# reliability

0th

Percentile

##### Internal: Reliability

Compute several reliability estimates. See the Reliability section of the cSEM website for details.

Keywords
internal
##### Usage
calculateRhoC(
.object = NULL,
.model_implied = FALSE,
.only_common_factors = TRUE,
.weighted = args_default()$.weighted )calculateRhoT( .object = NULL, .alpha = args_default()$.alpha,
.closed_form_ci = args_default()$.closed_form_ci, .only_common_factors = TRUE, .output_type = c("vector", "data.frame"), .weighted = args_default()$.weighted,
...
)
##### Arguments
.object

An R object of class cSEMResults resulting from a call to csem().

.model_implied

Logical. Should the RMS_theta be computed using the model-implied construct correlation matrix (TRUE) or the construct correlation matrix based on V(eta) = WSW' divided by the square root of the respective reliabilities (FALSE). Defaults to FALSE.

.only_common_factors

Logical. Should only concepts modeled as common factors be included when calculating one of the following quality critera: AVE, the Fornell-Larcker criterion, HTMT, and all reliability estimates. Defaults to TRUE.

.weighted

Logical. Should estimation be based on a score that uses the weights of the weight approach used to obtain .object?. Defaults to FALSE.

.alpha

An integer or a numeric vector of significance levels. Defaults to 0.05.

.closed_form_ci

Logical. Should a closed-form confidence interval be computed? Defaults to FALSE.

.output_type

Character string. The type of output. One of "vector" or "data.frame". Defaults to "vector".

...

Ignored.

##### Details

Since reliability is defined with respect to a classical true score measurement model only concepts modeled as common factors are considered by default. For concepts modeled as composites reliability may be estimated by setting .only_common_factors = FALSE, however, it is unclear how to interpret reliability in this case.

Reliability is traditionally based on a test score (proxy) based on unit weights. To compute congeneric and tau-equivalent reliability based on a score that uses the weights of the weight approach used to obtain .object use .weighted = TRUE instead.

For the tau-equivalent reliability ("rho_T" or "cronbachs_alpha") a closed-form confidence interval may be computed Trinchera2018cSEM by setting .closed_form_ci = TRUE (default is FALSE). If .alpha is a vector several CI's are returned.

The function is only applicable to objects inheriting class cSEMResults_default. For objects of class cSEMResults_multi and cSEMResults_2ndorder use assess().

##### Value

For calculateRhoC() and calculateRhoT() (if .output_type = "vector") a named numeric vector containing the reliability estimates. If .output_type = "data.frame" calculateRhoT() returns a data.frame with as many rows as there are constructs modeled as common factors in the model (unless .only_common_factors = FALSE in which case the number of rows equals the total number of constructs in the model). The first column contains the name of the construct. The second column the reliability estimate. If .closed_form_ci = TRUE the remaining columns contain lower and upper bounds for the (1 - .alpha) confidence interval(s).

##### Functions

• calculateRhoC: Calculate the congeneric reliability, also known as composite reliability or rho_A.

• calculateRhoT: Calculate the tau-equivalent reliability, also known as Cronbach's alpha or coefficient alpha. Since indicators are always standarized in cSEM, tau-equivalent reliability is identical to the parallel reliability.

##### References

assess(), cSEMResults