I demonstrate how to calculate Cronbach's coefficient alpha from the item covariance matrix or item correlation matrix. I also demonstrate how the alpha() function of Revelle's psych package can be used to (a) calculate alpha, and (b) calculate 95% confidence intervals for alpha.

The document contains a function that can be used to select items to maximise coefficient omega. The item selection is based on information statistics (i.e. the ratio of an item's squared unstandardized factor loading to its unique variance). The approach is described by McDonald (1999, p. 121 to 123).

A procedure to build a test from the bottom up. The process starts by finding the pair of items from a larger pool that has the largest covariance. A summated total score is obtained for these items. Next, the item that has the biggest covariance with this summated total score is found. A new total score is obtained and the next item with the biggest covariance with the summated total score is found, and so on. Reliability coefficients and a unidimensionality index (due to Bill Revelle) are given at each step of the process.

The code presents two methods of randomly splitting a data frame in two

Remove from a data frame rows containing only NAs

Using the TAM package to perform a rating scale model analysis of items with ordinal response categories

This document demonstrates how researchers can test for partial measurement invariance across groups with the lavaan package in R

This document demonstrates how one can perform sequential tests of measurement invariance with the lavaan package in R

Using the TAM package to perform a partial credit model analysis of items with ordinal response categories.

Testing classical test theory models with lavaan

The document shows how the psych package can be used to find the reliability of test scores.