| Type: | Package |
| Title: | Bayesian Test Reliability Estimation |
| Version: | 0.1.2 |
| Author: | Joshua Ray Tanzer |
| Maintainer: | Joshua Ray Tanzer <jtanzer@lifespan.org> |
| Description: | When samples contain missing data, are small, or are suspected of bias, estimation of scale reliability may not be trustworthy. A recommended solution for this common problem has been Bayesian model estimation. Bayesian methods rely on user specified information from historical data or researcher intuition to more accurately estimate the parameters. This package provides a user friendly interface for estimating test reliability. Here, reliability is modeled as a beta distributed random variable with shape parameters alpha=true score variance and beta=error variance (Tanzer & Harlow, 2020) <doi:10.1080/00273171.2020.1854082>. |
| Depends: | MCMCpack, GPArotation, TeachingDemos, blavaan, blme |
| Imports: | MASS, rstan |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.1.1 |
| NeedsCompilation: | no |
| Packaged: | 2021-01-26 16:18:07 UTC; CHS-User |
| Repository: | CRAN |
| Date/Publication: | 2021-01-26 17:00:06 UTC |
bcor: Bayesian Estimation of The Correlation Matrix
Description
This function estimates coefficient omega internal consistency reliability.
Usage
bcor(data, iter, burn, seed, CI, S0, nu0, mu0)
Arguments
data |
N by P data matrix. |
iter |
Number of iterations for the Gibbs sampler. |
burn |
Number of samples to burn in. |
seed |
Seed for the Gibbs sampler |
CI |
Credible interval quantile, as a decimal (ie, for 95 percent, 0.95). |
S0 |
Prior variance covariance matrix. |
nu0 |
Prior degrees of freedom for inverse Wishart prior distribution. |
mu0 |
Prior means for each column. |
Value
Returns median posterior estimates of the correlation matrix.
Examples
set.seed(999)
your_data=mvrnorm(n=15,mu=c(0,0),Sigma=matrix(c(4,3,3,9),nrow=2,ncol=2))
Mu0=c(0,0)
Sigma0=matrix(c(1,0.6,0.6,4),nrow=2,ncol=2)
Nu0=1
bcor(data=your_data,iter=5000,burn=2500,seed=999,CI=0.95,
mu0=Mu0,S0=Sigma0,nu0=Nu0)
bcov: Bayesian Estimation of the Variance Covariance Matrix
Description
This function estimates the variance covariance matrix for a
Usage
bcov(data, iter, burn, seed, CI, S0, nu0, mu0)
Arguments
data |
N by P data matrix. |
iter |
Number of iterations for the Gibbs sampler. |
burn |
Number of samples to burn in. |
seed |
Seed for the Gibbs sampler |
CI |
Credible interval quantile, as a decimal (ie, for 95 percent, 0.95). |
S0 |
Prior variance covariance matrix. |
nu0 |
Prior degrees of freedom for inverse Wishart prior distribution. |
mu0 |
Prior means for each column. |
Value
Returns median posterior estimates of the variance covariance matrix.
Examples
## Not run:
set.seed(999)
your_data=mvrnorm(n=15,mu=c(0,0),Sigma=matrix(c(4,3,3,9),nrow=2,ncol=2))
Mu0=c(0,0)
Sigma0=matrix(c(1,0.6,0.6,4),nrow=2,ncol=2)
Nu0=3-1
bcov(data=your_data,iter=5000,burn=2500,seed=999,CI=0.95,
mu0=Mu0,S0=Sigma0,nu0=Nu0)
## End(Not run)
bomega: Bayesian Estimation of Coefficient Omega
Description
This function estimates coefficient omega internal consistency reliability.
Usage
bomega(K, mod, alpha, beta, CI)
Arguments
K |
The number of test items. |
mod |
A measurement model estimated as a bsem object by blavaan. |
alpha |
Prior true score variance. |
beta |
Prior error variance. |
CI |
Credible interval quantile, as a decimal (ie, for 95 percent, 0.95). |
Value
Returns estimated median and quantile based credible limits for omega.
