R/pcm.R
In vthorrf/birm: Fitting Bayesian Item Response Models
Defines functions
pcm
Documented in
pcm
pcm <- function(x, levels=NULL, p=1, method="LA", Iters=100, Smpl=1000, Thin=1,
a.s=0.234, temp=1e-2, tmax=NULL, algo="GA", seed=666, Interval=1e-8){
### Start====
set.seed(seed)
#require(LaplacesDemon)
#require(compiler)
#require(parallel)
#require(tidyr)
#require(matrixStats)
CPUs = detectCores(all.tests = FALSE, logical = TRUE) - 1
if(CPUs == 0) CPUs = 1
### Convert data to long format====
if (is.null(levels)) levels <- max(x)
lonlong <- gather(data.frame(x), "item", "resp", colnames(x), factor_key=TRUE)
data_long <- data.frame(ID=rep(1:nrow(x), times=ncol(x)),lonlong)
### Choose model====
if (p == 1) {
## Partial Credit Model====
# Assemble data list
if (method == "MAP") {
mon.names <- "LL"
} else { mon.names <- "LP" }
parm.names <- as.parm.names(list( theta=rep(0,nrow(x)), b=rep(0,ncol(x) * levels) ))
pos.theta <- grep("theta", parm.names)
pos.b <- grep("b", parm.names)
PGF <- function(Data) {
theta <- rnorm(Data$n)
b <- rnorm(Data$v * Data$levels)
return(c(theta, b))
}
MyData <- list(parm.names=parm.names, mon.names=mon.names,
PGF=PGF, X=data_long, n=nrow(x), v=ncol(x), levels=levels,
pos.theta=pos.theta, pos.b=pos.b)
is.data(MyData)
# Model
Model <- function(parm, Data){
## Prior parameters
theta <- parm[Data$pos.theta]
b <- parm[Data$pos.b]
### Log-Priors
theta.prior <- sum(dnorm(theta, mean=0, sd=1, log=T))
b.prior <- sum(dnorm(b , mean=0, sd=1, log=T))
Lpp <- theta.prior + b.prior
### Log-Likelihood
thetaLL <- rep(theta, times=Data$v)
BsL <- rep(b , each=Data$n)
bLL <- matrix(BsL , nrow=nrow(Data$X), ncol=Data$levels)
eta <- thetaLL - bLL
exp.psum <- exp(matrixStats::rowCumsums(eta))
IRF <- exp.psum / rowSums(exp.psum)
IRF[which(IRF == 1)] <- 1 - 1e-7
LL <- sum( dcat(Data$X[,3], p=IRF, log=T) )
### Log-Posterior
LP <- LL + Lpp
### Estimates
yhat <- tryCatch(qcat(rep(.5, nrow(IRF)), p=IRF),
error=function(e) {
qbinom(rep(.5, nrow(IRF)), Data$levels-1,
rowMeans(IRF)) + min(Data$X[,3])
})
### Output
Modelout <- list(LP=LP, Dev=-2*LL, Monitor=LP, yhat=yhat, parm=parm)
return(Modelout)
}
Model <- compiler::cmpfun(Model)
Initial.Values <- GIV(Model, MyData, PGF=T)
is.model(Model, Initial.Values, MyData)
is.bayesian(Model, Initial.Values, MyData)
} else if (p == 2) {
## Generalized Partial Credit Model====
# Assemble data list
if (method == "MAP") {
mon.names <- "LL"
} else { mon.names <- "LP" }
parm.names <- as.parm.names(list( theta=rep(0,nrow(x)), b=rep(0,ncol(x) * levels),
Ds=rep(0,ncol(x)) ))
pos.theta <- grep("theta", parm.names)
pos.b <- grep("b", parm.names)
pos.Ds <- grep("Ds", parm.names)
PGF <- function(Data) {
theta <- rnorm(Data$n)
b <- rnorm(Data$v * Data$levels)
Ds <- rlnorm(Data$v)
return(c(theta, b, Ds))
}
MyData <- list(parm.names=parm.names, mon.names=mon.names,
