# Sequential modified federov algorithm for MNL model. Selects the choice set that minimizes the DB-error when added to an initial design, given (updated) parameter values. ```r SeqMOD( des = NULL, cand.set, n.alts, par.draws, prior.covar, alt.cte = NULL, no.choice = NULL, weights = NULL, parallel = TRUE, reduce = TRUE, allow.rep = FALSE ) ``` ## Arguments - `des`: A design matrix in which each row is a profile. If alternative specific constants are present, those should be included as the first column(s) of the design. Can be generated with `Modfed` or `CEA`. - `cand.set`: A numeric matrix in which each row is a possible profile. The `Profiles` function can be used to generate this matrix. - `n.alts`: Numeric value indicating the number of alternatives per choice set. - `par.draws`: A matrix or a list, depending on `alt.cte`. - `prior.covar`: Covariance matrix of the prior distribution. - `alt.cte`: A binary vector indicating for each alternative whether an alternative specific constant is desired. The default is `NULL`. - `no.choice`: An integer indicating the no choice alternative. The default is `NULL`. - `weights`: A vector containing the weights of the draws. Default is `NULL`, See also `ImpsampMNL`. - `parallel`: Logical value indicating whether computations should be done over multiple cores. - `reduce`: Logical value indicating whether the candidate set should be reduced or not. - `allow.rep`: Logical value indicating whether repeated choice sets are allowed in the design. ## Returns - **set**: A matrix representing a DB efficient choice set. - **error**: A numeric value indicating the DB-error of the whole design. ## Details This algorithm is ideally used in an adaptive context. The algorithm will select the next DB-efficient choice set given parameter values and possible previously generated choice sets. In an adaptive context these parameter values are updated after each observed response. Previously generated choice sets, which together form an initial design, can be provided in `des`. When no design is provided, the algorithm will select te most efficient choice set based on the fisher information of the prior covariance matrix `prior.covar`. If `alt.cte = NULL`, `par.draws` should be a matrix in which each row is a sample from the multivariate parameter distribution. In case that `alt.cte` is not `NULL`, a list containing two matrices should be provided to `par.draws`. The first matrix containing the parameter draws for the alternative specific parameters. The second matrix containing the draws for the rest of the parameters. The list of potential choice sets are created using `combn`. If `reduce` is `TRUE`, `allow.rep = FALSE` and vice versa. Furthermore, the list of potential choice sets will be screaned in order to select only those choice sets with a unique information matrix. If no alternative specific constants are used, `reduce` should always be `TRUE`. When alternative specific constants are used `reduce` can be `TRUE` so that the algorithm will be faster, but the combinations of constants and profiles will not be evaluated exhaustively. The `weights` argument can be used when the `par.draws` have weights. This is for example the case when parameter values are updated using `ImpsampMNL`. When `parallel` is `TRUE`, `detectCores` will be used to decide upon the number of available cores. That number minus 1 cores will be used to search for the optimal choice set. For small problems (6 parameters), `parallel = TRUE` can be slower. For larger problems the computation time will decrease significantly. **Note:** this function is more stable than `SeqCEA`, but it takes more time to get the output. This happens because this function makes an exhaustive search to get the choice set, whereas `SeqCEA` makes a random search. ## Examples ```r # DB efficient choice set, given a design and parameter draws. # Candidate profiles cs <- Profiles(lvls = c(3, 3, 3), coding = c("D", "D", "D")) m <- c(0.3, 0.2, -0.3, -0.2, 1.1, 2.4) # mean (total = 6 parameters). pc <- diag(length(m)) # covariance matrix set.seed(123) sample <- MASS::mvrnorm(n = 10, mu = m, Sigma = pc) # Initial design. des <- example_design # Efficient choice set to add. SeqMOD(des = des, cand.set = cs, n.alts = 2, par.draws = sample, prior.covar = pc, parallel = FALSE) # DB efficient choice set, given parameter draws. # with alternative specific constants des <- example_design2 cs <- Profiles(lvls = c(3, 3, 3), coding = c("D", "D", "D")) ac <- c(1, 1, 0) # Alternative specific constants. m <- c(0.3, 0.2, -0.3, -0.2, 1.1, 2.4, 1.8, 1.2) # mean pc <- diag(length(m)) # covariance matrix pos <- MASS::mvrnorm(n = 10, mu = m, Sigma = pc) sample <- list(pos[ , 1:2], pos[ , 3:8]) # Efficient choice set. SeqMOD(des = des, cand.set = cs, n.alts = 3, par.draws = sample, alt.cte = ac, prior.covar = pc, parallel = FALSE) ``` ## References \insertRef idefixidefix \insertRef juidefix

SeqMOD function