207 lines
6.9 KiB
Plaintext
207 lines
6.9 KiB
Plaintext
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R Under development (unstable) (2024-04-17 r86441) -- "Unsuffered Consequences"
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Copyright (C) 2024 The R Foundation for Statistical Computing
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Platform: aarch64-unknown-linux-gnu
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R is free software and comes with ABSOLUTELY NO WARRANTY.
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You are welcome to redistribute it under certain conditions.
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Type 'license()' or 'licence()' for distribution details.
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R is a collaborative project with many contributors.
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Type 'contributors()' for more information and
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'citation()' on how to cite R or R packages in publications.
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Type 'demo()' for some demos, 'help()' for on-line help, or
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'help.start()' for an HTML browser interface to help.
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Type 'q()' to quit R.
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> library(survival)
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> options(na.action=na.exclude) # preserve missings
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> options(contrasts=c('contr.treatment', 'contr.poly')) #ensure constrast type
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>
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> # Tests of the weighted Cox model
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> # This is section 1.3 of my appendix -- not yet found in the book
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> # though, it awaits the next edition
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> #
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> # Similar data set to test1, but add weights,
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> # a double-death/censor tied time
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> # a censored last subject
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> # The latter two are cases covered only feebly elsewhere.
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> #
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> # The data set testw2 has the same data, but done via replication
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> #
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> aeq <- function(x,y) all.equal(as.vector(x), as.vector(y))
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>
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> testw1 <- data.frame(time= c(1,1,2,2,2,2,3,4,5),
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+ status= c(1,0,1,1,1,0,0,1,0),
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+ x= c(2,0,1,1,0,1,0,1,0),
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+ wt = c(1,2,3,4,3,2,1,2,1),
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+ id = 1:9)
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> # Expanded data set
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> testw2 <- testw1[rep(1:9, testw1$wt), -4]
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> row.names(testw2) <- NULL
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> indx <- match(1:9, testw2$id)
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>
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> # Breslow estimate
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> byhand <- function(beta, newx=0) {
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+ r <- exp(beta)
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+ loglik <- 11*beta - (log(r^2 + 11*r +7) + 10*log(11*r +5) +2*log(2*r+1))
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+ hazard <- c(1/(r^2 + 11*r +7), 10/(11*r +5), 2/(2*r+1))
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+ xbar <- c((2*r^2 + 11*r)*hazard[1], 11*r/(11*r +5), r*hazard[3])
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+ U <- 11- (xbar[1] + 10*xbar[2] + 2*xbar[3])
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+ imat <- (4*r^2 + 11*r)*hazard[1] - xbar[1]^2 +
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+ 10*(xbar[2] - xbar[2]^2) + 2*(xbar[3] - xbar[3]^2)
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+
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+ temp <- cumsum(hazard)
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+ risk <- c(r^2, 1,r,r,1,r,1,r,1)
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+ expected <- risk* temp[c(1,1,2,2,2,2,2,3,3)]
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+
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+ # The matrix of weights, one row per obs, one col per death
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+ # deaths at 1,2,2,2, and 4
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+ riskmat <- matrix(c(1,1,1,1,1,1,1,1,1,
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+ 0,0,1,1,1,1,1,1,1,
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+ 0,0,1,1,1,1,1,1,1,
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+ 0,0,1,1,1,1,1,1,1,
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+ 0,0,0,0,0,0,0,1,1), ncol=5)
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+ wtmat <- diag(c(r^2, 2, 3*r, 4*r, 3, 2*r, 1, 2*r, 1)) %*% riskmat
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+
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+ x <- c(2,0,1,1,0,1,0,1,0)
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+ status <- c(1,0,1,1,1,0,0,1,0)
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+ wt <- c(1,2,3,4,3,2,1,2,1)
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+ # Table of sums for score and Schoenfeld resids
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+ hazmat <- riskmat %*% diag(c(1,3,4,3,2)/colSums(wtmat))
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+ dM <- -risk*hazmat #Expected part
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+ dM[1,1] <- dM[1,1] +1 # deaths at time 1
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+ for (i in 2:4) dM[i+1, i] <- dM[i+1,i] +1
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+ dM[8,5] <- dM[8,5] +1
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+ mart <- rowSums(dM)
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+ resid <-dM * outer(x, xbar[c(1,2,2,2,3)] ,'-')
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+
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+ # Increments to the variance of the hazard
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+ var.g <- cumsum(hazard^2/ c(1,10,2))
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+ var.d <- cumsum((xbar-newx)*hazard)
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+
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+ list(loglik=loglik, U=U, imat=imat, hazard=hazard, xbar=xbar,
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+ mart=c(1,0,1,1,1,0,0,1,0)-expected, expected=expected,
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+ score=rowSums(resid), schoen=c(2,1,1,0,1) - xbar[c(1,2,2,2,3)],
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+ varhaz=(var.g + var.d^2/imat)* exp(2*beta*newx))
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+ }
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>
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> aeq(byhand(0)$expected, c(1/19, 1/19, rep(103/152, 5), rep(613/456,2))) #verify
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[1] TRUE
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>
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> fit0 <- coxph(Surv(time, status) ~x, testw1, weights=wt,
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+ method='breslow', iter=0)
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> fit0b <- coxph(Surv(time, status) ~x, testw2, method='breslow', iter=0)
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> fit <- coxph(Surv(time, status) ~x, testw1, weights=wt, method='breslow')
