# Maximisation of the likelihood for one or more mixed traces of DNA **IMPORTANT: This is the `DNAmixturesLite` package, which is intended as a service to enable users to try `DNAmixtures` without purchasing a commercial licence for Hugin. When at all possible, we strongly recommend the use of `DNAmixtures` rather than this lite-version. See [https://dnamixtures.r-forge.r-project.org/](https://dnamixtures.r-forge.r-project.org/) for details on both packages.** **While the lite-version seeks to provide the full functionality of `DNAmixtures`, note that computations are much less efficient and that there are some differences in available functionality. Be aware that the present documentation is copied from `DNAmixtures` and thus may not accurately describe the implementation of this lite-version.** ```r mixML( mixture, pars, constraints = NULL, phi.eq = FALSE, val = NULL, trace = FALSE, order.unknowns = TRUE, ... ) ``` ## Arguments - `mixture`: A `DNAmixture` object. - `pars`: A `mixpar` parameter used as a starting value for the optimisation. - `constraints`: Equality constraint function as function of an array of parameters. - `phi.eq`: Should the mixture proportions be the same for all traces? Defaults to FALSE. - `val`: Vector of values to be satisfied for the equality constraints. - `trace`: Print the evaluations of the likelihood-function during optimisation? - `order.unknowns`: Should unknown contributors be ordered according to decreasing contributions? Defaults to TRUE. - `...`: Further arguments to be passed on to `solnp`. ## Returns A list containing - **mle**: The (suggested) MLE. - **lik**: The log of the likelihood (log e). as well as the output from the optimisation. ## Details The pre-specified constraints for the model parameter `pars` are for each mixture `r` * `0 \<= pars[[r, "rho"]] \< Inf` * `0 \<= pars[[r, "eta"]] \< Inf` * `0 \<= pars[[r, "xi"]] \<= 1` * `0 \<= pars[[r, "phi"]][i] \<= 1` * `sum(pars[[r, "phi"]]) == 1`. * If there are 2 or more unknown contributors, then the mixture proportions for the unknown contributors are ordered decreasingly with the first DNA mixture determining the order. Further constraints can be specified by the user; for this see examples below. ## Examples ```r data(MC15, USCaucasian) mix <- DNAmixture(list(MC15), C = list(50), k = 3, K = c("K1", "K2", "K3"), database = USCaucasian) startpar <- mixpar(rho = list(24), eta = list(37), xi = list(0.08), phi = list(c(K3 = 0.15, K1 = 0.8, K2 = 0.05))) ml <- mixML(mix, startpar) ml$mle data(MC15, USCaucasian) mix <- DNAmixture(list(MC15), C = list(50), k = 3, K = "K1", database = USCaucasian) startpar <- mixpar(rho = list(24), eta = list(37), xi = list(0.08), phi = list(c(U1 = 0.05, K1 = 0.8, U2 = 0.15))) ml <- mixML(mix, startpar) ml$mle ## The following advanced example has a model with two DNA samples ## and various parameter restrictions. ## Be aware that the computation is rather demanding and takes ## a long time to run with this lite-version of DNAmixtures. ## With DNAmixtures (based on HUGIN), it takes only about one minute. data(MC15, MC18, USCaucasian) mix <- DNAmixture(list(MC15, MC18), C = list(50, 38), k = 3, K = "K1", database = USCaucasian) startpar <- mixpar(rho = list(24, 25), eta = list(37, 40), xi = list(0.08, 0.1), phi = list(c(U1 = 0.05, K1 = 0.7, U2 = 0.25), c(K1 = 0.7, U2 = 0.1, U1 = 0.2))) eqxis <- function(x){ diff(unlist(x[,"xi"])) } ## Note that for these two traces, we do not expect phi to be equal. ## Here we set stutter equal for all traces ml.diff <- mixML(mix, startpar, eqxis, val = 0, phi.eq = FALSE) ## Equal mixture proportions across traces ml.eqphi <- mixML(mix, startpar, eqxis, val = 0, phi.eq = TRUE) ## Likelihood ratio test for equal mixture proportions pchisq(-2*(ml.eqphi$lik - ml.diff$lik), df = 1, lower.tail = FALSE) ``` ## See Also `DNAmixture` ## Author(s) Therese Graversen

mixML function