PGF=PGF, X=data_long, n=nrow(x), v=ncol(x), levels=levels,
pos.theta=pos.theta, pos.b=pos.b, pos.Ds=pos.Ds)
is.data(MyData)
# Model
Model <- function(parm, Data){
## Prior parameters
theta <- parm[Data$pos.theta]
b <- parm[Data$pos.b]
Ds <- interval( parm[Data$pos.Ds], 1e-100, Inf )
parm[Data$pos.Ds] <- Ds
### Log-Priors
theta.prior <- sum(dnorm(theta, mean=0 , sd=1 , log=T))
b.prior <- sum(dnorm(b , mean=0 , sd=1 , log=T))
Ds.prior <- sum(dlnorm(Ds , meanlog=0, sdlog=1, log=T))
Lpp <- theta.prior + b.prior + Ds.prior
### Log-Likelihood
thetaLL <- rep(theta, times=Data$v)
BsL <- rep(b , each=Data$n)
bLL <- matrix(BsL , nrow=nrow(Data$X), ncol=Data$levels)
DLL <- rep(Ds , each=Data$n)
eta <- DLL * (thetaLL - bLL)
exp.psum <- exp(matrixStats::rowCumsums(eta))
IRF <- exp.psum / rowSums(exp.psum)
IRF[which(IRF == 1)] <- 1 - 1e-7
LL <- sum( dcat(Data$X[,3], p=IRF, log=T) )
### Log-Posterior
LP <- LL + Lpp
### Estimates
yhat <- tryCatch(qcat(rep(.5, nrow(IRF)), p=IRF),
error=function(e) {
qbinom(rep(.5, nrow(IRF)), Data$levels-1,
rowMeans(IRF)) + min(Data$X[,3])
})
### Output
Modelout <- list(LP=LP, Dev=-2*LL, Monitor=LP, yhat=yhat, parm=parm)
return(Modelout)
}
Model <- compiler::cmpfun(Model)
Initial.Values <- GIV(Model, MyData, PGF=T)
is.model(Model, Initial.Values, MyData)
is.bayesian(Model, Initial.Values, MyData)
} else warning("Unknow model :(")
### Run!====
if (method=="VB") {
## Variational Bayes====
#Iters=1000; Samples=1000
Iters=Iters; Smpl=Smpl
Fit <- VariationalBayes(Model=Model, parm=Initial.Values, Data=MyData,
Covar=NULL, Interval=1e-6, Iterations=Iters,
Method="Salimans2", Samples=Smpl, sir=TRUE,
Stop.Tolerance=1e-5, CPUs=CPUs, Type="PSOCK")
} else if (method=="LA") {
## Laplace Approximation====
#Iters=100; Samples=1000
Iters=Iters; Smpl=Smpl
Fit <- LaplaceApproximation(Model, parm=Initial.Values, Data=MyData,
Interval=1e-6, Iterations=Iters,
Method="SPG", Samples=Smpl, sir=TRUE,
CovEst="Identity", Stop.Tolerance=1e-5,
CPUs=CPUs, Type="PSOCK")
} else if (method=="MCMC") {
## Hit-And-Run Metropolis====
Iters=Iters; Status=Iters/10; Thin=Thin; A=a.s
Fit <- LaplacesDemon(Model=Model, Data=MyData,
Initial.Values=Initial.Values,
Covar=NULL, Iterations=Iters,
Status=Status, Thinning=Thin,
Algorithm="HARM",
Specs=list(alpha.star=A, B=NULL))
} else if (method=="PMC") {
## Population Monte Carlo====
#Iters=10; Thin=11; Smpl=1000
Iters=Iters; Smpl=Smpl; Thin=Thin
Fit <- PMC(Model=Model, Data=MyData, Initial.Values=Initial.Values,
Covar=NULL, Iterations=Iters, Thinning=Thin, alpha=NULL,
M=2, N=Smpl, nu=1e3, CPUs=CPUs, Type="PSOCK")
} else if (method=="IQ") {
## Iterative Quadrature====
#Iters=100; Smpl=1000
Iters=Iters; Smpl=Smpl
Fit <- IterativeQuadrature(Model=Model, parm=Initial.Values,
Data=MyData, Covar=NULL,
Iterations=Iters, Algorithm="CAGH",
Specs=list(N=3, Nmax=10, Packages=NULL,
Dyn.libs=NULL),
