cens: Function to Fit Censored Data Using a gamlss.family...
In gamlss.cens: Fitting an interval response variable using gamlss.family distributions
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
This function can be used to fit censored or interval response variables.
It takes as an argument an existing gamlss.family distribution
and generates
a new gamlss.family object which then can be used to fit
right, left or interval censored data.
Usage
1
2
Arguments
family
a gamlss.family object, which is used to
define the distribution and the link functions of the various parameters.
The distribution families supported by gamlss()
can be found in gamlss.family and in the package gamlss.dist.
name
the characters you want to add to the name of new functions, by default is cens
type
what type of censoring is required, right, left or interval.
local
if TRUE the function will try to find the environment of gamlss to generate
the d and p functions required for the fitting,
if FALSE the functions will be generated in the global environment
delta
the delta increment used in the numerical derivatives
...
for extra arguments
Details
This function is created to help users to fit censored data using an existing
gamlss.family distribution.
It does this by taking an existing gamlss.family and changing
some of the components of the distribution to help the fitting process.
It particular it (i) creates a (d) function (for calculating the censored
likelihood) and a (p) function (for generating the quantile residuals)
within gamlss,
(ii) changes the global deviance function G.dev.incr,
the first derivative functions (see note below)
and other quantities from the original distribution.
Value
It returns a gamlss.family object which has all the components needed for fitting a distribution in gamlss.
Note
This function is experimental and could be changed in the future.
The function cens changes the first derivatives of the original gamlss family
d function to numerical derivatives for the new censored d function.
The default increment delta, for this numerical derivatives function,
is eps * pmax(abs(x), 1) where eps<-sqrt(.Machine$double.eps).
The default delta could be inappropriate for
specific applications and can be overwritten by using the argument delta.
Author(s)
Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk and Bob Rigby r.rigby@londonmet.ac.uk
References
Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),
Appl. Statist., 54, part 3, pp 507-554.
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R.
Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.com/).
Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.
Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.
See Also
Examples
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# comparing output with the survreg() of package survival
library(gamlss.dist)
library(survival)
#--------------------------------------------------------------------
# right censoring example
# example from survreg()
# fitting the exponential distribution
mexp<-survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian, dist='exponential')
gexp<-gamlss(Surv(futime, fustat) ~ ecog.ps + rx, data=ovarian, family=cens(EXP), c.crit=0.00001)
if(abs(-2*mexp$loglik[2]-deviance(gexp))>0.001) stop(paste("descrepancies in exponential models"))
if(sum(coef(mexp)-coef(gexp))>0.001) warning(paste("descrepancies in coef in exponential models"))
summary(mexp)
summary(gexp)
# fitting different distributions
# weibull
mwei <-survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian, dist='weibull')
gwei<-gamlss(Surv(futime, fustat) ~ ecog.ps + rx, data=ovarian, family=cens(WEI, delta=c(0.0001,0.0001)), c.crit=0.00001)
if(abs(-2*mwei$loglik[2]-deviance(gwei))>0.005) stop(paste("descrepancies in deviance in WEI"))
scoef <- sum(coef(mwei)-coef(gwei))
if(abs(scoef)>0.005) warning(cat("descrepancies in coef in WEI of ", scoef, "\n"))
# WEI3 is weibull parametrised with mu as the mean
gwei3 <- gamlss(Surv(futime, fustat) ~ ecog.ps + rx, data=ovarian, family=cens(WEI3))
# log normal
mlogno <-survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian, dist='lognormal')
glogno<-gamlss(Surv(futime, fustat) ~ ecog.ps + rx, data=ovarian, family=cens(LOGNO, delta=c(0.001,0.001)), c.cyc=0.00001)
if(abs(-2*mlogno$loglik[2]-deviance(glogno))>0.005) stop(paste("descrepancies in deviance in LOGNO"))
coef(mlogno);coef(glogno)
#--------------------------------------------------------------------
# now interval response variable
data(lip)
with(lip, y)
mg1<-survreg(y ~ poly(Tem,2)+poly(pH,2)+poly(aw,2), data=lip, dist="weibull")
gg1<- gamlss(y ~ poly(Tem,2)+poly(pH,2)+poly(aw,2), data=lip, family=cens(WEI,type="interval"),
c.crit=0.00001, n.cyc=200, trace=FALSE)
summary(mg1)
summary(gg1)
#--------------------------------------------------------------------
# now fitting discretised continuous distribution to count data
# fitting discretised Gamma
data(species)
mGA<-gamlss(Surv(fish,fish+1,type= "interval2")~log(lake)+I(log(lake)^2), sigma.fo=~log(lake),
data=species, family=cens(GA, type="interval"))
# fitting discretised inverse Gaussian
mIG<-gamlss(Surv(fish,fish+1,type= "interval2")~log(lake)+I(log(lake)^2), sigma.fo=~log(lake),
data=species, family=cens(IG, type="interval"))
AIC(mGA,mIG)
plot(fish~log(lake), data=species)
with(species, lines(log(lake)[order(lake)], fitted(mIG)[order(lake)]))
#--------------------------------------------------------------------
Example output
Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.1-2 **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.
