# Sequential Coordinate Exchange algorithm for MNL model. Selects the choice set that minimizes the DB-error when added to an initial design, given (updated) parameter values. ```r SeqCEA( des = NULL, lvls, coding, c.lvls = NULL, n.alts, par.draws, prior.covar, alt.cte = NULL, no.choice = NULL, weights = NULL, parallel = TRUE, reduce = TRUE, n.cs = NULL ) ``` ## 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` - `lvls`: A numeric vector which contains for each attribute the number of levels. - `coding`: Type of coding that needs to be used for each attribute. - `c.lvls`: A list containing numeric vectors with the attribute levels for each continuous attribute. The default is `NULL`. - `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. - `n.cs`: An integer indicating the number of possible random choice sets to consider in the search for the next best choice set possible. The default is `NULL`. ## 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 the 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 is created by selecting randomly a level for each attribute in an alternative/profile. `n.cs` controls the number of potential choice sets to consider. The default is `NULL`, which means that the number of possible choice sets is the product of attribute levels considered in the experiment. For instance, an experiment with 3 attribute and 3 levels each will consider 3^3 = 27 possible choice sets. 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 faster than `SeqMOD`, but the output is not as stable. This happens because this function makes a random search to get the choice set, whereas `SeqMOD` makes an exhaustive search. ## Examples ```r # DB efficient choice set, given a design and parameter draws. # 3 attributes with 3 levels each 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. SeqCEA(des = des, lvls = c(3, 3, 3), coding = c("D", "D", "D"), 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 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. SeqCEA(des = des, lvls = c(3, 3, 3), coding = c("D", "D", "D"), n.alts = 3, par.draws = sample, alt.cte = ac, prior.covar = pc, parallel = FALSE) ``` ## References \insertRef idefixidefix \insertRef juidefix \insertRef ceaidefix \insertRef cea_discreteidefix

SeqCEA function