Samples=Smpl, sir=T,
Stop.Tolerance=c(1e-5,1e-15),
Type="PSOCK", CPUs=CPUs)
} else if (method=="MAP") {
## Maximum a Posteriori====
#Iters=100; Smpl=1000
Iters=Iters; Status=Iters/10
Fit <- MAP(Model=Model, parm=Initial.Values, Data=MyData, algo=algo, seed=seed,
maxit=Iters, temp=temp, tmax=tmax, REPORT=Status, Interval=Interval)
} else {stop('Unknown optimization method.')}
### Results====
if (p == 1) {
if (method=="MAP") {
abil = Fit[["Model"]]$parm[pos.theta]
diff = matrix(Fit[["Model"]]$parm[pos.b], nrow=ncol(x))
rownames(diff) = colnames(x)
colnames(diff) = paste("Answer_Key",1:levels,sep="_")
FI = Fit$FI
Results <- list("Data"=MyData,"Fit"=Fit,"Model"=Model,
'abil'=abil,'diff'=diff,'FitIndexes'=FI)
} else {
if (method=="PMC") {
abil = Fit$Summary[grep("theta", rownames(Fit$Summary), fixed=TRUE),1]
diff = matrix(Fit$Summary[grep("b", rownames(Fit$Summary), fixed=TRUE),1],
nrow=ncol(x))
} else {
abil = Fit$Summary1[grep("theta", rownames(Fit$Summary1), fixed=TRUE),1]
diff = matrix(Fit$Summary1[grep("b", rownames(Fit$Summary1), fixed=TRUE),1],
nrow=ncol(x))
}
rownames(diff) = colnames(x)
colnames(diff) = paste("Answer_Key",1:levels,sep="_")
Dev <- Fit$Deviance
mDD <- Dev - min(Dev)
pDD <- Dev[min(which(mDD < 100)):length(Dev)]
pV <- var(pDD)/2
Dbar <- mean(pDD)
#Dbar = mean(Dev)
#pV <- var(Dev)/2
DIC = list(DIC=Dbar + pV, Dbar=Dbar, pV=pV)
Results <- list("Data"=MyData,"Fit"=Fit,"Model"=Model,
'abil'=abil,'diff'=diff,'DIC'=DIC)
}
} else if (p == 2) {
if (method=="MAP") {
abil = Fit[["Model"]]$parm[pos.theta]
diff = matrix(Fit[["Model"]]$parm[pos.b], nrow=ncol(x))
rownames(diff) = colnames(x)
colnames(diff) = paste("Answer_Key",1:levels,sep="_")
disc = Fit[["Model"]]$parm[pos.Ds]
FI = Fit$FI
Results <- list("Data"=MyData,"Fit"=Fit,"Model"=Model,
'abil'=abil,'diff'=diff,"disc"=disc,'FitIndexes'=FI)
} else {
if (method=="PMC") {
abil = Fit$Summary[grep("theta", rownames(Fit$Summary), fixed=TRUE),1]
diff = matrix(Fit$Summary[grep("b", rownames(Fit$Summary), fixed=TRUE),1],
nrow=ncol(x))
disc = Fit$Summary[grep("Ds", rownames(Fit$Summary), fixed=TRUE),1]
} else {
abil = Fit$Summary1[grep("theta", rownames(Fit$Summary1), fixed=TRUE),1]
diff = matrix(Fit$Summary1[grep("b", rownames(Fit$Summary1), fixed=TRUE),1],
nrow=ncol(x))
disc = Fit$Summary1[grep("Ds", rownames(Fit$Summary1), fixed=TRUE),1]
}
rownames(diff) = colnames(x)
colnames(diff) = paste("Answer_Key",1:levels,sep="_")
Dev <- Fit$Deviance
mDD <- Dev - min(Dev)
pDD <- Dev[min(which(mDD < 100)):length(Dev)]
pV <- var(pDD)/2
Dbar <- mean(pDD)
#Dbar = mean(Dev)
#pV <- var(Dev)/2
DIC = list(DIC=Dbar + pV, Dbar=Dbar, pV=pV)
Results <- list("Data"=MyData,"Fit"=Fit,"Model"=Model,
'abil'=abil,'diff'=diff,"disc"=disc,'DIC'=DIC)
}
} else warning("Can't return any result :P")
return(Results)
}
vthorrf/birm documentation built on Dec. 24, 2021, 2:22 a.m.