Loading required package: survival
GAMLSS-RS iteration 1: Global Deviance = 194.3967
GAMLSS-RS iteration 2: Global Deviance = 194.3963
GAMLSS-RS iteration 3: Global Deviance = 194.3962
GAMLSS-RS iteration 4: Global Deviance = 194.3961
GAMLSS-RS iteration 5: Global Deviance = 194.3961
GAMLSS-RS iteration 6: Global Deviance = 194.3961
GAMLSS-RS iteration 7: Global Deviance = 194.3961
Call:
survreg(formula = Surv(futime, fustat) ~ ecog.ps + rx, data = ovarian,
dist = "exponential")
Value Std. Error z p
(Intercept) 6.962 1.322 5.27 1.4e-07
ecog.ps -0.433 0.587 -0.74 0.46
rx 0.582 0.587 0.99 0.32
Scale fixed at 1
Exponential distribution
Loglik(model)= -97.2 Loglik(intercept only)= -98
Chisq= 1.67 on 2 degrees of freedom, p= 0.43
Number of Newton-Raphson Iterations: 4
n= 26
******************************************************************
Family: c("EXPrc", "right censored Exponential")
Call:
gamlss(formula = Surv(futime, fustat) ~ ecog.ps + rx, family = cens(EXP),
data = ovarian, c.crit = 1e-05)
Fitting method: RS()
------------------------------------------------------------------
Mu link function: log
Mu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.9608 0.8457 8.231 2.62e-08 ***
ecog.ps -0.4324 0.3934 -1.099 0.283
rx 0.5812 0.3922 1.482 0.152
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
No. of observations in the fit: 26
Degrees of Freedom for the fit: 3
Residual Deg. of Freedom: 23
at cycle: 7
Global Deviance: 194.3961
AIC: 200.3961
SBC: 204.1704
******************************************************************
Warning message:
In summary.gamlss(gexp) :
summary: vcov has failed, option qr is used instead
GAMLSS-RS iteration 1: Global Deviance = 194.6214
GAMLSS-RS iteration 2: Global Deviance = 194.1882
GAMLSS-RS iteration 3: Global Deviance = 194.1719
GAMLSS-RS iteration 4: Global Deviance = 194.1707
GAMLSS-RS iteration 5: Global Deviance = 194.17
GAMLSS-RS iteration 6: Global Deviance = 194.1696
GAMLSS-RS iteration 7: Global Deviance = 194.1693
GAMLSS-RS iteration 8: Global Deviance = 194.1692
GAMLSS-RS iteration 9: Global Deviance = 194.1691
GAMLSS-RS iteration 10: Global Deviance = 194.1691
GAMLSS-RS iteration 11: Global Deviance = 194.169
GAMLSS-RS iteration 12: Global Deviance = 194.169
GAMLSS-RS iteration 13: Global Deviance = 194.169
GAMLSS-RS iteration 14: Global Deviance = 194.169
GAMLSS-RS iteration 1: Global Deviance = 194.88
GAMLSS-RS iteration 2: Global Deviance = 194.2411
GAMLSS-RS iteration 3: Global Deviance = 194.1826
GAMLSS-RS iteration 4: Global Deviance = 194.1731
GAMLSS-RS iteration 5: Global Deviance = 194.1709
GAMLSS-RS iteration 6: Global Deviance = 194.1702
GAMLSS-RS iteration 1: Global Deviance = 192.6928
GAMLSS-RS iteration 2: Global Deviance = 191.9227
GAMLSS-RS iteration 3: Global Deviance = 191.8977
GAMLSS-RS iteration 4: Global Deviance = 191.8955
GAMLSS-RS iteration 5: Global Deviance = 191.8951
(Intercept) ecog.ps rx
5.8784403 -0.2292750 0.8133591
(Intercept) ecog.ps rx
5.8729054 -0.2259548 0.8104691
[1] 1- 1- 1- 1- [11, 18] 1- 1- 1-