Examples
your_data=data.frame(mvrnorm(n=20,mu=c(0,0,0,0,0),
Sigma=matrix(c(4,2,2,2,2,
2,4,2,2,2,
2,2,4,2,2,
2,2,2,4,2,
2,2,2,2,4),
nrow=5, ncol=5)))
colnames(your_data)=c("x1","x2","x3","x4","x5")
mod='tau=~x1+x2+x3+x4+x5'
fit=bsem(mod,data=your_data)
bomega(K=5,mod=fit,alpha=3.51,beta=1.75,CI=0.95)
bomega_general: Bayesian Estimation of Coefficient Omega, General Form
Description
This function estimates coefficient omega internal consistency reliability.
Usage
bomega_general(lambda, psi, alpha, beta, CI)
Arguments
lambda |
vector of item loadings. |
psi |
vector of item variances. |
alpha |
Prior true score variance. |
beta |
Prior error variance. |
CI |
Credible interval quantile, as a decimal (ie, for 95 percent, 0.95). |
Value
Returns estimated median and quantile based credible limits for omega.
Examples
lambda=c(0.7,0.5,0.6,0.7)
psi=c(0.2,0.4,0.3)
alpha=3.51
beta=1.75
bomega_general(lambda=lambda,psi=psi,alpha=alpha,beta=beta,CI=0.95)
brxx_Cor: Bayesian Estimation of Reliability from Correlation
Description
This function estimates reliability from a correlation
Usage
brxx_Cor(x, y, alpha, beta, iter, burn, seed, CI, S0, nu0, mu0, items)
Arguments
x |
First variable. |
y |
Second variable. |
alpha |
Prior true score variance (covariance between tests) |
beta |
Prior error variance (product of standard deviations minus covariance) |
iter |
Number of iterations for the Gibbs sampler. |
burn |
Number of samples to burn in. |
seed |
Seed for the Gibbs sampler |
CI |
Credible interval quantile, as a decimal (ie, for 95 percent, 0.95). |
S0 |
Prior variance covariance matrix. |
nu0 |
Prior degrees of freedom for inverse Wishart prior distribution. |
mu0 |
Prior means for each column. |
items |
Number of test items. |
Value
Returns median posterior estimates of the variance covariance matrix.
Examples
set.seed(999)
your_data=mvrnorm(n=15,mu=c(0,0),Sigma=matrix(c(4,5,5,9),nrow=2,ncol=2))
x=your_data[,1]
y=your_data[,2]
Mu0=c(0,0)
Sigma0=matrix(c(1,0.6,0.6,4),nrow=2,ncol=2)
Nu0=3-1
brxx_Cor(x=x,y=y,iter=5000,burn=2500,seed=999,CI=0.95,
mu0=Mu0,S0=Sigma0,nu0=Nu0,items=10)
brxx_Cor_general: Bayesian Estimation of Reliability from Correlation, General Form
Description
This function estimates reliability from correlation given the correlation estimate.
Usage
brxx_Cor_general(cor, alpha, beta, CI, items)
Arguments
cor |
Correlation estimate. |
alpha |
Prior true score variance. |
beta |
Prior error variance. |
CI |
Credible interval quantile, as a decimal (ie, for 95 percent, 0.95). |
items |
Number of test items. |
Value
Returns estimated median and quantile based credible limits for reliability.
Examples
brxx_Cor_general(cor=0.85,alpha=3.51,beta=1.75,CI=0.95,items=10)
brxx_ICC: Bayesian Estimation of Reliability from ICC
Description
This function estimates reliability from intraclass correlation coefficient
Usage
brxx_ICC(mod, alpha, beta, CI, items)
Arguments
mod |
A mixed effects model object estimated by blmer. |
alpha |
Prior true score variance (subject variance) |
beta |
Prior error variance (residual variance) |
CI |
Credible interval quantile, as a decimal (ie, for 95 percent, 0.95). |
items |
Number of test items. |
Value
Returns estimated median and quantile based credible limits for ICC.
