# Multiple Imputation with Generalized Additive Models for Location, Scale, and Shape. Imputes univariate missing data using a generalized model for location, scale and shape. ```r mice.impute.gamlss(y, ry, x, family = NO, n.ind.par = 2, fitted.gam = NULL, gam.mod = list(type = "pb"), EV = TRUE, ...) mice.impute.gamlssNO(y, ry, x, fitted.gam = NULL, EV = TRUE, ...) mice.impute.gamlssBI(y, ry, x, fitted.gam = NULL, EV = TRUE, ...) mice.impute.gamlssJSU(y, ry, x, fitted.gam = NULL, EV = TRUE, ...) mice.impute.gamlssPO(y, ry, x, fitted.gam = NULL, EV = TRUE, ...) mice.impute.gamlssTF(y, ry, x, fitted.gam = NULL, EV = TRUE, ...) mice.impute.gamlssGA(y, ry, x, fitted.gam = NULL, EV = TRUE, ...) mice.impute.gamlssZIBI(y, ry, x, fitted.gam = NULL, EV = TRUE, ...) mice.impute.gamlssZIP(y, ry, x, fitted.gam = NULL, EV = TRUE, ...) fit.gamlss(y, ry, x, family = NO, n.ind.par = 2, gam.mod = list(type = "pb"), ...) ``` ## Arguments - `y`: Numeric vector with incomplete data. - `ry`: Response pattern of 'y' ('TRUE'=observed, 'FALSE'=missing). - `x`: Design matrix with 'length(y)' rows and 'p' columns containing complete covariates. - `family`: Distribution family to be used by GAMLSS. It defaults to NO but a range of families can be defined by calling the corresponding "gamlssFAMILY" method. - `n.ind.par`: Number of parameters from the distribution family to be individually estimated. - `fitted.gam`: A predefined bootstrap gamlss method returned by `fit.gamlss`. Mice by default refits the model with each imputation. The parameter is here for a future faster modified mice function. - `gam.mod`: list with the parameters of the GAMLSS imputation model. - `EV`: Logical value to determine whether to correct or not extreme imputed values. This can arise due to too much flexibility of the gamlss model. - `...`: extra arguments for the control of the gamlss fitting function ## Returns Numeric vector with imputed values for missing `y` values ## Details Imputation of `y` using generalized additive models for location, scale, and shape. A model is fitted with the observed part of the data set. Then a bootstrap sample is generated and used to refit the model and generate imputations. The function `fit.gamlss` handles the fitting and the bootstrap and returns a method to generated imputations. Being gamlss a flexible non parametric method, there may be problems with the fitting and imputation depending on the sample size. The imputation functions try to handle anomalies automatically, but results should be still inspected. ## Examples ```r require(lattice) # Create the imputed data sets predMat <- matrix(rep(0,25), ncol = 5) predMat[4,1] <- 1 predMat[4,5] <- 1 predMat[2,1] <- 1 predMat[2,5] <- 1 predMat[2,4] <- 1 predMat[3,1] <- 1 predMat[3,5] <- 1 predMat[3,4] <- 1 predMat[3,2] <- 1 imputed.sets <- mice(sample.data, m = 2, method = c("", "gamlssPO", "gamlss", "gamlssBI", ""), visitSequence = "monotone", predictorMatrix = predMat, maxit = 1, seed = 973, n.cyc = 1, bf.cyc = 1, cyc = 1) fit <- with(imputed.sets, lm(y ~ X.1 + X.2 + X.3 + X.4)) summary(pool(fit)) stripplot(imputed.sets) ``` ## References de Jong, R., van Buuren, S. & Spiess, M. (2016) Multiple Imputation of Predictor Variables Using Generalized Additive Models. Communications in Statistics -- Simulation and Computation, 45(3), 968--985. de Jong, Roel. (2012). “Robust Multiple Imputation.” Universität Hamburg. [http://ediss.sub.uni-hamburg.de/volltexte/2012/5971/](http://ediss.sub.uni-hamburg.de/volltexte/2012/5971/). Rigby, R. A., and Stasinopoulos, D. M. (2005). Generalized Additive Models for Location, Scale and Shape. Journal of the Royal Statistical Society: Series C (Applied Statistics) 54 (3): 507–54. ## Author(s) Daniel Salfran daniel.salfran@uni-hamburg.de

mice.impute.gamlss function