Package ICE. R topics documented: February 19, 2015
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1 Package ICE February 19, 2015 Title Iterated Conditional Expectation Version 0.69 Author W. John Braun Kernel Estimators for Interval-Censored Data LazyLoad true LazyData true Depends R (>= 2.0.1), KernSmooth, stats ZipData no Maintainer W. John Braun <braun@stats.uwo.ca> License GPL (>= 2) NeedsCompilation yes Repository CRAN Date/Publication :53:05 R topics documented: bickde ICGG ICHemophiliac ickde icllde iclocpoly inmost likelihoodcv motor.ic Index 9 1
2 2 bickde bickde Bandwidth choice for Interval-Censored Kernel Density Estimation Likelihood Cross-Validation bandwidth choice for interval-censored kernel density estimates. Also computed is the direct-plug-in estimate (using the KernSmooth function dpik based on the interval midpoints. bickde(, factor) factor A scalar factor which gives upper and lower bounds for the initial interval for the golden section search relative to a preliminary value computed by dpik. Default value is 10 which specifies an initial interval of (dpik/10, dpik*10). Details Maximization of the likelihood is accomplished by golden section search using the optimize() function. This can be very SLOW. A scalar value. Author(s) W.J. Braun References Braun, J., Duchesne, T. and Stafford, J.E. (2005) Local likelihood density estimation for interval censored. Canadian Journal of Statistics 33: # Not run # bickde(ichemophiliac)
3 ICGG 3 ICGG Gentleman and Geyer s Data Gentleman and Geyer s Data. (ICGG) Format Source A frame with 6 observations on the following 2 variables. left the left interval endpoint right the right interval endpoint Gentleman, R. and Geyer, C. (1994) Maximum Likelihood for Interval Censored Data: Consistency and Computation. Biometrika. library(kernsmooth) tmp <- apply(icgg, 1, mean) h <- dpik(tmp) # tmp now contains the interval midpoints # direct-plug-in bandwidth selected for # interval midpoints par(mfrow=c(1,2)) estimate <- ickde(icgg, h=h, m=200) plot(estimate, type="l", main="one fixed point") estimate <- ickde(icgg, f=c(rep(1,60),rep(0,90),rep(1,60)), h=.1) plot(estimate, type="l", main="another fixed point") ICHemophiliac Hemophiliac Data Set Time (interval-censored) to onset of HIV infection. (ICHemophiliac)
4 4 ickde Format a matrix with 2 columns. The first column contains the left endpoints of the intervals, and the second column contains the right endpoints. ickde Interval-Censored Kernel Density Estimation Iterated conditional expectation kernel density estimation using a local constant. The bandwidth is assumed fixed. (See the example for a way to get a quick ballpark estimate of the bandwidth.) The gaussian, epanechnikov and biweight kernels can be used. Note that the bandwidth estimate would have to be adjusted before using with epanechnikov or biweight. ickde(i, h, f, m, n.iterations = 10, x1, xm, right.limit = 10000,kernel="gaussian", old=true) I h f m n.iterations x1 xm right.limit kernel old A scalar bandwidth An initial estimate of the density at a sequence of grid points (optional; if this is used, do not specify m) The number of (equally-spaced) grid points at which the density is to be estimated The maximum number of iterations allowed The left-most grid point (optional) The right-most grid point (optional) For right-censored, the value to be used as an artificial right endpoint for the intervals character argument indicated choice of kernel; current choices are "gaussian", "epanechnikov", "biweight" logical value, indicating whether denominators in conditional expectation calculation should use the previous value of the density estimate. An object of class IC Author(s) W.J. Braun
