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RELIAB <correlation_matrix>,<factor_matrix>,<factor_correlation_matrix>,L
computes reliabilities of measurement scales according to a measurement
model, which is usually estimated by the maximum likelihood factor analysis
(see: FACTA?). The <factor_correlation_matrix> is given by the ROTATE
operation. If the factors are orthogonal, the matrix can be omitted.

L is the (optional) first line for the results.
The residual covariance and correlation matrices are saved to the matrix
files RCOV.M and RCORR.M, respectively. The assumptions of the measurement
model may be tested by studying these matrices. In an orthogonal factor
model, the residual matrix should be diagonal. The off-diagonal elements
(the covariances/correlations of the measurement errors) may reveal some
interesting properties of the current model.

The specification MSN=<matrix_of_means,standard_deviations_and_N's> 
(typically MSN=MSN.M) implies computing of Cronbach's alpha for all
scales. However, Cronbach's alpha is not recommended, since
Tarkkonen's measure is better in every circumstance, see Vehkalahti (2000).

For typical applications, sucro /RELIAB is preferable.

The measurement scales corresponding to the factors are called factor
images. The weights of the scales are the (rotated) factor loadings. The
reliabilities of the factor images give information on the structural
validity of the factor solution.

When the scales are linear combinations of the observed variables, the
coefficients of weights are often given by other Survo operations, such as
LINREG or /FCOEFF. They may also be set by the user, according to some
theory, for example. The coefficient matrix is referred to by the
specification WEIGHT.

By default, the reliability of an unweighted sum of the variables is
computed, since it is a classical measurement scale is psychometrics.

The reliabilities of second order scales can be computed by using the
specification WEIGHT2. Then the coefficient matrix is formed automatically
by first removing the Constant-rows of the weight-matrices and then
multiplying WEIGHT and WEIGHT2. In this case, the resulting second order scale
coefficients are saved in the matrix file WEIGHT2.M .

  M = More information on reliability of measurement scales 

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