Examples
your_data_wide=mvrnorm(20,c(0,0),matrix(c(1,0.8,0.8,1),nrow=2,ncol=2))
your_data_long=c(as.vector(your_data_wide[,1]),as.vector(your_data_wide[,2]))
time=c(rep(0,20),rep(1,20))
id=c(rep(1:20,2))
mod=blmer(your_data_long~time+(1|id))
brxx_ICC(mod=mod,alpha=3.51,beta=1.75,CI=0.95,items=10)
brxx_ICC_general: Bayesian Estimation of Reliability from ICC, General Form
Description
This function estimates reliability from intraclass correlation given correlation.
Usage
brxx_ICC_general(WS, Resid, alpha, beta, CI, items)
Arguments
WS |
Within subjects variance estimate. |
Resid |
Residual variance estimate. |
alpha |
Prior true score variance. |
beta |
Prior error variance. |
CI |
Credible interval quantile, as a decimal (ie, for 95 percent, 0.95). |
items |
Number of test items. |
Value
Returns estimated median and quantile based credible limits for reliability.
Examples
WS=20.4
Resid=3.6
alpha=3.51
beta=1.75
brxx_ICC_general(WS=WS,Resid=Resid,alpha=alpha,beta=beta,CI=0.95,items=5)
brxx_general: Bayesian Estimation of Reliability from Variance Estimates
Description
This function estimates reliability from given true and error variance estimates.
Usage
brxx_general(a, b, alpha, beta, CI, items)
Arguments
a |
True score variance estimate. |
b |
Error variance estimate. |
alpha |
Prior true score variance. |
beta |
Prior error variance. |
CI |
Credible interval quantile, as a decimal (ie, for 95 percent, 0.95). |
items |
Number of test items. |
Value
Returns estimated median and quantile based credible limits for reliability.
Examples
a=18.7
b=3.3
alpha=3.51
beta=1.75
brxx_general(a=a,b=b,alpha=alpha,beta=beta,CI=0.95,items=10)
prep: Prepare Data File for Bayesian Analysis
Description
This function prepares data for analysis using Stan factor analysis code.
Usage
prep(data, nfactors, Prior)
Arguments
data |
N by P data matrix. |
nfactors |
Number of factors to extract. |
Prior |
Prior loading matrix. |
Value
Returns a formatted data file for use with Stan MCMC sampler.
Examples
set.seed(999)
your_data=data.frame(mvrnorm(n=20,mu=c(0,0,0,0,0),
Sigma=matrix(c(4,2,2,2,2,
2,4,2,2,2,
2,2,4,2,2,
2,2,2,4,2,
2,2,2,2,4),
nrow=5, ncol=5)))
colnames(your_data)=c("x1","x2","x3","x4","x5")
your_data_miss=matrix(ncol=5,nrow=20)
for (i in 1:20){
for (p in 1:5){
your_data_miss[i,p]=ifelse(runif(1,0,1)<0.2,NA,your_data[i,p])
}
}
formatted_data=prep(your_data_miss,nfactors=3)
process: rotates and calulates reliability for Stan output
Description
This function processes Stan loading matrix data.
Usage
process(Loading_Matrix, Format, Rotate)
Arguments
Loading_Matrix |
S by P*Q matrix of loading samples. |
Format |
list formatted data file provided for Stan |
Rotate |
If Q>1, rotation (for options, see GPArotation package) |
Value
Returns rotated loadings, uniqueness, communality, and reliability.
Examples
## Not run:
your_data_s=standardize(your_data)
formatted_data=prep(your_data_s,nfactors=3)
out=sampling(model, data=formatted_data, iter=5000, seed=999)
res=as.matrix(out)
unpacked=unpack(Samples=res,Format=formatted_data)
processed=process(Loading_Matrix=unpacked$Loading_Matrix,
Format=formatted_data,
Rotate="oblimin")
## End(Not run)
scree: Scree Plot with Pairwise Complete Cases
Description
This function provides a scree plot when data may be missing.
Usage
scree(data)
Arguments
data |
N by P data matrix. |
Value
Returns eigenvalues and scree plot.
