# Score based variance estimation for multiple imputation This function implements the score based variance estimation approach described by von Hippel and Bartlett (2021), which is based on earlier work by Wang and Robins (1998). ```r scoreBased(imps, analysisFun, scoreFun, pd = NULL, dfComplete = NULL, ...) ``` ## Arguments - `imps`: A list of imputed datasets produced by one of the imputation functions in `mlmi` or another package. - `analysisFun`: A function to analyse the imputed datasets that when applied to a dataset returns a list containing a vector `est`. - `scoreFun`: A function whose first argument is a dataset and whose second argument is a vector of parameter values. It should return a matrix of subject level scores evaluated at the parameter value passed to it. - `pd`: If `imps` was not generated by one of the imputation functions in `mlmi`, this argument must be specified to indicate whether the imputations were generated using posterior draws (TRUE) or not (FALSE). - `dfComplete`: The complete data degrees of freedom. If `analysisFun` returns a vector of parameter estimates, `dfComplete` should be a vector of the same length. If not specified, it is assumed that the complete data degrees of freedom is effectively infinite (1e+05). - `...`: Other parameters that are to be passed through to `analysisFun`. ## Returns A list containing the overall parameter estimates, its corresponding covariance matrix, and degrees of freedom for each parameter. ## Examples ```r #simulate a partially observed dataset set.seed(1234) n <- 100 x <- rnorm(n) y <- x+rnorm(n) y[1:50] <- NA temp <- data.frame(x,y) #impute using normUniImp, without posterior draws imps <- normUniImp(temp, y~x, M=10, pd=FALSE) #define a function which performs our desired analysis on a dataset, returning #the parameter estimates yonx <- function(inputData) { fitmod <- lm(y~x, data=inputData) list(est=c(fitmod$coef,sigma(fitmod)^2)) } #define a function which when passed a dataset and parameter #vector, calculates the likelihood score vector myScore <- function(inputData, parm) { beta0 <- parm[1] beta1 <- parm[2] sigmasq <- parm[3] res <- inputData$y - beta0 - beta1*inputData$x cbind(res/sigmasq, (res*inputData$x)/sigmasq, res^2/(2*sigmasq^2)-1/(2*sigmasq)) } #call scoreBased to perform variance estimation scoreBased(imps, analysisFun=yonx, scoreFun=myScore) ``` ## References Wang N., Robins J.M. (1998) Large-sample theory for parametric multiple imputation procedures. Biometrika 85(4): 935-948. tools:::Rd_expr_doi("10.1093/biomet/85.4.935") . von Hippel P.T. and Bartlett J.W. Maximum likelihood multiple imputation: faster, more efficient imputation without posterior draws. Statistical Science 2021; 36(3) 400-420 tools:::Rd_expr_doi("10.1214/20-STS793") .

scoreBased function