# Estimated asymptotic variance matrix for MLE Provided that the user specifies the MLE as well as the constraints used in the maximisation, this function computes an estimate of the variance of the MLE based on the observed information. The observed information is obtained by numerically deriving the Hessian of the log-likelihood function. **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 varEst(mixture, mle, npars, method = "Richardson", ...) ## S3 method for class 'mixVarEst' summary(object, transform = FALSE, ...) ## S3 method for class 'summary.mixVarEst' print( x, digits = max(3, getOption("digits") - 3), scientific = FALSE, print.gap = 3L, ... ) ``` ## Arguments - `mixture`: A `DNAmixture`. - `mle`: A `mixpar`, typically obtained by `mixML`. - `npars`: A list of integers specifying the number of each of the four parameters `rho`, `eta`, `xi` and `phi`. Allowed values are - **`0`**: The parameter is fixed, but might differ across mixtures. - **`1`**: The parameter is equal across mixtures. - **`N`**: There is one parameter for each of the `N` mixtures in the model. - `method`: Method for numeric differentiation used in `hessian` - `...`: Arguments to be passed on to other methods. - `object`: An object of class `mixVarEst`, typically obtained by a call to `varEst`. - `transform`: Should the parameterisation $(\mu, \sigma)$ be used? Defaults to `FALSE`. - `x`: An object of class `"summary.mixVarEst"`. - `digits`: Number of significant digits to print - `scientific`: Should scientific notation be used? - `print.gap`: Distance between columns in the printing of the summary. ## Returns The mle and the estimated covariance matrix in different parametrisations - **`cov` and `mle`**: $\rho, \eta, \xi, \phi$ - **`cov.trans` and `mle.trans`**: $\mu, \sigma, \xi, \phi$ - **`cov.res`**: A non-singular covariance matrix for a reparametrisation of $\rho, \eta, \xi, \phi$, collapsing the parameters according to the specified constrains and removing one contributor from $\phi$. An integer suffix is used to indicate which mixture the parameter is associated with. In the restricted covariance matrix, all fixed parameters are left out. If parameters are equal accross mixtures, the suffix for this parameter will be `.1`. If parameters are unconstrained and there are `N` mixtures in the model, suffixes are `.1, ..., .N` ## Details As the user can apply highly customized constraints to the model parameters when maximising with `mixML`, it is a complicated matter to write a generic function for computing the asymptotic variance matrix. We have thus restricted attention to the case where each of the (multi-dimensional) parameters `rho`, `eta`, `xi` and `phi` can be either * fixed at known values * unknown, but common across traces * unconstrained ## Examples ```r data(MC18, USCaucasian) mixHp <- DNAmixture(list(MC18), k = 3, K = c("K1", "K2", "K3"), C = list(50), database = USCaucasian) p <- mixpar(rho = list(30), eta = list(34), xi = list(0.08), phi = list(c(K1 = 0.71, K3 = 0.1, K2 = 0.19))) mlHp <- mixML(mixHp, pars = p) ## Find the estimated covariance matrix of the MLE V.Hp <- varEst(mixHp, mlHp$mle, npars = list(rho=1,eta=1,xi=1,phi=1)) V.Hp$cov ## using (rho, eta) V.Hp$cov.trans ## using (mu, sigma) ## The summary is a table containing the MLE and their standard errors summary(V.Hp) data(MC18, USCaucasian) mixmult <- DNAmixture(list(MC18), C = list(50), k = 3, K = c("K1", "K2"), database = USCaucasian) startpar <- mixpar(rho = list(30), eta = list(28), xi = list(0.08), phi = list(c(U1 = 0.2, K1 = 0.7, K2 = 0.1))) ml.mult <- mixML(mixmult, startpar) Vmult <- varEst(mixmult, ml.mult$mle, list(rho=1,eta=1,xi=1,phi=1)) summary(Vmult) ## Be aware that the following two advanced examples are computationally demanding and ## typically have a runtime of several minutes with the lite-version of DNAmixtures. data(MC15, MC18, USCaucasian) mix <- DNAmixture(list(MC15, MC18), C = list(50, 38), k = 3, K = c("K1", "K2"), database = USCaucasian) startpar <- mixpar(rho = list(30, 30), eta = list(28, 35), xi = list(0.08, 0.1), phi = list(c(U1 = 0.05, K1 = 0.7, K2 = 0.25), c(K1 = 0.7, K2 = 0.1, U1 = 0.2))) eqxis <- function(x){ diff(unlist(x[,"xi"])) } ## Here we set stutter equal for all traces ml.diff <- mixML(mix, startpar, eqxis, val = 0, phi.eq = FALSE) V.diff <- varEst(mix, ml.diff$mle, list(rho=2,eta=2,xi=1,phi=2)) summary(V.diff) ## Fixing stutter to 0.07 xival <- function(x){unlist(x[,"xi"])} ml.eq <- mixML(mix, startpar, xival, val = c(0.07, 0.07), phi.eq = FALSE) V.eq <- varEst(mix, ml.eq$mle, list(rho=2,eta=2,xi=0,phi=2)) summary(V.eq) ```

varEst function