[9] 1- [ 2, 4] 1- [ 1, 2] 1- [ 2, 4] 39+ 1-
[17] 1- [18, 25] 39+ 39+ 1- 1- [ 1, 2] [ 4, 11]
[25] [18, 25] 1- [ 1, 2] [ 1, 2] [ 4, 11] [18, 25] 1- 1-
[33] [ 2, 4] 39+ 39+ [ 2, 4] [ 2, 4] 39+ 39+ 39+
[41] 1- [ 4, 11] [ 4, 11] 39+ 39+ 1- [ 4, 11] [ 4, 11]
[49] 39+ 39+ [ 2, 4] 39+ 39+ 39+ 39+ [ 4, 11]
[57] 39+ 39+ 39+ 39+ 1- [ 4, 11] 39+ 39+
[65] 39+ [ 4, 11] 39+ [ 4, 11] 39+ 39+ [ 4, 11] 39+
[73] 39+ 39+ 39+ 39+ 39+ 39+ 39+ 39+
[81] [ 1, 2] 39+ 39+ 39+ 39+ [ 4, 11] 39+ 39+
[89] 39+ 39+ [25, 32] 39+ 39+ 39+ 39+ 39+
[97] 39+ 39+ 39+ 39+ [ 2, 4] 39+ 39+ 39+
[105] 39+ [ 4, 11] 39+ 39+ 39+ 39+ 39+ 39+
[113] 39+ 39+ 39+ 39+ 39+ 39+ 39+ 39+
Call:
survreg(formula = y ~ poly(Tem, 2) + poly(pH, 2) + poly(aw, 2),
data = lip, dist = "weibull")
Value Std. Error z p
(Intercept) 4.686 0.290 16.17 < 2e-16
poly(Tem, 2)1 -30.798 3.024 -10.19 < 2e-16
poly(Tem, 2)2 1.357 1.674 0.81 0.417
poly(pH, 2)1 -18.078 2.361 -7.66 1.9e-14
poly(pH, 2)2 3.894 1.685 2.31 0.021
poly(aw, 2)1 -27.596 2.760 -10.00 < 2e-16
poly(aw, 2)2 -1.072 1.554 -0.69 0.491
Log(scale) -0.208 0.153 -1.36 0.173
Scale= 0.812
Weibull distribution
Loglik(model)= -69 Loglik(intercept only)= -165.4
Chisq= 192.77 on 6 degrees of freedom, p= 6.6e-39
Number of Newton-Raphson Iterations: 13
n= 120
******************************************************************
Family: c("WEIic", "interval censored Weibull")
Call: gamlss(formula = y ~ poly(Tem, 2) + poly(pH, 2) + poly(aw, 2),
family = cens(WEI, type = "interval"), data = lip, c.crit = 1e-05,
n.cyc = 200, trace = FALSE)
Fitting method: RS()
------------------------------------------------------------------
Mu link function: log
Mu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.68997 0.07424 63.170 < 2e-16 ***
poly(Tem, 2)1 -30.83741 0.81330 -37.917 < 2e-16 ***
poly(Tem, 2)2 1.36136 0.81330 1.674 0.0969 .
poly(pH, 2)1 -18.10342 0.81330 -22.259 < 2e-16 ***
poly(pH, 2)2 3.89797 0.81330 4.793 5.04e-06 ***
poly(aw, 2)1 -27.63020 0.81330 -33.973 < 2e-16 ***
poly(aw, 2)2 -1.07515 0.81330 -1.322 0.1888
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
Sigma link function: log
Sigma Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.2067 0.0676 3.058 0.00276 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
No. of observations in the fit: 120
Degrees of Freedom for the fit: 8
Residual Deg. of Freedom: 112
at cycle: 106
Global Deviance: 138.0923
AIC: 154.0923
SBC: 176.3922
******************************************************************
Warning message:
In summary.gamlss(gg1) :
summary: vcov has failed, option qr is used instead
GAMLSS-RS iteration 1: Global Deviance = 604.3054
GAMLSS-RS iteration 2: Global Deviance = 604.3006
GAMLSS-RS iteration 3: Global Deviance = 604.3006
GAMLSS-RS iteration 1: Global Deviance = 602.8633
GAMLSS-RS iteration 2: Global Deviance = 602.8628
df AIC
mIG 5 612.8628
mGA 5 614.3006
gamlss.cens documentation built on May 2, 2019, 6:49 p.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
This function can be used to fit censored or interval response variables.
