## Installation

You can install the released version of Bayesrel from CRAN with:

``install.packages("Bayesrel")``

or install the latest version of Bayesrel from [github] (https://github.com) with the help of the remotes-package:

``remotes::install_github("juliuspf/Bayesrel")``

## Example

### Unidimensional data

This is a basic example which shows you how to compute alpha, lambda2, the glb, and omega for an example real data set:

``````library(Bayesrel)
## basic example code
## load example data set from the package
## run the main reliability function
res <- strel(asrm)
## get a full result output
summary(strel)
## return the probability that coefficient alpha is larger than .70
pStrel(res, estimate = "alpha", low.bound = .70)

## get the posterior median of, e.g., alpha instead of the mean:
median(res\$Bayes\$samp\$Bayes_alpha)``````

### Multidimensional data

This is a basic example which shows you how to compute omega_t and omega_h for an example real data set:

``````library(Bayesrel)
## basic example code
## run the Bayesian omegas, specify 5 group factors
res <- bomegas(upps, n.factors = 5, missing = "listwise")
## get a full result output
summary(res)
## return the probability that coefficient omega_t is larger than .70
pOmegas(res, cutoff.t = .70)
## plot posterior predictive check for the higher-order (second-order) factor model
secoFit(res, upps)``````

In the example above we implicitly assumed that the items of the data set were ordered so that, with 5 group factors, the first four items load on the first factor, items 5-8 load on the second factor and so on. When the data is not organized this way and/or the items cannot be distributed among the factors evenly, one can specify a model syntax relating the items to the group factors in lavaan style:

``````model <- "
f1 =~ U17_r + U22_r + U29_r + U34_r
f2 =~ U4 + U14 + U19 + U27
f3 =~ U6 + U16 + U28 + U48
f4 =~ U23_r + U31_r + U36_r + U46_r
f5 =~ U10_r + U20_r + U35_r + U52_r
"``````

The factor names are arbitrary and only need to be distinguishable. Here the item names are the columns names in the data set. Another way to specify the syntax is:

``````model <- "
f1 =~ x1+x2+x3+x4
f2 =~ x5+x6+x7+x8
f3 =~ x9+x10+x11+x12
f4 =~ x13+x14+x15+x16
f5 =~ x17+x18+x19+x20
"``````

Here the manifest variable names can be chosen freely, just note that the numbers need to correspond to the column numbers of the data set. Note that you cannot mix both approaches, the column name and the column number approach.

The reliability is then estimated as follows:

``res <- bomegas(upps, n.factors = 5, model = model, missing = "listwise")``