Substantive Model Compatible Multiple Imputation (Single Level)
Computes substantive model compatible multiple imputation (Bartlett et al., 2015;
Bartlett & Morris, 2015). Several regression functions are allowed (see dep_type).
mice.impute.smcfcs(y, ry, x, wy=NULL, sm, dep_type="norm", sm_type="norm",
fac_sd_proposal=1, mh_iter=20, ...)y |
Incomplete data vector of length |
ry |
Vector of missing data pattern ( |
x |
Matrix ( |
wy |
Logical vector indicating positions where imputations should be conducted. |
sm |
Formula for substantive model. |
dep_type |
Distribution type for variable which is imputed.
Possible choices are |
sm_type |
Distribution type for dependent variable in substantive model.
One of the distribution mentioned in |
fac_sd_proposal |
Starting value for factor of standard deviation in Metropolis-Hastings sampling. |
mh_iter |
Number iterations in Metropolis-Hasting sampling |
... |
Further arguments to be passed |
Imputed values are drawn based on a Metropolis-Hastings sampling algorithm in which the standard deviation of the proposal distribution is adaptively tuned.
A vector of length nmis=sum(!ry) with imputed values.
Bartlett, J. W., & Morris, T. P. (2015). Multiple imputation of covariates by substantive-model compatible fully conditional specification. Stata Journal, 15(2), 437-456.
Bartlett, J. W., Seaman, S. R., White, I. R., Carpenter, J. R., & Alzheimer's Disease Neuroimaging Initiative (2015). Multiple imputation of covariates by fully conditional specification: Accommodating the substantive model. Statistical Methods in Medical Research, 24(4), 462-487. doi: 10.1177/0962280214521348
See the smcfcs package for an alternative implementation of substantive model multiple imputation in a fully conditional specification approach.
## Not run:
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# EXAMPLE 1: Substantive model with interaction effects
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library(mice)
library(mdmb)
#--- simulate data
set.seed(98)
N <- 1000
x <- stats::rnorm(N)
z <- 0.5*x + stats::rnorm(N, sd=.7)
y <- stats::rnorm(N, mean=.3*x - .2*z + .7*x*z, sd=1 )
dat <- data.frame(x,z,y)
dat[ seq(1,N,3), c("x","y") ] <- NA
#--- define imputation methods
imp <- mice::mice(dat, maxit=0)
method <- imp$method
method["x"] <- "smcfcs"
# define substantive model
sm <- y ~ x*z
# define formulas for imputation models
formulas <- as.list( rep("",ncol(dat)))
names(formulas) <- colnames(dat)
formulas[["x"]] <- x ~ z
formulas[["y"]] <- sm
formulas[["z"]] <- z ~ 1
#- Yeo-Johnson distribution for x
dep_type <- list()
dep_type$x <- "yj"
#-- do imputation
imp <- mice::mice(dat, method=method, sm=sm, formulas=formulas, m=1, maxit=10,
dep_type=dep_type)
summary(imp)
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# EXAMPLE 2: Substantive model with quadratic effects
#############################################################################
#** simulate data with missings
set.seed(50)
n <- 1000
x <- stats::rnorm(n)
z <- stats::rnorm(n)
y <- 0.5 * z + x + x^2 + stats::rnorm(n)
mm <- stats::runif(n)
x[sample(1:n, size=370, prob=mm)] <- NA
z[sample(1:n, size=480, prob=mm)] <- NA
y[sample(1:n, size=500, prob=mm)] <- NA
df <- data.frame(x=x,y=y,z=z)
#** imputation
imp <- mice::mice(df, method="smcfcs", sm=y ~ z + x + I(x^2), m=6, maxit=10)
summary(imp)
#** analysis
summary(mice::pool(with(imp, stats::lm(y ~ z + x + I(x^2)))))
#** imputation using the smcfcs package
df$x_sq <- df$x^2
nonmice <- smcfcs::smcfcs(df, smtype="lm", smformula=y ~ z + x + x_sq,
method=c("norm", "", "norm", "x^2"))
mice::pool(lapply(nonmice$impDatasets, function(x) stats::lm(y ~ z + x + x_sq, data=x)))
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