ui.probit: Uncertainty intervals for probit regression

In ui: Uncertainty Intervals and Sensitivity Analysis for Missing Data

Description

This function allows you to derive uncertainty intervals for probit regression when there is missing data in the binary outcome. The uncertainty intervals can be used as a sensitivity analysis to ignorability (missing at random), and are derived by maximum likelihood. Note that rho=0 render the same results as a complete case analysis.

Usage

ui.probit(out.formula, mis.formula = NULL, data, rho = c(-0.3, 0.3),
  progress = TRUE, max.grid = 0.1, alpha = 0.05, method = "NR")

Arguments

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	Vector containing the values of rho for which we want to fit the likelihood.
progress	If TRUE prints out process time for each maximization of the likelihood.
max.grid	Maximum distance between two elements in rho, if two wide there can difficulties with convergence of the maximum likelihood.
alpha	Default 0.05 corresponding to a confidence level of 95 for CI and UI.
method	Maximization method to be passed through maxLik

Details

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

Value

A list containing:

coef	Estimated coefficients (outcome regression) for different values of rho.
rho	The values of rho for which the likelihood is maximized.
vcov	Covariance matrix.
ci	Confidence intervals for different values of rho.
ui	Uncertainty intervals.
out.model	Outcome regression model when rho=0.
mis.model	Regression model for missingness mechanism (selection).
se	Standard errors from outcome regression.
value	Value of maximum likelihood for different values of rho.
y	Outcome vector.
z	Indicator variable of observed outcome.
X.y	Covariate matrix for outcome regression.
X.z	Covariate matrix for missingness mechanism (selection regression model).
max.info	Information about the maximization procedure. Includes whether it converged, message, method and number of iterations.

Author(s)

Minna Genbäck

References

Genbäck, M., Ng, N., Stanghellini, E., de Luna, X. (2018). Predictors of Decline in Self-reported Health: Addressing Non-ignorable Dropout in Longitudinal Studies of Aging. European journal of ageing, 15(2), 211-220.

Examples

library(MASS)
n<-500

delta<-c(0.5,0.6,0.1,-1,1)
beta<-c(-0.3,-0.5,0,-0.4,-0.3)

X<-cbind(rep(1,n),rnorm(n),runif(n),rbinom(n,2,0.5),rbinom(n,1,0.5))
x<-X[,-1]
rho=0.4
error<-mvrnorm(n,c(0,0),matrix(c(1,rho,rho,1),2))

zstar<-X%*%delta+error[,1]
z<-as.numeric(zstar>0)

ystar<-X%*%beta+error[,2]
y<-as.integer(ystar>0)
y[z==0]<-NA
data=data.frame(y=y,x1=x[,1],x2=x[,2],x3=x[,3],x4=x[,4])

m<-ui.probit(y~x1+x2+x3+x4,data=data,rho=c(0,0.5))
m
plot(m)
profile(m)

Example output

Optimization for rho = 0.1 
   Time elapsed: 0.709 s 
Optimization for rho = 0.2 
   Time elapsed: 0.734 s 
Optimization for rho = 0.3 
   Time elapsed: 0.695 s 
Optimization for rho = 0.4 
   Time elapsed: 0.783 s 
Optimization for rho = 0.5 
   Time elapsed: 0.7 s 

Call:
ui.probit(out.formula = y ~ x1 + x2 + x3 + x4, data = data, rho = c(0,     0.5))


Confidence intervals (CI) derived assuming ignorable dropout (rho=0)
Uncertainty intervals (UI) derived assuming 0<=rho<=0.5

               Est               ci               ui
(Intercept) -0.033  (-0.474, 0.408)   (-0.75, 0.408)
x1          -0.493 (-0.708, -0.278) (-0.708, -0.106)
x2          -0.165  (-0.772, 0.443)  (-0.772, 0.459)
x3          -0.243  (-0.539, 0.052)  (-0.716, 0.052)
x4          -0.502  (-0.88, -0.124)   (-0.88, 0.105)

ui documentation built on Nov. 11, 2019, 5:07 p.m.