This function gives the equivalent latent classes which have the same category success probabilities for each category or item.

LC2LG(Q, sequential = FALSE, att.str = NULL)

Arguments

Q

A required \(J \times K\) binary Q-matrix. J represents test length and K represents the number of attributes of this test. Entry 1 at row j and column k represents the \(k^{th}\) attribute is measured by item \(j\), and 0 means item \(j\) does not measure attribute \(k\).

sequential

logical; whether the Q-matrix is a Qc-matrix for sequential models?

att.str

attribute structure. See GDINA for details.

Value

An item or category by latent class matrix. In the G-DINA model, if item j measures \(Kj\) attributes, \(2^K\) latent classes can be combined into \(2^{Kj}\) latent groups. This matrix gives which latent group each of \(2^K\) latent classes belongs to for each item.

Examples

#> A1 A2 A3 #> [1,] 0 0 0 #> [2,] 1 0 0 #> [3,] 0 1 0 #> [4,] 0 0 1 #> [5,] 1 1 0 #> [6,] 1 0 1 #> [7,] 0 1 1 #> [8,] 1 1 1
q <- matrix(scan(text = "0 1 0 1 0 1 1 1 0"),ncol = 3) q
#> [,1] [,2] [,3] #> [1,] 0 1 1 #> [2,] 1 0 1 #> [3,] 0 1 0
LC2LG(Q = q)
#> 000 100 010 001 110 101 011 111 #> [1,] 1 1 2 3 2 3 4 4 #> [2,] 1 2 1 3 2 4 3 4 #> [3,] 1 1 2 1 2 1 2 2