R Package Documentation
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Defines functions pcm
Documented in pcm
pcm <- function(x, levels=NULL, p=1, method="LA", Iters=100, Smpl=1000, Thin=1,
a.s=0.234, temp=1e-2, tmax=NULL, algo="GA", seed=666, Interval=1e-8){
### Start====
set.seed(seed)
#require(LaplacesDemon)
#require(compiler)
#require(parallel)
#require(tidyr)
#require(matrixStats)
CPUs = detectCores(all.tests = FALSE, logical = TRUE) - 1
if(CPUs == 0) CPUs = 1
### Convert data to long format====
if (is.null(levels)) levels <- max(x)
lonlong <- gather(data.frame(x), "item", "resp", colnames(x), factor_key=TRUE)
data_long <- data.frame(ID=rep(1:nrow(x), times=ncol(x)),lonlong)
### Choose model====
if (p == 1) {
## Partial Credit Model====
# Assemble data list
if (method == "MAP") {
mon.names <- "LL"
} else { mon.names <- "LP" }
parm.names <- as.parm.names(list( theta=rep(0,nrow(x)), b=rep(0,ncol(x) * levels) ))
pos.theta <- grep("theta", parm.names)
pos.b <- grep("b", parm.names)
PGF <- function(Data) {
theta <- rnorm(Data$n)
b <- rnorm(Data$v * Data$levels)
return(c(theta, b))
}
MyData <- list(parm.names=parm.names, mon.names=mon.names,
PGF=PGF, X=data_long, n=nrow(x), v=ncol(x), levels=levels,
pos.theta=pos.theta, pos.b=pos.b)
is.data(MyData)
# Model
Model <- function(parm, Data){
## Prior parameters
theta <- parm[Data$pos.theta]
b <- parm[Data$pos.b]
### Log-Priors
theta.prior <- sum(dnorm(theta, mean=0, sd=1, log=T))
b.prior <- sum(dnorm(b , mean=0, sd=1, log=T))
Lpp <- theta.prior + b.prior
### Log-Likelihood
thetaLL <- rep(theta, times=Data$v)
BsL <- rep(b , each=Data$n)
bLL <- matrix(BsL , nrow=nrow(Data$X), ncol=Data$levels)
eta <- thetaLL - bLL
exp.psum <- exp(matrixStats::rowCumsums(eta))
IRF <- exp.psum / rowSums(exp.psum)
IRF[which(IRF == 1)] <- 1 - 1e-7
LL <- sum( dcat(Data$X[,3], p=IRF, log=T) )
### Log-Posterior
LP <- LL + Lpp
### Estimates
yhat <- tryCatch(qcat(rep(.5, nrow(IRF)), p=IRF),
error=function(e) {
qbinom(rep(.5, nrow(IRF)), Data$levels-1,
rowMeans(IRF)) + min(Data$X[,3])
})
### Output
Modelout <- list(LP=LP, Dev=-2*LL, Monitor=LP, yhat=yhat, parm=parm)
return(Modelout)
}
Model <- compiler::cmpfun(Model)
Initial.Values <- GIV(Model, MyData, PGF=T)
is.model(Model, Initial.Values, MyData)
is.bayesian(Model, Initial.Values, MyData)
} else if (p == 2) {
## Generalized Partial Credit Model====
# Assemble data list
if (method == "MAP") {
mon.names <- "LL"
} else { mon.names <- "LP" }
parm.names <- as.parm.names(list( theta=rep(0,nrow(x)), b=rep(0,ncol(x) * levels),
Ds=rep(0,ncol(x)) ))
pos.theta <- grep("theta", parm.names)
pos.b <- grep("b", parm.names)
pos.Ds <- grep("Ds", parm.names)
PGF <- function(Data) {
theta <- rnorm(Data$n)
b <- rnorm(Data$v * Data$levels)
Ds <- rlnorm(Data$v)
return(c(theta, b, Ds))
}
MyData <- list(parm.names=parm.names, mon.names=mon.names,
