3.2 CDM Notations

The response vector of examinee \(i\) will be denoted by \(Y_i, i =1, 2, ..., N\)

The response vector contains \(J\) items, as in, \(\mathbf{Y}_i=(Y_{i1},\ldots,Y_{ij},\ldots,Y_{iJ})\)

The attribute profile of examinee \(i\) will be denoted by \(\alpha_i=(\alpha_{i1},\ldots,\alpha_{iK})\)

Each attribute vector or profile defines a unique latent class. For latent class \(c\), we have

\[ \alpha_c=(\alpha_{c1},\ldots,\alpha_{cK}) \]

Thus, \(K\) attributes define \(2^K\) latent classes