composite {quest}

Composite Reliability of a Score

Description

composite computes the composite reliability coefficient (sometimes referred to as omega) for a set of variables/items. The composite reliability computed in composite assumes a undimensional factor model with no error covariances. In addition to the coefficient itself, its standard error and confidence interval are returned, the average standardized factor loading from the factor model and number of variables/items, and (optional) model fit indices of the factor model. Note, any reverse coded items need to be recoded ahead of time so that all variables/items are keyed in the same direction.

Usage

composite(
  data,
  vrb.nm,
  level = 0.95,
  std = FALSE,
  ci.type = "delta",
  boot.ci.type = "bca.simple",
  R = 200L,
  fit.measures = c("chisq", "df", "tli", "cfi", "rmsea", "srmr"),
  se = "standard",
  test = "standard",
  missing = "fiml",
  ...
)

Arguments

data

data.frame of data.

vrb.nm

character vector of colnames in data specifying the set of variables/items.

level

double vector of length 1 with a value between 0 and 1 specifying what confidence level to use.

std

logical element of length 1 specifying if the composite reliability should be computed for the standardized version of the variables data[vrb.nm].

ci.type

character vector of length 1 specifying which type of confidence interval to compute. The "delta" option uses the delta method to compute a standard error and a symmetrical confidence interval. The "boot" option uses bootstrapping to compute an asymmetrical confidence interval as well as a (pseudo) standard error.

boot.ci.type

character vector of length 1 specifying which type of bootstrapped confidence interval to compute. The options are: 1) "norm", 2) "basic", 3) "perc", 4) "bca.simple". Only used if ci.type = "boot". See parameterEstimates and its boot.ci.type argument for details.

R

integer vector of length 1 specifying how many bootstrapped resamples to compute. Note, as the number of bootstrapped resamples increases, the computation time will increase. Only used if ci.type is "boot".

fit.measures

character vector specifying which model fit indices to include in the return object. The default option includes the chi-square test statistic ("chisq"), degrees of freedom ("df"), tucker-lewis index ("tli"), comparative fit index ("cfi"), root mean square error of approximation ("rmsea"), and standardized root mean residual ("srmr"). If NULL, then no model fit indices are included in the return object. See fitMeasures for details.

se

character vector of length 1 specifying which type of standard errors to compute. If ci.type = "boot", then the input value is ignored and set to "bootstrap". See lavOptions and its se argument for details.

test

character vector of length 1 specifying which type of test statistic to compute. If ci.type = "boot", then the input value is ignored and set to "bootstrap". See lavOptions and its test argument for details.

missing

character vector of length 1 specifying how to handle missing data. The default is "fiml" for full information maximum likelihood). See lavOptions and its missing argument for details.

...

other arguments passed to cfa. Use at your own peril as some argument values could cause the function to break.

Details

The factor model is estimated using the R package lavaan. The reliability coefficients are calculated based on the square of the sum of the factor loadings divided by the sum of the square of the sum of the factors loadings and the sum of the error variances (Raykov, 2001).

composite is only able to use the "ML" estimator at the moment and cannot model items as categorical/ordinal. However, different versions of standard errors and test statistics are possible. For example, the "MLM" estimator can be specified by se = "robust.sem" and test = "satorra.bentler"; the "MLR" estimator can be specified by se = "robust.huber.white" and test = "yuan.bentler.mplus". See lavOptions and scroll down to Estimation options.

Value

double vector where the first element is the composite reliability coefficient ("est") followed by its standard error ("se"), then its confidence interval ("lwr" and "upr"), the average standardized factor loading of the factor model ("average_l") and number of variables ("nvrb"), and finally any of the fit.measures requested.

References

Raykov, T. (2001). Estimation of congeneric scale reliability using covariance structure analysis with nonlinear constraints. British Journal of Mathematical and Statistical Psychology, 54(2), 315–323.

See Also

composites cronbach

Examples

# data
dat <- psych::bfi[1:250, 2:5] # the first item is reverse coded

# delta method CI
composite(data = dat, vrb.nm = names(dat), ci.type = "delta")
composite(data = dat, vrb.nm = names(dat), ci.type = "delta", level = 0.99)
composite(data = dat, vrb.nm = names(dat), ci.type = "delta", std = TRUE)
composite(data = dat, vrb.nm = names(dat), ci.type = "delta", fit.measures = NULL)
composite(data = dat, vrb.nm = names(dat), ci.type = "delta",
   se = "robust.sem", test = "satorra.bentler", missing = "listwise") # MLM estimator
composite(data = dat, vrb.nm = names(dat), ci.type = "delta",
   se = "robust.huber.white", test = "yuan.bentler.mplus", missing = "fiml") # MLR estimator

## Not run: 
# bootstrapped CI
composite(data = dat, vrb.nm = names(dat), level = 0.95,
   ci.type = "boot") # slightly different estimate for some reason...
composite(data = dat, vrb.nm = names(dat), level = 0.95, ci.type = "boot",
   boot.ci.type = "perc", R = 250L) # probably want to use more resamples - this is just an example

## End(Not run)

# compare to semTools::reliability
psymet_obj <- composite(data = dat, vrb.nm = names(dat))
psymet_est <- unname(psymet_obj["est"])
lavaan_obj <- lavaan::cfa(model = make.latent(names(dat)), data = dat,
   std.lv = TRUE, missing = "fiml")
semTools_obj <- semTools::reliability(lavaan_obj)
semTools_est <- semTools_obj["omega", "latent"]
all.equal(psymet_est, semTools_est)