PGF=PGF, X=data_long, n=nrow(x), v=ncol(x), levels=levels,
pos.theta=pos.theta, pos.b=pos.b, pos.Ds=pos.Ds)
is.data(MyData)
# Model
Model <- function(parm, Data){
## Prior parameters
theta <- parm[Data$pos.theta]
b <- parm[Data$pos.b]
Ds <- interval( parm[Data$pos.Ds], 1e-100, Inf )
parm[Data$pos.Ds] <- Ds
### Log-Priors
theta.prior <- sum(dnorm(theta, mean=0 , sd=1 , log=T))
b.prior <- sum(dnorm(b , mean=0 , sd=1 , log=T))
Ds.prior <- sum(dlnorm(Ds , meanlog=0, sdlog=1, log=T))
Lpp <- theta.prior + b.prior + Ds.prior
### Log-Likelihood
thetaLL <- rep(theta, times=Data$v)
BsL <- rep(b , each=Data$n)
bLL <- matrix(BsL , nrow=nrow(Data$X), ncol=Data$levels)
DLL <- rep(Ds , each=Data$n)
eta <- DLL * (thetaLL - bLL)
exp.psum <- exp(matrixStats::rowCumsums(eta))
IRF <- exp.psum / rowSums(exp.psum)
IRF[which(IRF == 1)] <- 1 - 1e-7
LL <- sum( dcat(Data$X[,3], p=IRF, log=T) )
### Log-Posterior
LP <- LL + Lpp
### Estimates
yhat <- tryCatch(qcat(rep(.5, nrow(IRF)), p=IRF),
error=function(e) {
qbinom(rep(.5, nrow(IRF)), Data$levels-1,
rowMeans(IRF)) + min(Data$X[,3])
})
### Output
Modelout <- list(LP=LP, Dev=-2*LL, Monitor=LP, yhat=yhat, parm=parm)
return(Modelout)
}
Model <- compiler::cmpfun(Model)
Initial.Values <- GIV(Model, MyData, PGF=T)
is.model(Model, Initial.Values, MyData)
is.bayesian(Model, Initial.Values, MyData)
} else warning("Unknow model :(")
### Run!====
if (method=="VB") {
## Variational Bayes====
#Iters=1000; Samples=1000
Iters=Iters; Smpl=Smpl
Fit <- VariationalBayes(Model=Model, parm=Initial.Values, Data=MyData,
Covar=NULL, Interval=1e-6, Iterations=Iters,
Method="Salimans2", Samples=Smpl, sir=TRUE,
Stop.Tolerance=1e-5, CPUs=CPUs, Type="PSOCK")
} else if (method=="LA") {
## Laplace Approximation====
#Iters=100; Samples=1000
Iters=Iters; Smpl=Smpl
Fit <- LaplaceApproximation(Model, parm=Initial.Values, Data=MyData,
Interval=1e-6, Iterations=Iters,
Method="SPG", Samples=Smpl, sir=TRUE,
CovEst="Identity", Stop.Tolerance=1e-5,
CPUs=CPUs, Type="PSOCK")
} else if (method=="MCMC") {
## Hit-And-Run Metropolis====
Iters=Iters; Status=Iters/10; Thin=Thin; A=a.s
Fit <- LaplacesDemon(Model=Model, Data=MyData,
Initial.Values=Initial.Values,
Covar=NULL, Iterations=Iters,
Status=Status, Thinning=Thin,
Algorithm="HARM",
Specs=list(alpha.star=A, B=NULL))
} else if (method=="PMC") {
## Population Monte Carlo====
#Iters=10; Thin=11; Smpl=1000
Iters=Iters; Smpl=Smpl; Thin=Thin
Fit <- PMC(Model=Model, Data=MyData, Initial.Values=Initial.Values,
Covar=NULL, Iterations=Iters, Thinning=Thin, alpha=NULL,
M=2, N=Smpl, nu=1e3, CPUs=CPUs, Type="PSOCK")
} else if (method=="IQ") {
## Iterative Quadrature====
#Iters=100; Smpl=1000
Iters=Iters; Smpl=Smpl
Fit <- IterativeQuadrature(Model=Model, parm=Initial.Values,
Data=MyData, Covar=NULL,
Iterations=Iters, Algorithm="CAGH",
Specs=list(N=3, Nmax=10, Packages=NULL,
