# Maximum likehood estimation for (SecSSE) with parameter as complex functions. Cladogenetic version Maximum likehood estimation under cla Several examined and concealed States-dependent Speciation and Extinction (SecSSE) where some paramaters are functions of other parameters and/or factors. Offers the option of cladogenesis ```r cla_secsse_ml_func_def_pars( phy, traits, num_concealed_states, idparslist, idparsopt, initparsopt, idfactorsopt, initfactors, idparsfix, parsfix, idparsfuncdefpar, functions_defining_params, cond = "proper_cond", root_state_weight = "proper_weights", sampling_fraction, tol = c(1e-04, 1e-05, 1e-07), maxiter = 1000 * round((1.25)^length(idparsopt)), optimmethod = "simplex", num_cycles = 1, loglik_penalty = 0, is_complete_tree = FALSE, take_into_account_root_edge = FALSE, verbose = TRUE, num_threads = 1, atol = 1e-12, rtol = 1e-12, method = "odeint::bulirsch_stoer", use_normalization = TRUE ) ``` ## Arguments - `phy`: phylogenetic tree of class `phylo`, rooted and with branch lengths. Alternatively, multiple phylogenetic trees can be provided as the `multiPhylo` class. - `traits`: vector with trait states for each tip in the phylogeny. The order of the states must be the same as the tree tips. For help, see `vignette("starting_secsse", package = "secsse")`. When providing a `multiPhylo` set of multiple phylognies, traits should be a list where each entry in the list corresponds to the matching phylogeny on that position. - `num_concealed_states`: number of concealed states, generally equivalent to the number of examined states in the dataset. - `idparslist`: overview of parameters and their values. - `idparsopt`: a numeric vector with the ID of parameters to be estimated. - `initparsopt`: a numeric vector with the initial guess of the parameters to be estimated. - `idfactorsopt`: id of the factors that will be optimized. There are not fixed factors, so use a constant within `functions_defining_params`. - `initfactors`: the initial guess for a factor (it should be set to `NULL` when no factors). - `idparsfix`: a numeric vector with the ID of the fixed parameters. - `parsfix`: a numeric vector with the value of the fixed parameters. - `idparsfuncdefpar`: id of the parameters which will be a function of optimized and/or fixed parameters. The order of id should match `functions_defining_params`. - `functions_defining_params`: a list of functions. Each element will be a function which defines a parameter e.g. `id_3 <- (id_1 + id_2) / 2`. See example. - `cond`: condition on the existence of a node root: `"maddison_cond"`, `"proper_cond"` (default). For details, see vignette. - `root_state_weight`: the method to weigh the states: `"maddison_weights"`, `"proper_weights"` (default) or `"equal_weights"`. It can also be specified for the root state: the vector `c(1, 0, 0)` indicates state 1 was the root state. When using a `multiPhylo` object, root_state_weight should be list where each entry in the list corresponds to the root_state_weight for each tree. - `sampling_fraction`: vector that states the sampling proportion per trait state. It must have as many elements as there are trait states. When using a `multiPhylo` object, sampling fraction should be list where each entry in the list corresponds to the sampling proportion for each tree. - `tol`: A numeric vector with the maximum tolerance of the optimization algorithm. Default is `c(1e-04, 1e-05, 1e-05)`. - `maxiter`: max number of iterations. Default is `1000 * round((1.25) ^ length(idparsopt))`. - `optimmethod`: A string with method used for optimization. Default is `"simplex"`. Alternative is `"subplex"`. Both are called from `DDD::optimizer()`, simplex is implemented natively in `DDD`, while subplex is ultimately called from `subplex::subplex()`. - `num_cycles`: Number of cycles of the optimization. When set to `Inf`, the optimization will be repeated until the result is, within the