composites {quest}

Composite Reliability of Multiple Scores

Description

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

Usage

composites(
  data,
  vrb.nm.list,
  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.list

list of character vectors containing colnames in data specifying the multiple sets 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/items data[unlist(vrb.nm.list)].

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 implicitly 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 implicitly 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 models are 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).

composites 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 for details.

Value

data.frame containing the composite reliability of each set of variables/items.

est

estimate of the reliability coefficient

se

standard error of the reliability coefficient

lwr

lower bound of the confidence interval of the reliability coefficient

upr

upper bound of the confidence interval of the reliability coefficient

average_l

average standardized factor loading from the factor model

nvrb

number of variables/items

???

any model fit indices requested by the fit.measures argument

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

composite cronbachs

Examples

dat0 <- psych::bfi[1:250, ]
dat1 <- str2str::pick(x = dat0, val = c("A1","C4","C5","E1","E2","O2","O5",
   "gender","education","age"), not = TRUE, nm = TRUE)
vrb_nm_list <- lapply(X = str2str::sn(c("E","N","C","A","O")), FUN = function(nm) {
   str2str::pick(x = names(dat1), val = nm, pat = TRUE)})
composites(data = dat1, vrb.nm.list = vrb_nm_list)
## Not run: 
start_time <- Sys.time()
composites(data = dat1, vrb.nm.list = vrb_nm_list, ci.type = "boot",
   R = 5000L) # the function is not optimized for speed at the moment
   # since it will bootstrap separately for each set of variables/items
end_time <- Sys.time()
print(end_time - start_time) # takes 10 minutes on my laptop

## End(Not run)
composites(data = attitude,
   vrb.nm.list = list(names(attitude))) # also works with only one set of variables/items