irtProb (version 1.2)

utilities: Utility Functions

Description

Some functions to help in the generation of binary data or to interpret m4pl models results. rmultinomial is used to draw n values from a x vector of values according to a multinomial probability distribution. rmultinomial is different from the stats::rmultinom function in that it return only the value of the selected draw and not a binary vector corresponding tho the position of the draw

propCorrect computes the expected proportion of correct responses to a test according to the item and person parameters of a m4pl models.

Usage

rmultinomial(x, n = 100, prob = rep(1, length(x))/length(x))
 propCorrect(theta, S, C, D, s, b, c, d)

Arguments

x

numeric: vector of values to draw from.

n

numeric: number of draws.

prob

numeric: probability assigned to each value of the x vector. Default to equiprobability.

theta

numeric; vector of person proficiency ($\theta$) levels scaled on a normal z score.

S

numeric: positive vector of personal fluctuation parameters ($\sigma$).

C

numeric: positive vector of personal pseudo-guessing parameters ($\chi$, a probability between 0 and 1).

D

numeric: positive vector of personal inattention parameters ($\delta$, a probability between 0 and 1).

s

numeric: positive vector of item fluctuation parameters.

b

numeric: vector of item difficulty parameters.

c

numeric: positive vector of item pseudo-guessing parameters (a probability between 0 and 1).

d

numeric: positive vector of item inattention parameters (a probability between 0 and 1).

Value

propCorrect

numeric:

return n draws from a multinimial distribution.

rmultinomial

numeric:

return the expected proportion of correcte responses to a test.

