An R package for doing inference with coefficient alpha
(Cronbach, 1951) and standardized alpha (Falk & Savalei, 2011). Many
methods are supported, with special emphasis on small samples and
non-normality.
The package is not available on CRAN yet, so use the
following command from inside R:
# install.packages("remotes")
remotes::install_github("JonasMoss/alphaci")Call the library function and load some data:
library("alphaci")
library("psychTools")
x <- bfi[, 1:5]
x[, 1] <- 7 - x[, 1] # Reverse-coded item.
head(x)
#> A1 A2 A3 A4 A5
#> 61617 5 4 3 4 4
#> 61618 5 4 5 2 5
#> 61620 2 4 5 4 4
#> 61621 3 4 6 5 5
#> 61622 5 3 3 4 5
#> 61623 1 6 5 6 5Then calculate an asymptotically distribution-free confidence interval for ,
alphaci(x)
#> Call: alphaci(x = x)
#>
#> 95% confidence interval (n = 2709).
#> 0.025 0.975
#> 0.6828923 0.7246195
#>
#> Sample estimates.
#> alpha sd
#> 0.7037559 0.5536964You can also calculate confidence intervals for standardized alpha
alphaci_std(x)
#> Call: alphaci_std(x = x)
#>
#> 95% confidence interval (n = 2709).
#> 0.025 0.975
#> 0.6828923 0.7246195
#>
#> Sample estimates.
#> alpha sd
#> 0.7037559 0.5536964alphaci supports three basic asymptotic confidence
interval constructios. The asymptotically distribution-free interval of
Maydeu-Olivares et al. 2007, the pseudo-elliptical construction of Yuan
& Bentler (2002), and the normal method of van Zyl et al.,
(1999).
| Method | Description |
|---|---|
adf |
The asymptotic distribution free method (Maydeu-Olivares et al. 2007). The method is asymptotically correct, but has poor small-sample performance. |
elliptical |
The elliptical or pseudo-elliptical kurtosis correction (Yuan &
Bentler, 2002). Uses the unbiased sample estimator of the common
kurtosis (Joanes, 1998). Has better small-sample performance than
adf and normal if the kurtosis is large and
is
small. |
normal |
Assumes normality of (van Zyl et al., 1999). This method is not recommended since it yields too short confidence intervals when the excess kurtosis of is larger than . |
Standardized alpha, computed with alpha_std, support the
same type arguments. Their formulas can be derived using
the methods of Hayashi and Kamata (2005) and Neudecker (2007).
In addition, you may transform the intervals using one of four transforms:
The option bootstrap does studentized bootstrapping
Efron, B. (1987) with n_reps repetitions. If
bootstrap = FALSE, an ordinary normal approximation will be
used. The studentized bootstrap intervals are is a second-order correct,
so its confidence intervals will be better than the normal approximation
when is
sufficiently large.
Finally, the option parallel = TRUE can be used, which
is suitable if covariance matrix is compound symmetric. If the
distribution is normal or (pseudo-)elliptic, it can be used to simplify
the expression for the asymptotic variance of alpha and standardized
alpha to
where is the common kurtosis parameter.
There are several R packages that make confidence
intervals for coefficient alpha, but not much support for standardized
alpha. Most packages use some sort of normality assumption.
The alpha and alpha.ci functions of psych
calculates confidence intervals for coefficient alpha following normal
theory. semTools
calculates numerous reliability coefficients with its
reliability function. The Cronbach
package provides confidence intervals based on normal theory, as does
the alpha.CI function of psychometric.
Confidence intervals for both alphas can, in principle, be calculated
using structural equation modeling together with the delta method.
Packages such as lavaan
can be used for this purpose, but this is seldom done.
If you encounter a bug, have a feature request or need some help, open a Github issue. Create a pull requests to contribute.