Examples
set.seed(999)
your_data=data.frame(mvrnorm(n=20,mu=c(0,0,0,0,0),
Sigma=matrix(c(4,2,2,2,2,
2,4,2,2,2,
2,2,4,2,2,
2,2,2,4,2,
2,2,2,2,4),
nrow=5, ncol=5)))
colnames(your_data)=c("x1","x2","x3","x4","x5")
your_data_miss=matrix(ncol=5,nrow=20)
for (i in 1:20){
for (p in 1:5){
your_data_miss[i,p]=ifelse(runif(1,0,1)<0.2,NA,your_data[i,p])
}
}
scree(your_data_miss)
standardize: Standardization of Data Matrix
Description
This function standardizes an N by P data matrix, as is strongly recommended before using any of the brxx reliability estimation functions
Usage
standardize(data)
Arguments
data |
N by P data matrix. |
Value
Returns an item level standardized data matrix.
Examples
set.seed(999)
your_data=data.frame(mvrnorm(n=20,mu=c(0,0,0,0,0,0,0),
Sigma=matrix(c(4,2,2,2,2,2,2,
2,4,2,2,2,2,2,
2,2,4,2,2,2,2,
2,2,2,4,2,2,2,
2,2,2,2,4,2,2,
2,2,2,2,2,4,2,
2,2,2,2,2,2,4),
nrow=7, ncol=7)))
your_data_miss=matrix(ncol=5,nrow=20)
for (i in 1:20){
for (p in 1:5){
your_data_miss[i,p]=ifelse(runif(1,0,1)<0.2,NA,your_data[i,p])
}
}
standardize(your_data_miss)
summarize: Summarize Stan output as median, SD, and HPD quantiles
Description
This function converts raw MCMC sample data into matrix formatted summaries
Usage
summarize(Samples, nrow, ncol, CI)
Arguments
Samples |
S by theta matrix of sampled parameter estimates. |
nrow |
Number of rows of target summary matrix |
ncol |
Number of columns of target summary matrix |
CI |
Creddible interval quantile, as a decimal (ie, for 95 percent, 0.95) |
Value
Returns median, SD, and HPD CI limits
Examples
## Not run:
your_data_s=standardize(your_data)
formatted_data=prep(your_data_s,nfactors=3)
out=sampling(model, data=formatted_data, iter=5000, seed=999)
res=as.matrix(out)
unpacked=unpack(Samples=res,Format=formatted_data)
processed=process(Loading_Matrix=unpacked$Loading_Matrix,
Format=formatted_data,
Rotate="oblimin")
summarize(processed$Loadings,
nrow=Formatted_data$P,
ncol=Formatted_data$Q)$Table
summarize(processed$Communality,
nrow=Formatted_data$P,
ncol=1)$Table
summarize(processed$Uniqueness,
nrow=Formatted_data$P,
ncol=1)$Table
summarize(processed$G_Factor,
nrow=Formatted_data$P,
ncol=1)$Table
summarize(processed$Interfactor_Correlations,
nrow=Formatted_data$Q,
ncol=Formatted_data$Q)$Table
summarize(processed$Omega,
nrow=1,
ncol=1)$Table
summarize(unpacked$Tau_Matrix,
nrow=Formatted_data$P,
ncol=1)$Table
## End(Not run)
unpack: Unpack Stan output for factor analysis samples from Stan
Description
This function unpacks raw Stan samples output.
Usage
unpack(Samples, Format)
Arguments
Samples |
S by theta matrix of sample parameter estimates. |
Format |
list formatted data file provided for Stan |
Value
Returns four matrices:
1). S by Q latent score matrix, x.
2). S by Q*P loading matrix, lambda.
3). S by P mean matrix, tau.
4). S by P loading variance matrix, alpha.
Examples
## Not run:
your_data_s=standardize(your_data)
formatted_data=prep(your_data_s,nfactors=3)
out=sampling(model, data=formatted_data, iter=5000, seed=999)
res=as.matrix(out)
unpacked=unpack(Samples=res,Format=formatted_data)
## End(Not run)