IBM® SPSS® Amos™ 28

q = the number of parameters.

= the vector of parameters (of order q).

G = the number of groups.

= the number of observations in group g.

, the total number of observations in all groups combined.

= the number of observed variables in group g.

= the number of sample moments in group g. When means and intercepts are explicit model parameters, the relevant sample moments are means, variances and covariances, so that . Otherwise, only sample variances and covariances are counted so that .

, the number of sample moments in all groups combined.

, the number of degrees of freedom for testing the model.

= the r-th observation on the i-th variable in group g.

= the r-th observation in group g.

= the sample covariance matrix for group g.

= the covariance matrix for group g, according to the model.

= the mean vector for group g, according to the model.

= the population covariance matrix for group g.

= the population mean vector for group g.

, the distinct elements of arranged in a single column vector.

.

r = the nonnegative integer specified by the ChiCorrect method. By default r = G. When the Emulisrel6 method is used, r = G, and cannot be changed by using ChiCorrect.

n = N – r.

= the vector of order p containing the sample moments for all groups. That is, contains the elements of , and also (if means and intercepts are explicit model parameters) .

= the vector of order p containing the population moments for all groups. That is, contains the elements of , and also (if means and intercepts are explicit model parameters) . The ordering of the elements of must match the ordering of the elements of .

= the vector of order p containing the population moments for all groups according to the model. That is, contains the elements of , and also (if means and intercepts are explicit model parameters) . The ordering of the elements of must match the ordering of the elements of .

= the function (of ) that is minimized in fitting the model to the sample.

= the value of that minimizes