It takes as an argument an existing gamlss.family distribution
and generates
a new gamlss.family object which then can be used to fit
right, left or interval censored data.
Usage
1 2 |
Arguments
family |
a |
name |
the characters you want to add to the name of new functions, by default is |
type |
what type of censoring is required, |
local |
if TRUE the function will try to find the environment of |
delta |
the delta increment used in the numerical derivatives |
... |
for extra arguments |
Details
This function is created to help users to fit censored data using an existing
gamlss.family distribution.
It does this by taking an existing gamlss.family and changing
some of the components of the distribution to help the fitting process.
It particular it (i) creates a (d) function (for calculating the censored
likelihood) and a (p) function (for generating the quantile residuals)
within gamlss,
(ii) changes the global deviance function G.dev.incr,
the first derivative functions (see note below)
and other quantities from the original distribution.
Value
It returns a gamlss.family object which has all the components needed for fitting a distribution in gamlss.
Note
This function is experimental and could be changed in the future.
The function cens changes the first derivatives of the original gamlss family
d function to numerical derivatives for the new censored d function.
The default increment delta, for this numerical derivatives function,
is eps * pmax(abs(x), 1) where eps<-sqrt(.Machine$double.eps).
The default delta could be inappropriate for
specific applications and can be overwritten by using the argument delta.
Author(s)
Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk and Bob Rigby r.rigby@londonmet.ac.uk
References
Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.com/).
Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | # comparing output with the survreg() of package survival
library(gamlss.dist)
library(survival)
#--------------------------------------------------------------------
# right censoring example
# example from survreg()
# fitting the exponential distribution
mexp<-survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian, dist='exponential')
gexp<-gamlss(Surv(futime, fustat) ~ ecog.ps + rx, data=ovarian, family=cens(EXP), c.crit=0.00001)
if(abs(-2*mexp$loglik[2]-deviance(gexp))>0.001) stop(paste("descrepancies in exponential models"))
if(sum(coef(mexp)-coef(gexp))>0.001) warning(paste("descrepancies in coef in exponential models"))
summary(mexp)
summary(gexp)
# fitting different distributions
# weibull
mwei <-survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian, dist='weibull')
gwei<-gamlss(Surv(futime, fustat) ~ ecog.ps + rx, data=ovarian, family=cens(WEI, delta=c(0.0001,0.0001)), c.crit=0.00001)
if(abs(-2*mwei$loglik[2]-deviance(gwei))>0.005) stop(paste("descrepancies in deviance in WEI"))
scoef <- sum(coef(mwei)-coef(gwei))
if(abs(scoef)>0.005) warning(cat("descrepancies in coef in WEI of ", scoef, "\n"))
# WEI3 is weibull parametrised with mu as the mean
gwei3 <- gamlss(Surv(futime, fustat) ~ ecog.ps + rx, data=ovarian, family=cens(WEI3))
# log normal
mlogno <-survreg(Surv(futime, fustat) ~ ecog.ps + rx, ovarian, dist='lognormal')
glogno<-gamlss(Surv(futime, fustat) ~ ecog.ps + rx, data=ovarian, family=cens(LOGNO, delta=c(0.001,0.001)), c.cyc=0.00001)
if(abs(-2*mlogno$loglik[2]-deviance(glogno))>0.005) stop(paste("descrepancies in deviance in LOGNO"))
coef(mlogno);coef(glogno)
#--------------------------------------------------------------------
# now interval response variable
data(lip)
with(lip, y)
mg1<-survreg(y ~ poly(Tem,2)+poly(pH,2)+poly(aw,2), data=lip, dist="weibull")
gg1<- gamlss(y ~ poly(Tem,2)+poly(pH,2)+poly(aw,2), data=lip, family=cens(WEI,type="interval"),
c.crit=0.00001, n.cyc=200, trace=FALSE)
summary(mg1)
summary(gg1)
#--------------------------------------------------------------------
# now fitting discretised continuous distribution to count data
# fitting discretised Gamma
data(species)
mGA<-gamlss(Surv(fish,fish+1,type= "interval2")~log(lake)+I(log(lake)^2), sigma.fo=~log(lake),
data=species, family=cens(GA, type="interval"))
# fitting discretised inverse Gaussian
mIG<-gamlss(Surv(fish,fish+1,type= "interval2")~log(lake)+I(log(lake)^2), sigma.fo=~log(lake),
data=species, family=cens(IG, type="interval"))
AIC(mGA,mIG)
plot(fish~log(lake), data=species)
with(species, lines(log(lake)[order(lake)], fitted(mIG)[order(lake)]))
#--------------------------------------------------------------------
|
Example output
Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.1-2 **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.
