Function Guttman scaling --> Item analysis and individual scoring based on Guttman's model.
The GUTTMAN function fits Guttman’s perfect scale model to a set of binary items. The program can fit the model in two ways: (a) the item ordering is provided by the user, or (b) the program automatically orders the items according to their difficulty indices. In both cases the ordering is assumed to be in the direction of increasing difficulty (i.e. lower p).
In the computing section there are two sub-functions for fitting the model in these two ways: (a) automatic selection, which orders the items automatically according to their difficulty, and (b) user selection, requiring the user to select the items in the right order of difficulty.
The output is organized in three parts. The first part displays the inter-item correlation matrix and prints the five highest correlations and the five lowest correlations together with the corresponding item pairs. The second part provides item and total-score descriptive statistics: item means or difficulty indices (i.e. p and q values) as well as the mean and standard deviation of the total test scores. The third part provides indices at the global and item level that allow the fit of the Guttman model to be assessed. The global indices are: the coefficient of reproducibility total (CRT), the marginal minimum reproducibility (MMR) the percentage of improvement (PI) and the coefficient of scalability (CS). The indices at the item level are the item coefficients of reproducibility (CRi). In all cases the indices are displayed together with their recommended cut-off values.
Download example data file: Guttman_scaling.zip