5 icllde 5 References Braun, J., Duchesne, T. and Stafford, J.E. (2005) Local likelihood density estimation for interval censored. Canadian Journal of Statistics 33: tmp <- apply(ichemophiliac, 1, mean) h <- try(dpik(tmp), silent=t) # dpik() will work if KernSmooth is loaded if (class(h)!="numeric" ) h <-.9 # this makes the example work # if KernSmooth is not loaded estimate <- ickde(ichemophiliac, m=200, h=h) plot(estimate, type="l") icllde Interval-Censored Local Linear Density Estimation This is the local linear version of ickde. icllde(i, h, f, m, n.iterations = 10, x1, xm, right.limit = 10000, kernel="gaussian") I h f m n.iterations x1 xm right.limit kernel A scalar bandwidth An initial estimate of the density at a sequence of grid points (optional) The number of (equally-spaced) grid points at which the density is to be estimated The maximum number of iterations allowed The minimum grid point (optional) The maximum grid point (optional) For right-censored, the value to be used as an artificial right endpoint for the intervals character argument indicated choice of kernel; current choices are "gaussian", "epanechnikov", "biweight" An object of class IC
6 6 iclocpoly (ICHemophiliac) estimate <- icllde(ichemophiliac, m=200, h=.9) plot(estimate, type="l") iclocpoly Interval-Censored Local Polynomial Regression Estimation Local polynomial regression estimation for interval-censored. iclocpoly(x, y=null, y.ic, degree=0, h, niter=10, kernel="normal", gridsize=401) x y y.ic degree h niter kernel gridsize uncensored explanatory variable vector uncensored portion of response vector (optional) two-column matrix of left and right interval endpoints for censored responses degree of local polynomial bandwidth number of iterations smoothing kernel to be used; default is "normal"; other choices as in the function locpoly number of gridpoints; again as in locpoly A list consisting of the explanatory variable x and the imputed responses y as well as the estimate of sigma. Usually, one would apply locpoly with a similar bandwidth to obtain the final fitted model. library(kernsmooth) (motor.ic) estimate <- iclocpoly(x=motor.ic$v1, y.ic = cbind(motor.ic$y.l, motor.ic$y.r), degree=0, h=1) plot(motor.ic$v1, motor.ic$v2) lines(locpoly(estimate$x, estimate$y, bandwidth=1, degree=0),col=4)
7 inmost 7 inmost Innermost Intervals for Interval-Censored Data This function calculates the innermost intervals (Turnbull s algorithm) for interval-censored. Right-censored is not allowed at this point. inmost(, eps) eps A scalar additive value which jitters the slightly to break ties. A 2 column matrix of the left and right endpoints of the innermost intervals. Author(s) W.J. Braun References Turnbull (1976) The empirical distribution function with arbitrarily grouped, censored and truncated. Journal of the Royal Statistical Society Series B, 38: likelihoodcv Log Cross-Validated Likelihood Log Cross-Validated Likelihood for interval-censored. The likelihood is the product of integrals over the innermost intervals. Leave-one-out cross-validation here is accomplished by leaving out each innermost interval and re-computing the integral using the remaining. likelihoodcv(p,, m=101)
8 8 motor.ic p m A scalar specifying the bandwidth used in the kernel density estimate. numeric quantity which controls the number of grid points used in the density estimate A scalar value. Author(s) W.J. Braun References Braun, J., Duchesne, T. and Stafford, J.E. (2005) Local likelihood density estimation for interval censored. Canadian Journal of Statistics 33: motor.ic Motorcycle Data with artificial interval-censored responses Format The original motorcycle with exponential random variables added and subtracted to the responses to create interval-censored responses. (motor.ic) A frame with 4 variables V1 time, the explanatory vector V2 acceleration, the response y.l y - an exponential random variable y.r y + an exponential random variable
9 Index Topic sets ICGG, 3 ICHemophiliac, 3 motor.ic, 8 Topic models bickde, 2 ickde, 4 icllde, 5 iclocpoly, 6 inmost, 7 likelihoodcv, 7 bickde, 2 ICGG, 3 ICHemophiliac, 3 ickde, 4 icllde, 5 iclocpoly, 6 inmost, 7 likelihoodcv, 7 motor.ic, 8 9
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