# Refine the Q-matrix by minimizing the residual sum of square (RSS) Refine the Q-matrix by minimizing the residual sum of square (RSS) betweenn the real responses and ideal responses. Examinee attribute profiles are estimated using the nonparametric method (plain Hamming) implemented by `AlphaNP`. ```r Qrefine(Y, Q, gate=c("AND", "OR"), max.ite = 50) ``` ## Arguments - `Y`: A matrix of binary responses. Rows represent persons and columns represent items. 1=correct, 0=incorrect. - `Q`: The Q-matrix of the test. Rows represent items and columns represent attributes. 1=attribute required by the item, 0=attribute not required by the item. - `gate`: `"AND"`: the examinee needs to possess all attributes required by an item in order to answer it correctly; `"OR"`: the examinee needs to possess only one of the attributes required by an item in order to answer it correctly. - `max.ite`: The maximum number of iterations allowed. ## Returns - **patterns**: All possible attribute profiles. Rows represent different patterns of attribute profiles and columns represent attributes. 1=examinee masters the attribute, 0=examinee does not master the attribute. - **initial.Q**: The initial Q-matrix. Rows represent items and columns represent attributes. 1=attribute required by the item, 0=attribute not required by the item. This is the preliminary Q-matrix to be refined. - **initial.class**: The row indices of `patterns` in the initial estimation of examinee attribute profiles. - **terminal.class**: The The row indices on `patterns` in the terminal estimation of examinee attribute profiles after the Q-matrix has been refined. - **modified.Q**: The modified Q-matrix. Rows represent items and columns represent attributes. 1=attribute required by the item, 0=attribute not required by the item. - **modified.entries**: The modified q-entries. Column 1 is the item ID of the modified entry; column 2 is the attribute ID of the modified entry. ## See Also `AlphaNP`, `print.Qrefine`, `plot.Qrefine` ## References Chiu, C. Y. (2013). Statistical Refinement of the Q-matrix in Cognitive Diagnosis. **Applied Psychological Measurement, 37**(8), 598-618. ## Examples ```r # Generate item and examinee profiles natt <- 3 nitem <- 4 nperson <- 16 Q <- rbind(c(1, 0, 0), c(0, 1, 0), c(0, 0, 1), c(1, 1, 1)) alpha <- rbind(c(0, 0, 0), c(1, 0, 0), c(0, 1, 0), c(0, 0, 1), c(1, 1, 0), c(1, 0, 1), c(0, 1, 1), c(1, 1, 1)) alpha <- rbind(alpha, alpha) # Generate DINA model-based response data slip <- c(0.1, 0.15, 0.2, 0.25) guess <- c(0.1, 0.15, 0.2, 0.25) my.par <- list(slip=slip, guess=guess) data <- matrix(NA, nperson, nitem) eta <- matrix(NA, nperson, nitem) for (i in 1:nperson) { for (j in 1:nitem) { eta[i, j] <- prod(alpha[i,] ^ Q[j, ]) P <- (1 - slip[j]) ^ eta[i, j] * guess[j] ^ (1 - eta[i, j]) u <- runif(1) data[i, j] <- as.numeric(u < P) } } # Generate misspecified Q-matrix Q_mis <- Q Q_mis[c(1,2), 1] <- 1 - Q_mis[c(1,2), 1] # Run Qrefine and create diagnostic plots Qrefine.out <- Qrefine(data, Q_mis, gate="AND", max.ite=50) print(Qrefine.out) plot(Qrefine.out) ```

Qrefine function