See Also

Multinom

Examples

## Not run: 
# ## Comparison of the results from the multinomial and multinom functions
#  x <- c(1,4,9)
#  # Values draws
#  rmultinomial(x=x, n=10)
#  # Binary vectors draws
#  rmultinom(n=10, size = 1, prob=rep(1,length(x))/length(x))
# 
# ## Computation of the expected proportion of correct responses varying values
#  # of theta (-3 to 3) and of pseudo-guessing (C = 0.0 to 0.6) person parameters
#  nItems  <- 40
#  a       <- rep(1.702,nItems); b <- seq(-3,3,length=nItems)
#  c       <- rep(0,nItems); d <- rep(1,nItems)
#  theta   <- seq(-3.0, 3.0, by=1.0)
#  C       <- seq( 0.0, 1.0, by=0.1)
#  D       <- S <- 0
#  
#  results <- matrix(NA, ncol=length(C), nrow=length(theta))
#  colnames(results) <- C; rownames(results) <- theta
#  for (i in (1:length(theta))) {
#   results[i,] <- propCorrect(theta = theta[i], S = 0, C = C, D = 0,
#                              s = 1/a, b = b, c = c, d = d)
#   }
#   round(results, 2)
# 
# ## Computation of the expected proportion of correct responses varying values
#  # of theta (-3 to 3) and of pseudo-guessing (C = 0.0 to 0.6) person parameters
#  # if we choose the correct modelisation itegrating the C pseudo-guessing papameter
#  # and if we choose according to a model selection by LL criteria
#  nItems <- 40
#  a      <- rep(1.702,nItems); b <- seq(-3,3,length=nItems)
#  c      <- rep(0,nItems); d <- rep(1,nItems)
#  nSubjects <- 300
#  theta     <- rmultinomial(c(-1), nSubjects)
#  S         <- rmultinomial(c(0), nSubjects)
#  C         <- rmultinomial(seq(0,0.9,by=0.1), nSubjects)
#  D         <- rmultinomial(c(0), nSubjects)
#  set.seed(seed = 100)
#  X         <- ggrm4pl(n=nItems, rep=1,
#                       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")
#  total     <- rowSums(X)
#  pourcent  <- total/nItems * 100
#  pCorrect  <- numeric(dim(essai)[1])
#  for ( i in (1:dim(essai)[1]))
#   pCorrect[i] <- propCorrect(essai$T[i],0,0,0,s=1/a,b=b,c=c,d=d)
#  resultLL  <- summary(essai, report="add", criteria="LL")
#  resultLL  <- data.frame(resultLL, theta=theta, TS=S, TC=C, errorT=resultLL$T - theta,
#                          total=total, pourcent=pourcent, tpcorrect=pCorrect)
#  # If the only theta model is badly choosen
#  results <- resultLL[which(resultLL$MODEL == "T" ),]
#  byStats <- "TC"; ofStats <- "tpcorrect"
#  MeansByThetaT <- cbind(
#   aggregate(results[ofStats], by=list(Theta=factor(results[,byStats]) ),
#             mean, na.rm=TRUE),
#   aggregate(results[ofStats], by=list(Theta=factor(results[,byStats])), sd, na.rm=TRUE),
#   aggregate(results["SeT"], by=list(Theta=factor(results[,byStats])), mean, na.rm=TRUE),
#   aggregate(results[ofStats], by=list(theta=factor(results[,byStats])), length)
#   )[,-c(3,5,7)]
#   names(MeansByThetaT) <- c("C", "pCorrect", "seE", "SeT", "n")
#   MeansByThetaT[,-c(1,4,5)] <- round(MeansByThetaT[,-c(1,4,5)], 2)
#   MeansByThetaT[,-c(4,5)]
#  # Only for the TC model
#  results <- resultLL[which(resultLL$MODEL == "TC" ),]
#  byStats <- "TC"; ofStats <- "tpcorrect"
#  MeansByThetaC <- cbind(
#   aggregate(results[ofStats], by=list(Theta=factor(results[,byStats]) ),
#             mean, na.rm=TRUE),
#   aggregate(results[ofStats], by=list(Theta=factor(results[,byStats])), sd, na.rm=TRUE),
#   aggregate(results["SeT"], by=list(Theta=factor(results[,byStats])), mean, na.rm=TRUE),
#   aggregate(results[ofStats], by=list(theta=factor(results[,byStats])), length)
#   )[,-c(3,5,7)]
#   names(MeansByThetaC) <- c("C", "pCorrect", "seE", "SeT", "n")
#   MeansByThetaC[,-c(1,4,5)] <- round(MeansByThetaC[,-c(1,4,5)], 2)
#   MeansByThetaC[,-c(4,5)]
#  # For the model choosen according to the LL criteria
#  results <- resultLL[which(resultLL$critLL == TRUE),]
#  byStats <- "TC"; ofStats <- "tpcorrect"
#  MeansByThetaLL <- cbind(
#   aggregate(results[ofStats], by=list(Theta=factor(results[,byStats]) ),
#             mean, na.rm=TRUE),
#   aggregate(results[ofStats], by=list(Theta=factor(results[,byStats])), sd, na.rm=TRUE),
#   aggregate(results["SeT"], by=list(Theta=factor(results[,byStats])), mean, na.rm=TRUE),
#   aggregate(results[ofStats], by=list(theta=factor(results[,byStats])), length)
#   )[,-c(3,5,7)]
#   names(MeansByThetaLL) <- c("C", "pCorrect", "seE", "SeT", "n")
#   MeansByThetaLL[,-c(1,4,5)] <- round(MeansByThetaLL[,-c(1,4,5)], 2)
#   MeansByThetaLL[,-c(4,5)]
#   # Grapical comparison of the estimation of the 
#   # by means of the 3 preceeding models
#   plot(MeansByThetaT$pCorrect   ~ levels(MeansByThetaT$C),  type="l", lty=1,
#        xlab="Pseudo-Guessing", ylab="% of Correct Responses")
#   lines(MeansByThetaC$pCorrect  ~ levels(MeansByThetaC$C),  type="l", lty=2)
#   lines(MeansByThetaLL$pCorrect ~ levels(MeansByThetaLL$C), type="l", lty=3)
#   text(x=0.60, y=0.80, "Without correction", cex=0.8)
#   text(x=0.50, y=0.38, "Without Knowledge of the Correct Model", cex=0.8)
#   text(x=0.65, y=0.50, "With Knowledge of the Correct Model", cex=0.8)
#  ## End(Not run)