# Log-likelihood for cognitive diagnostic models This function returns the log-likelihood of a particular examinee's responses to a set of cognitive diagnostic items. Currently supported cognitive diagnostic models include the DINA model, DINO model, NIDA model, G-NIDA model, and R-RUM model. This function is called by the `AlphaMLE` function and the `JMLE` function in the package. ```r CDL(Y, Q, par, alpha, model = c("DINA", "DINO", "NIDA", "GNIDA", "RRUM"), undefined.flag) ``` ## Arguments - `Y`: A vector of binary examinee responses. 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. - `par`: A list of parameters. DINA & DINO --- `par$slip`: a vector of slipping parameters for each item; `par$guess`: a vector of guessing parameters for each item. NIDA --- `par$slip`: a vector of slipping parameters for each attribute; `par$guess`: a vector of guessing parameters for each attribute. GNIDA --- `par$slip`: a matrix (items by attributes) of slipping parameters; `par$guess`: a matrix (items by attributes) of guessing parameters. RRUM --- `par$pi`: a vector of pi parameters for each item; `par$r`: a matrix (items by attributes) of r parameters. - `alpha`: A vector of examinee ability profile. 1=examinee masters the attribute, 0=examinee does not master the attribute. - `model`: Currently supports five models: `"DINA"`, `"DINO"`, `"NIDA"`, `"GNIDA"`, and `"RRUM"`. The default is `"DINA"`. - `undefined.flag`: A binary vector indicating whether the parameters of each item are undefined. 1=undefined, 0=defined. ## Returns - **loglike**: The log likelihood function value for the given data. ## See Also `AlphaMLE`, `JMLE` ## Examples ```r # Generate item and examinee profiles nitem <- 4 Q <- rbind(c(1, 0, 0), c(0, 1, 0), c(0, 0, 1), c(1, 1, 1)) alpha <- c(1, 0, 0) # Generate DINA model-based response data slip <- rep(0.1, nitem) guess <- rep(0.1, nitem) my.par <- list(slip=slip, guess=guess) data <- NA eta <- NA for (i in 1:nitem) { eta[i] <- prod(alpha ^ Q[i, ]) P <- (1 - slip[i]) ^ eta[i] * guess[i] ^ (1 - eta[i]) u <- runif(1) data[i] <- as.numeric(u < P) } # Using the function to compute the log-likelihood of the given data CDL(data, Q, my.par, alpha, model="DINA", undefined.flag=rep(0, nitem)) ```

CDL function