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> fitb <- coxph(Surv(time, status) ~x, testw2, method='breslow')
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>
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> aeq(resid(fit0, type='mart'), (resid(fit0b, type='mart'))[indx])
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[1] TRUE
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> aeq(resid(fit0, type='scor'), (resid(fit0b, type='scor'))[indx])
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[1] TRUE
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> aeq(unique(resid(fit0, type='scho')), unique(resid(fit0b, type='scho')))
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[1] TRUE
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>
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> truth0 <- byhand(0,pi)
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> aeq(fit0$loglik[1], truth0$loglik)
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[1] TRUE
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> aeq(1/truth0$imat, fit0$var)
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[1] TRUE
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> aeq(truth0$mart, fit0$residuals)
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[1] TRUE
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> aeq(truth0$schoen, resid(fit0, 'schoen'))
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[1] TRUE
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> aeq(truth0$score, resid(fit0, 'score'))
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[1] TRUE
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> sfit <- survfit(fit0, list(x=pi), censor=FALSE)
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> aeq(sfit$std.err^2, truth0$varhaz)
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[1] TRUE
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> aeq(-log(sfit$surv), cumsum(truth0$hazard))
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[1] TRUE
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>
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> truth <- byhand(0.85955744, .3)
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> aeq(truth$loglik, fit$loglik[2])
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[1] TRUE
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> aeq(1/truth$imat, fit$var)
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[1] TRUE
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> aeq(truth$mart, fit$residuals)
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[1] TRUE
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> aeq(truth$schoen, resid(fit, 'schoen'))
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[1] TRUE
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> aeq(truth$score, resid(fit, 'score'))
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[1] TRUE
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>
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> sfit <- survfit(fit, list(x=.3), censor=FALSE)
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> aeq(sfit$std.err^2, truth$varhaz)
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[1] TRUE
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> aeq(-log(sfit$surv), (cumsum(truth$hazard)* exp(fit$coefficients*.3)))
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[1] TRUE
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>
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>
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> fit0
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Call:
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coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt,
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method = "breslow", iter = 0)
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coef exp(coef) se(coef) z p
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x 0.0000 1.0000 0.5858 0 1
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Likelihood ratio test=0 on 1 df, p=1
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n= 9, number of events= 5
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> summary(fit)
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Call:
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coxph(formula = Surv(time, status) ~ x, data = testw1, weights = wt,
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method = "breslow")
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n= 9, number of events= 5
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coef exp(coef) se(coef) z Pr(>|z|)
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x 0.8596 2.3621 0.7131 1.205 0.228
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exp(coef) exp(-coef) lower .95 upper .95
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x 2.362 0.4233 0.5839 9.556
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Concordance= 0.637 (se = 0.161 )
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Likelihood ratio test= 1.69 on 1 df, p=0.2
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Wald test = 1.45 on 1 df, p=0.2
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Score (logrank) test = 1.52 on 1 df, p=0.2
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> resid(fit0, type='score')
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1 2 3 4 5 6
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1.24653740 0.03601108 0.10056700 0.10056700 -0.22180142 -0.21193300
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7 8 9
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0.46569858 -0.10082189 0.91014302
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> resid(fit0, type='scho')
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1 2 2 2 4
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1.3157895 0.3125000 0.3125000 -0.6875000 0.3333333
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>
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> resid(fit, type='score')
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1 2 3 4 5 6
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0.88681615 0.02497653 0.03608964 0.03608964 -0.54297652 -0.12528780
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7 8 9
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0.29564605 -0.09476911 0.58400064
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> resid(fit, type='scho')
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1 2 2 2 4
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1.0368337 0.1613774 0.1613774 -0.8386226 0.1746960
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> aeq(resid(fit, type='mart'), (resid(fitb, type='mart'))[indx])
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[1] TRUE
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> aeq(resid(fit, type='scor'), (resid(fitb, type='scor'))[indx])
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[1] TRUE
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> aeq(unique(resid(fit, type='scho')), unique(resid(fitb, type='scho')))
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[1] TRUE
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> rr1 <- resid(fit, type='mart')
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> rr2 <- resid(fit, type='mart', weighted=T)
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> aeq(rr2/rr1, testw1$wt)
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[1] TRUE
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>
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> rr1 <- resid(fit, type='score')
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> rr2 <- resid(fit, type='score', weighted=T)
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> aeq(rr2/rr1, testw1$wt)
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[1] TRUE
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>
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>
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> proc.time()
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user system elapsed
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0.423 0.031 0.452
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