binom.score: Binomial Scores

In vthorrf/CIRM: Procedures for IRT modeling

Description

Estimate theta parameters of binomial distributions as scores for item easiness and person ability.

Usage

latent.vs(x,levels,what="item",method="freq")

Arguments

x	An data set.
levels	How many levels does the scale has.
what	Says if it estimates bias for "person" or for "item".
method	The statistical framework of the binomial test. "freq" if frequentist is desired. "bayes" if bayesian is desired. "bsp" if semiparametric bayesian is desired.

Value

A list that depends if Bayesian or frequentist method are used. The frequentist contains the following components:

easi or abil	A vector of estimates of easiness or ability, depending on the desired outcome.
sd	The standard deviation of the estimates.
bic	BIC fit index for each estimate.
aic	AIC fit index for each estimate.

The parametric Bayesian contains the following components:

easi or abil	A vector of estimates of easiness or ability, depending on the desired outcome.
sd	The standard deviation of the estimates.
dic	DIC fit index for each estimate.

The semiparametric Bayesian contains the following components:

easi or abil	A vector of estimates of easiness or ability, depending on the desired outcome.
sd	The standard deviation of the estimates.
ess	Effective sample size; the sample size adjusted for autocorrelation.

Examples

### Random Data with 100 observations and 10 variables with 5 levels of response
n = 100; v = 10; l = 5
Data <- matrix(NA,nrow=n,ncol=v)
psi <- seq(length=n,-3,3); theta <- seq(length=v,-3,3); eta <- matrix(NA,ncol=v,nrow=n)
seed <- matrix(c(1:(n*v)),nrow=n,ncol=v)
for(i in 1:n)
{
  for(j in 1:v)
  {
    set.seed(seed[i,j])
    eta[i,j] <- exp(psi[i]-theta[j])/(1+exp(psi[i]-theta[j]))
    Data[i,j] <- rbinom(1,l-1,eta[i,j])
  }
}
rm(n,v,eta,seed,i,j)

### Create Frequentist Scores
AbilF <- latent.vs(Data,l,what="person",method="freq")
Af <- AbilF$abil
EasiF <- latent.vs(Data,l,what="item",method="freq")
Ef <- EasiF$easi

### Create Bayesian Scores
AbilB <- latent.vs(Data,l,what="person",method="bayes")
Ab <- AbilB$abil
EasiB <- latent.vs(Data,l,what="item",method="bayes")
Eb <- EasiB$easi

### Create semiparametric Bayesian Scores
AbilS <- latent.vs(Data,l,what="person",method="bsp")
As <- AbilS$abil
EasiS <- latent.vs(Data,l,what="item",method="bsp")
Es <- EasiS$easi

### Compare
cor(data.frame(cbind(Af,Ab,As,psi)))
plot(data.frame(cbind(Af,Ab,As,psi)))

cor(data.frame(cbind(Ef,Eb,Es,theta)))
plot(data.frame(cbind(Ef,Eb,Es,theta)))

vthorrf/CIRM documentation built on Nov. 5, 2019, 12:05 p.m.