Lambda4 (version 3.0)

quant.lambda4: Compute Quantile Lambda 4

Description

Quantile maximize lambda4 is a statistic that can be used in most measurement situations. In particular this function generates a vector t of length equal to the number of items. Each value in the vector consists of either a +1 or -1 (randomly generated). Next, in a random order each value in the t-vector is switched. The value kept (+1 or -1) is the value that resulted in the highest reliability estimate. This procedure is repeated by default 1000 times but can also be user specified. The user can then specify the quantile of this vector but it defaults to .5.

Usage

quant.lambda4(x, starts = 1000, quantiles = 0.5, missing = "complete", show.lambda4s = FALSE, standardize = FALSE)

Arguments

x

Can be either a data matrix or a covariance matrix

starts

How many split-half reliability estimates used

quantiles

The quantiles of the generated splits. It defaults to .5 because it makes the most sense at this time. (The simulation manuscript is under review).

missing

How to handle missing values.

show.lambda4s

If TRUE then Shows the vector of lambda4s if FALSE then the vector is hidden

standardize

Results are standardized by using the correlation matrix instead of the covariance matrix for computation.

Value

lambda4.quantile

The user specified quantile value of the vector of maximized split-reliability

lambda4.optimal

Maximum split-half reliability (Maximized Lambda4

l4.vect

A vector of lambda4 (split-half reliability) calculations

References

Guttman L (1945). "A Basis for Analyzing Test-Retest Reliability." Psychometrika, 10, 255-282.

Callender J, Osburn H (1977). "A Method for Maximizing and Cross-Validating Split-Half Reliability Coefficients." Educational and Psychological Measurement, 37, 819-826.

Callender J, Osburn H (1979). "An Empirical Comparison of Coefficient Alpha, Guttman's Lambda2 and Msplit Maximized Split-Half Reliability Estimates." Journal of Educational Measurement, 16, 89-99. Guttman L (1945). "A Basis for Analyzing Test-Retest Reliability." Psychometrika, 10, 255-282.

Callender J, Osburn H (1977). "A Method for Maximizing and Cross-Validating Split-Half Reliability Coefficients." Educational and Psychological Measurement, 37, 819-826.

Callender J, Osburn H (1979). "An Empirical Comparison of Coefficient Alpha, Guttman's Lambda2 and Msplit Maximized Split-Half Reliability Estimates." Journal of Educational Measurement, 16, 89-99.

Sijtsma K (2009). "On the Use, Misuse, and Very Limited Usefulness of Cronbach's Alpha." Psychometrika, 74(1), 107-120.

Examples

quant.lambda4(Rosenberg, starts=1000, quantile=c(.05,.5,.95))