ui.ols: Uncertainty intervals for OLS regression
In ui: Uncertainty Intervals and Sensitivity Analysis for Missing Data

Description Usage Arguments Details Value Author(s) References Examples

This function allows you to derive uncertainty intervals for OLS regression when there is missing data in the continuous outcome. The uncertainty intervals can be used as a sensitivity analysis to ignorability (missing at random). Note that rho=0 render the same results as a complete case analysis.

1 2	ui.ols(out.formula, mis.formula = NULL, data, rho = c(-0.3, 0.3), alpha = 0.05, gridn = 101)

`out.formula`	Formula for outcome regression.
`mis.formula`	Formula for missingness mechanism. If NULL the same covariates as in the outcome regression will be used.
`data`	data.frame containing the variables in the formula.
`rho`	The limits of rho for which the uncertainty interval should be constructed.
`alpha`	Default 0.05 corresponding to a confidence level of 95 for CI and UI.
`gridn`	The number of distinct points within the interval `rho` at which confidence intervals should be constructed. Default is 101.

In order to visualize the results, you can use plot.uiols, or profile.uiols.

A list containing:

`call`	The matched call
`ci`	Confidence intervals for different values of `rho`
`ui`	Uncertainty intervals
`coef`	Estimated coefficients (outcome regression) for different values of `rho`
`out.model`	Outcome regression model when rho=0.
`mis.model`	Regression model for missingness mechanism (selection).
`rho`	The range of `rho` for which we want to construct an uncertainty interval
`gridrho`	The values of `rho` for which bias and standard errors are derived
`sigma`	Consistant estimate of sigma
`se`	Standard error for different values of `rho`
`ciols`	Confidence intervals from a complete case analysis
`ident.bound`	Bounds for the coefficient estimates.

Minna Genbäck

Genbäck, M., Stanghellini, E., de Luna, X. (2015). Uncertainty Intervals for Regression Parameters with Non-ignorable Missingness in the Outcome. Statistical Papers, 56(3), 829-847.

library(MASS)
n<-500
delta<-c(0.5,0.3,0.1)
beta<-c(0.8,-0.2,0.3)
X<-cbind(rep(1,n),rnorm(n),rbinom(n,1,0.5))
x<-X[,-1]
rho=0.4
error<-mvrnorm(n,c(0,0),matrix(c(1,rho*2,rho*2,4),2))
zstar<-X%*%delta+error[,1]
z<-as.numeric(zstar>0)
y<-X%*%beta+error[,2]
y[z==0]<-NA
data<-data.frame(y,x,z)
ui<-ui.ols(y~X1+X2,data=data,rho=c(-0.5,0.5))
ui
plot(ui)