1d:T693,# Hessian of the observed datat Multivariate Normal Log-Likelihood with Incomplete Data The Hessian of the normal-theory observed data log-likelihood function, evaluated at a given value of the mean vector and the covariance matrix, when data are incomplete. The output is a symmetric matrix with rows/columns corresponding to elements in the mean vector and lower diagonal of the covariance matrix. ```r Ddf(data, mu, sig) ``` ## Arguments - `data`: A matrix consisting of at least two columns. Values must be numerical with missing data indicated by NA. - `mu`: A row matrix consisting of the values of the mean at which points the Hessian of the log-likelihood is to be computed. - `sig`: A symmetric covariance matrix at at which points the Hessian of the log-likelihood is to be computed. ## Returns - **dd**: The resulting Hessian matrix - **se**: Negative of the inverse of the Hessian matrix ## Details While mu is a vector, it has to be input as a matrix object. See example nelow. ## Note There must be no rows in data that contain no observations. ## Examples ```r set.seed <- 50 n <- 200 p <- 4 pctmiss <- 0.2 y <- matrix(rnorm(n * p),nrow = n) missing <- matrix(runif(n * p), nrow = n) < pctmiss y[missing] <- NA mu <- c(0,0,0,0) sig <- matrix(c(1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1),4,4) Ddf(data=y, as.matrix(mu), sig) ``` ## References Jamshidian, M. and Bentler, P. M. (1999). ``ML estimation of mean and covariance structures with missing data using complete data routines.'' **Journal of Educational and Behavioral Statistics,** 24, 21-41, tools:::Rd_expr_doi("10.2307/1165260") . ## Author(s) Mortaza Jamshidian, Siavash Jalal, and Camden Jansen1e:T49a,M7.49933 0.25C3.49635 0.25 0.25 3.49593 0.25 7.50024C0.25 10.703 2.32715 13.4206 5.2081 14.3797C5.57084 14.446 5.70302 14.2222 5.70302 14.0299C5.70302 13.8576 5.69679 13.4019 5.69323 12.797C3.67661 13.235 3.25112 11.825 3.25112 11.825C2.92132 10.9874 2.44599 10.7644 2.44599 10.7644C1.78773 10.3149 2.49584 10.3238 2.49584 10.3238C3.22353 10.375 3.6

Ddf function