tolerance, equal to the starting values, with a maximum of 10 cycles. - `loglik_penalty`: the size of the penalty for all parameters; default is 0 (no penalty). - `is_complete_tree`: logical specifying whether or not a tree with all its extinct species is provided. If set to `TRUE`, it also assumes that all **all** extinct lineages are present on the tree. Defaults to `FALSE`. - `take_into_account_root_edge`: if TRUE, the LL integration is continued along the root edge. This also affects conditioning (as now, conditioning no longer needs to assume a speciation event at the start of the tree) - `verbose`: sets verbose output; default is `TRUE` when `optimmethod` is `"simplex"`. If `optimmethod` is set to `"simplex"`, then even if set to `FALSE`, optimizer output will be shown. - `num_threads`: number of threads to be used. Default is one thread. - `atol`: A numeric specifying the absolute tolerance of integration. - `rtol`: A numeric specifying the relative tolerance of integration. - `method`: integration method used, available are: `"odeint::runge_kutta_cash_karp54"`, `"odeint::runge_kutta_fehlberg78"`, `"odeint::runge_kutta_dopri5"`, `"odeint::bulirsch_stoer"` and `"odeint::runge_kutta4"`. Default method is: `"odeint::bulirsch_stoer"`. - `use_normalization`: normalize the density vector during integration, more accurate but slower (default = TRUE) ## Returns Parameter estimated and maximum likelihood ## Examples ```r # Example of how to set the arguments for an ML search. The ML search is # stopped after 10 iterations to keep the run time short. library(secsse) library(DDD) set.seed(16) phylotree <- ape::rbdtree(0.07,0.001,Tmax=50) startingpoint <- bd_ML(brts = ape::branching.times(phylotree)) intGuessLamba <- startingpoint$lambda0 intGuessMu <- startingpoint$mu0 traits <- sample(c(0,1,2), ape::Ntip(phylotree), replace = TRUE) # get some traits num_concealed_states <- 3 idparslist <- cla_id_paramPos(traits, num_concealed_states) idparslist$lambdas[1,] <- c(1,2,3,1,2,3,1,2,3) idparslist[[2]][] <- 4 masterBlock <- matrix(c(5,6,5,6,5,6,5,6,5),ncol = 3, nrow=3, byrow = TRUE) diag(masterBlock) <- NA diff.conceal <- FALSE idparslist[[3]] <- q_doubletrans(traits,masterBlock,diff.conceal) idparsfuncdefpar <- c(3,5,6) idparsopt <- c(1,2) idparsfix <- c(0,4) initparsopt <- c(rep(intGuessLamba,2)) parsfix <- c(0,0) idfactorsopt <- 1 initfactors <- 4 # functions_defining_params is a list of functions. Each function has no # arguments and to refer # to parameters ids should be indicated as 'par_' i.e. par_3 refers to # parameter 3. When a # function is defined, be sure that all the parameters involved are either # estimated, fixed or # defined by previous functions (i.e, a function that defines parameter in # 'functions_defining_params'). The user is responsible for this. In this # example, par_3 # (i.e., parameter 3) is needed to calculate par_6. This is correct because # par_3 is defined # in the first function of 'functions_defining_params'. Notice that factor_1 # indicates a value # that will be estimated to satisfy the equation. The same factor can be # shared to define several parameters. functions_defining_params <- list() functions_defining_params[[1]] <- function() { par_3 <- par_1 + par_2 } functions_defining_params[[2]] <- function() { par_5 <- par_1 * factor_1 } functions_defining_params[[3]] <- function() { par_6 <- par_3 * factor_1 } tol = c(1e-02, 1e-03, 1e-04) optimmethod = 'subplex' cond <- 'proper_cond' root_state_weight <- 'proper_weights' sampling_fraction <- c(1,1,1) maxiter <- 10 model <- cla_secsse_ml_func_def_pars(phylotree, traits, num_concealed_states, idparslist, idparsopt, initparsopt, idfactorsopt, initfactors, idparsfix, parsfix, idparsfuncdefpar, functions_defining_params, cond, root_state_weight, sampling_fraction, tol, maxiter, optimmethod, num_cycles = 1) # ML -136.5796 if run till completion ```

cla_secsse_ml_func_def_pars function