gtheory {quest}

Generalizability Theory Reliability of a Score

Description

gtheory uses generalizability theory to compute the reliability coefficient of a score. It assumes single-level data where the rows are cases and the columns are variables/items. Generaliability theory coefficients in this case are the same as intraclass correlations (ICC). The default computes ICC(3,k), which is identical to cronbach's alpha, from cross.vrb = TRUE. When cross.vrb is FALSE, ICC(2,k) is computed, which takes mean differences between variables/items into account. gtheory is a wrapper function for ICC.

Usage

gtheory(
  data,
  vrb.nm,
  ci.type = "classic",
  level = 0.95,
  cross.vrb = TRUE,
  R = 200L,
  boot.ci.type = "perc"
)

Arguments

data

data.frame of data.

vrb.nm

character vector of colnames from data specifying the variables/items.

ci.type

character vector of length = 1 specifying the type of confidence interval to compute. There are currently two options: 1) "classic" = traditional ICC-based confidence intervals (see details), 2) "boot" = bootstrapped confidence intervals.

level

double vector of length 1 specifying the confidence level from 0 to 1.

cross.vrb

logical vector of length 1 specifying whether the variables/items should be crossed when computing the generalizability theory coefficient. If TRUE, then only the covariance structure of the variables/items will be incorperated into the estimate of reliability. If FALSE, then the mean structure of the variables/items will be incorperated.

R

integer vector of length 1 specifying the number of bootstrapped resamples to use. Only used if ci.type = "boot".

boot.ci.type

character vector of length 1 specifying the type of bootstrapped confidence interval to compute. The options are 1) "perc" for the regular percentile method, 2) "bca" for bias-corrected and accelerated percentile method, 3) "norm" for the normal method that uses the bootstrapped standard error to construct symmetrical confidence intervals with the classic formula around the bias-corrected estimate, and 4) "basic" for the basic method. Note, "stud" for the studentized method is NOT an option. See boot.ci as well as confint2.boot for details.

Details

When ci.type = "classic" the confidence intervals are computed according to the formulas laid out by McGraw, Kenneth, and Wong, (1996). These are taken from the ICC function in the psych package. They are appropriately non-symmetrical given ICCs are not unbounded and range from 0 to 1. Therefore, there is no standard error associated with the coefficient. Note, they differ from the confidence intervals available in the cronbach function. When ci.type = "boot" the standard deviation of the empirical sampling distribution is returned as the standard error, which may or may not be trustworthy depending on the value of the ICC and sample size.

Value

double vector containing the generalizability theory coefficient, it's standard error (if ci.type = "boot"), and it's confidence interval.

References

McGraw, Kenneth O. and Wong, S. P. (1996), Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1, 30-46. + errata on page 390.

See Also

gtheorys gtheory_ml cronbach

Examples

gtheory(attitude, vrb.nm = names(attitude), ci.type = "classic")
## Not run: 
gtheory(attitude, vrb.nm = names(attitude), ci.type = "boot")
gtheory(attitude, vrb.nm = names(attitude), ci.type = "boot",
   R = 250L, boot.ci.type = "bca")

## End(Not run)

# comparison to cronbach's alpha:
gtheory(attitude, names(attitude))
gtheory(attitude, names(attitude), cross.vrb = FALSE)
a <- suppressMessages(psych::alpha(attitude)[["total"]]["raw_alpha"])
psych::alpha.ci(a, n.obs = 30, n.var = 7, digits = 7) # slightly different confidence interval