Loading required package: survival
GAMLSS-RS iteration 1: Global Deviance = 194.3967
GAMLSS-RS iteration 2: Global Deviance = 194.3963
GAMLSS-RS iteration 3: Global Deviance = 194.3962
GAMLSS-RS iteration 4: Global Deviance = 194.3961
GAMLSS-RS iteration 5: Global Deviance = 194.3961
GAMLSS-RS iteration 6: Global Deviance = 194.3961
GAMLSS-RS iteration 7: Global Deviance = 194.3961
Call:
survreg(formula = Surv(futime, fustat) ~ ecog.ps + rx, data = ovarian,
dist = "exponential")
Value Std. Error z p
(Intercept) 6.962 1.322 5.27 1.4e-07
ecog.ps -0.433 0.587 -0.74 0.46
rx 0.582 0.587 0.99 0.32
Scale fixed at 1
Exponential distribution
Loglik(model)= -97.2 Loglik(intercept only)= -98
Chisq= 1.67 on 2 degrees of freedom, p= 0.43
Number of Newton-Raphson Iterations: 4
n= 26
******************************************************************
Family: c("EXPrc", "right censored Exponential")
Call:
gamlss(formula = Surv(futime, fustat) ~ ecog.ps + rx, family = cens(EXP),
data = ovarian, c.crit = 1e-05)
Fitting method: RS()
------------------------------------------------------------------
Mu link function: log
Mu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.9608 0.8457 8.231 2.62e-08 ***
ecog.ps -0.4324 0.3934 -1.099 0.283
rx 0.5812 0.3922 1.482 0.152
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
No. of observations in the fit: 26
Degrees of Freedom for the fit: 3
Residual Deg. of Freedom: 23
at cycle: 7
Global Deviance: 194.3961
AIC: 200.3961
SBC: 204.1704
******************************************************************
Warning message:
In summary.gamlss(gexp) :
summary: vcov has failed, option qr is used instead
GAMLSS-RS iteration 1: Global Deviance = 194.6214
GAMLSS-RS iteration 2: Global Deviance = 194.1882
GAMLSS-RS iteration 3: Global Deviance = 194.1719
GAMLSS-RS iteration 4: Global Deviance = 194.1707
GAMLSS-RS iteration 5: Global Deviance = 194.17
GAMLSS-RS iteration 6: Global Deviance = 194.1696
GAMLSS-RS iteration 7: Global Deviance = 194.1693
GAMLSS-RS iteration 8: Global Deviance = 194.1692
GAMLSS-RS iteration 9: Global Deviance = 194.1691
GAMLSS-RS iteration 10: Global Deviance = 194.1691
GAMLSS-RS iteration 11: Global Deviance = 194.169
GAMLSS-RS iteration 12: Global Deviance = 194.169
GAMLSS-RS iteration 13: Global Deviance = 194.169
GAMLSS-RS iteration 14: Global Deviance = 194.169
GAMLSS-RS iteration 1: Global Deviance = 194.88
GAMLSS-RS iteration 2: Global Deviance = 194.2411
GAMLSS-RS iteration 3: Global Deviance = 194.1826
GAMLSS-RS iteration 4: Global Deviance = 194.1731
GAMLSS-RS iteration 5: Global Deviance = 194.1709
GAMLSS-RS iteration 6: Global Deviance = 194.1702
GAMLSS-RS iteration 1: Global Deviance = 192.6928
GAMLSS-RS iteration 2: Global Deviance = 191.9227
GAMLSS-RS iteration 3: Global Deviance = 191.8977
GAMLSS-RS iteration 4: Global Deviance = 191.8955
GAMLSS-RS iteration 5: Global Deviance = 191.8951
(Intercept) ecog.ps rx
5.8784403 -0.2292750 0.8133591
(Intercept) ecog.ps rx
5.8729054 -0.2259548 0.8104691