Dyn.libs=NULL),
Samples=Smpl, sir=T,
Stop.Tolerance=c(1e-5,1e-15),
Type="PSOCK", CPUs=CPUs)
} else if (method=="MAP") {
## Maximum a Posteriori====
#Iters=100; Smpl=1000
Iters=Iters; Status=Iters/10
Fit <- MAP(Model=Model, parm=Initial.Values, Data=MyData, algo=algo, seed=seed,
maxit=Iters, temp=temp, tmax=tmax, REPORT=Status, Interval=Interval)
} else {stop('Unknown optimization method.')}
### Results====
if (p == 1) {
if (method=="MAP") {
abil = Fit[["Model"]]$parm[pos.theta]
diff = matrix(Fit[["Model"]]$parm[pos.b], nrow=ncol(x))
rownames(diff) = colnames(x)
colnames(diff) = paste("Answer_Key",1:levels,sep="_")
FI = Fit$FI
Results <- list("Data"=MyData,"Fit"=Fit,"Model"=Model,
'abil'=abil,'diff'=diff,'FitIndexes'=FI)
} else {
if (method=="PMC") {
abil = Fit$Summary[grep("theta", rownames(Fit$Summary), fixed=TRUE),1]
diff = matrix(Fit$Summary[grep("b", rownames(Fit$Summary), fixed=TRUE),1],
nrow=ncol(x))
} else {
abil = Fit$Summary1[grep("theta", rownames(Fit$Summary1), fixed=TRUE),1]
diff = matrix(Fit$Summary1[grep("b", rownames(Fit$Summary1), fixed=TRUE),1],
nrow=ncol(x))
}
rownames(diff) = colnames(x)
colnames(diff) = paste("Answer_Key",1:levels,sep="_")
Dev <- Fit$Deviance
mDD <- Dev - min(Dev)
pDD <- Dev[min(which(mDD < 100)):length(Dev)]
pV <- var(pDD)/2
Dbar <- mean(pDD)
#Dbar = mean(Dev)
#pV <- var(Dev)/2
DIC = list(DIC=Dbar + pV, Dbar=Dbar, pV=pV)
Results <- list("Data"=MyData,"Fit"=Fit,"Model"=Model,
'abil'=abil,'diff'=diff,'DIC'=DIC)
}
} else if (p == 2) {
if (method=="MAP") {
abil = Fit[["Model"]]$parm[pos.theta]
diff = matrix(Fit[["Model"]]$parm[pos.b], nrow=ncol(x))
rownames(diff) = colnames(x)
colnames(diff) = paste("Answer_Key",1:levels,sep="_")
disc = Fit[["Model"]]$parm[pos.Ds]
FI = Fit$FI
Results <- list("Data"=MyData,"Fit"=Fit,"Model"=Model,
'abil'=abil,'diff'=diff,"disc"=disc,'FitIndexes'=FI)
} else {
if (method=="PMC") {
abil = Fit$Summary[grep("theta", rownames(Fit$Summary), fixed=TRUE),1]
diff = matrix(Fit$Summary[grep("b", rownames(Fit$Summary), fixed=TRUE),1],
nrow=ncol(x))
disc = Fit$Summary[grep("Ds", rownames(Fit$Summary), fixed=TRUE),1]
} else {
abil = Fit$Summary1[grep("theta", rownames(Fit$Summary1), fixed=TRUE),1]
diff = matrix(Fit$Summary1[grep("b", rownames(Fit$Summary1), fixed=TRUE),1],
nrow=ncol(x))
disc = Fit$Summary1[grep("Ds", rownames(Fit$Summary1), fixed=TRUE),1]
}
rownames(diff) = colnames(x)
colnames(diff) = paste("Answer_Key",1:levels,sep="_")
Dev <- Fit$Deviance
mDD <- Dev - min(Dev)
pDD <- Dev[min(which(mDD < 100)):length(Dev)]
pV <- var(pDD)/2
Dbar <- mean(pDD)
#Dbar = mean(Dev)
#pV <- var(Dev)/2
DIC = list(DIC=Dbar + pV, Dbar=Dbar, pV=pV)
Results <- list("Data"=MyData,"Fit"=Fit,"Model"=Model,
'abil'=abil,'diff'=diff,"disc"=disc,'DIC'=DIC)
}
} else warning("Can't return any result :P")
return(Results)
}
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