choosen
 res2[which(res2$MODEL == "TSCD") ,]
 # Show only the results for the 5th subject, the with the TSCD model choosen
 res1[which(res1$ID == 5) ,]
 # Same, but without critLL
 essai[which(essai$ID == 5) ,]

## Simulation whith cheating
 # High proficiency students responding at random to 20
 # easiest ones)
 XHProficiency             <- X
 pourcHasard               <- 0.20; nHasard <- abs(dim(X)[2]*pourcHasard)
 XHProficiency[,1:nHasard] <- rbinom(dim(X)[1]*nHasard, 1, 0.5)
 XHProficiency             <- m4plModelShow(XHProficiency, b=b, s=1/a, c=c, d=d,
                                            m=0, prior="uniform")
 XHProficiency             <- modelChooseAdd(XHProficiency, criteria=criteria)
 XHProficiency             <- XHProficiency[which(XHProficiency$critLL == TRUE),]
 mean(XHProficiency$T);sd(XHProficiency$T,na.rm=TRUE);XHProficiency[1:10,]
 meanModels(XHProficiency, statistic=c("LL","BIC","T","SeT","S","C","D"))
 table(XHProficiency$MODEL)
 
 # Low proficiency students responding at random to 20
 # (more difficult ones)
 XLProficiency                             <- X
 pourcHasard                               <- 0.20
 nHasard                                   <- abs(dim(X)[2]*pourcHasard)
 XLProficiency[,(nItems-nHasard+1):nItems] <- rbinom(dim(X)[1]*nHasard, 1, 0.5)
 XLProficiency                             <- m4plModelShow(XLProficiency, b=b,
                                              s=1/a, c=c, d=d, m=0, prior="uniform")
 XLProficiency                             <- modelChooseAdd(XLProficiency,
                                                             criteria=criteria)
 XLProficiency <- XLProficiency[which(XLProficiency$critLL == TRUE),]
 mean(XLProficiency$T);sd(XLProficiency$T,na.rm=TRUE);XLProficiency[1:10,]
 meanModels(XLProficiency, statistic=c("LL","BIC","T","SeT","S","C","D"))
 table(XLProficiency$MODEL)

 # High proficiency students giving incorrect responses to 20
 # (easiest ones)
 XHProficiency             <- X
 pourcCheat                <- 0.20; nCheat  <- abs(dim(X)[2]*pourcCheat)
 XHProficiency[,1:nCheat]  <- rep(0, dim(X)[1]*dim(X)[2]*pourcCheat)
 XHProficiency             <- m4plModelShow(XHProficiency, b=b, s=1/a, c=c, d=d,
                                            m=0, prior="uniform")
 XHProficiency             <- modelChooseAdd(XHProficiency, criteria=criteria)
 XHProficiency             <- XHProficiency[which(XHProficiency$critLL == TRUE),]
 mean(XHProficiency$T);sd(XHProficiency$T,na.rm=TRUE);XHProficiency[1:10,]
 meanModels(XHProficiency, statistic=c("LL","BIC","T","SeT","S","C","D"))
 table(XHProficiency$MODEL)
 
 # Low proficiency students giving correct responses to 20
 # (more difficult ones)
 XLProficiency                             <- X
 pourcCheat                                <- 0.20
 nCheat                                    <- abs(dim(X)[2]*pourcCheat);
 XLProficiency[,(nItems-nCheat+1):nItems]  <- rep(1, dim(X)[1]*dim(X)[2]*pourcCheat)
 XLProficiency                             <- m4plModelShow(XLProficiency, b=b,
                                              s=1/a, c=c, d=d, m=0, prior="uniform")
 XLProficiency                             <- modelChooseAdd(XLProficiency,
                                                             criteria=criteria)
 XLProficiency <- XLProficiency[which(XLProficiency$critLL == TRUE),]
 mean(XLProficiency$T);sd(XLProficiency$T,na.rm=TRUE);XLProficiency[1:10,]
 meanModels(XLProficiency, statistic=c("LL","BIC","T","SeT","S","C","D"))
 table(XLProficiency$MODEL)
 
## End(Not run)