[1] 1- 1- 1- 1- [11, 18] 1- 1- 1-
[9] 1- [ 2, 4] 1- [ 1, 2] 1- [ 2, 4] 39+ 1-
[17] 1- [18, 25] 39+ 39+ 1- 1- [ 1, 2] [ 4, 11]
[25] [18, 25] 1- [ 1, 2] [ 1, 2] [ 4, 11] [18, 25] 1- 1-
[33] [ 2, 4] 39+ 39+ [ 2, 4] [ 2, 4] 39+ 39+ 39+
[41] 1- [ 4, 11] [ 4, 11] 39+ 39+ 1- [ 4, 11] [ 4, 11]
[49] 39+ 39+ [ 2, 4] 39+ 39+ 39+ 39+ [ 4, 11]
[57] 39+ 39+ 39+ 39+ 1- [ 4, 11] 39+ 39+
[65] 39+ [ 4, 11] 39+ [ 4, 11] 39+ 39+ [ 4, 11] 39+
[73] 39+ 39+ 39+ 39+ 39+ 39+ 39+ 39+
[81] [ 1, 2] 39+ 39+ 39+ 39+ [ 4, 11] 39+ 39+
[89] 39+ 39+ [25, 32] 39+ 39+ 39+ 39+ 39+
[97] 39+ 39+ 39+ 39+ [ 2, 4] 39+ 39+ 39+
[105] 39+ [ 4, 11] 39+ 39+ 39+ 39+ 39+ 39+
[113] 39+ 39+ 39+ 39+ 39+ 39+ 39+ 39+
Call:
survreg(formula = y ~ poly(Tem, 2) + poly(pH, 2) + poly(aw, 2),
data = lip, dist = "weibull")
Value Std. Error z p
(Intercept) 4.686 0.290 16.17 < 2e-16
poly(Tem, 2)1 -30.798 3.024 -10.19 < 2e-16
poly(Tem, 2)2 1.357 1.674 0.81 0.417
poly(pH, 2)1 -18.078 2.361 -7.66 1.9e-14
poly(pH, 2)2 3.894 1.685 2.31 0.021
poly(aw, 2)1 -27.596 2.760 -10.00 < 2e-16
poly(aw, 2)2 -1.072 1.554 -0.69 0.491
Log(scale) -0.208 0.153 -1.36 0.173
Scale= 0.812
Weibull distribution
Loglik(model)= -69 Loglik(intercept only)= -165.4
Chisq= 192.77 on 6 degrees of freedom, p= 6.6e-39
Number of Newton-Raphson Iterations: 13
n= 120
******************************************************************
Family: c("WEIic", "interval censored Weibull")
Call: gamlss(formula = y ~ poly(Tem, 2) + poly(pH, 2) + poly(aw, 2),
family = cens(WEI, type = "interval"), data = lip, c.crit = 1e-05,
n.cyc = 200, trace = FALSE)
Fitting method: RS()
------------------------------------------------------------------
Mu link function: log
Mu Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.68997 0.07424 63.170 < 2e-16 ***
poly(Tem, 2)1 -30.83741 0.81330 -37.917 < 2e-16 ***
poly(Tem, 2)2 1.36136 0.81330 1.674 0.0969 .
poly(pH, 2)1 -18.10342 0.81330 -22.259 < 2e-16 ***
poly(pH, 2)2 3.89797 0.81330 4.793 5.04e-06 ***
poly(aw, 2)1 -27.63020 0.81330 -33.973 < 2e-16 ***
poly(aw, 2)2 -1.07515 0.81330 -1.322 0.1888
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
Sigma link function: log
Sigma Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.2067 0.0676 3.058 0.00276 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
------------------------------------------------------------------
No. of observations in the fit: 120
Degrees of Freedom for the fit: 8
Residual Deg. of Freedom: 112
at cycle: 106
Global Deviance: 138.0923
AIC: 154.0923
SBC: 176.3922
******************************************************************
Warning message:
In summary.gamlss(gg1) :
summary: vcov has failed, option qr is used instead
GAMLSS-RS iteration 1: Global Deviance = 604.3054
GAMLSS-RS iteration 2: Global Deviance = 604.3006
GAMLSS-RS iteration 3: Global Deviance = 604.3006
GAMLSS-RS iteration 1: Global Deviance = 602.8633
GAMLSS-RS iteration 2: Global Deviance = 602.8628
df AIC
mIG 5 612.8628
mGA 5 614.3006
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