gof.lmm: Goodness-of fit test for LMM

In rokblagus/gofLMM: Goodness-of-fit for linear mixed effects model (gofLMM)

Goodness-of fit test for LMM

Description

Goodness-of fit test based on cumulative sum stochastic process

Usage

gof.lmm(
  fit,
  residuals = c("individual", "cluster"),
  std.type = c(1, 2),
  use.correction.for.imbalance = FALSE,
  subset.fix = NULL,
  type = c("simulation", "sign.flip", "permutation"),
  M = 100,
  order.by.original = TRUE,
  force.permutation.with.O = FALSE,
  verbose = FALSE,
  flip.cluster = TRUE,
  use.normal = FALSE,
  use.mammen = FALSE,
  use.sigmoid = FALSE,
  lambda = 0.5,
  transform = TRUE
)

Arguments

fit	The result of a call to "nlme". The model must be fitted with control=lmeControl( returnObject = TRUE) and keep.data=TRUE. An error message is returned otherwise. ID variable must be numeric and ordered from 1:N ! Canno't use transofrmations of the outcome variable directly in the formula i.e. lme(sqrt(y)~x) will return p=1!
residuals	Residuals to be used when constructing the process. Possible values are "individual" and "cluster" for \textitindividual and \textitcluster-speciffic residuals, respectively.
std.type	Type of standardization to be used for the residuals when constructing the process. Currently implemeneted options are 1 and 2 for S_i=\hat\sigma^-1/2I_n_i and $S_i=\hatV_i^-1/2$.
use.correction.for.imbalance	Logical. use $n_i^-1/2 S_i$ when standardizing the residuals. Defaults to FALSE.
subset.fix	Two-sided formula. If nonnull, the process $W^F^s$ will be constructed using the variables defined on the RHS of the formula. Deafults to NULL and the process $W^F^s$ is not constructed.
type	How to obtain the processes $W^m$. Possible values are "simulation" for the simulation approach, "sign.flip" for the sign-flipping approach and "permutation" for the permutation approach. When using type="permutation", sign-flipping will be used by default if not specified otherwise by the argument force.permutation.with.O.
M	Number of random simulations/sign-flipps/permutations. Defaults to 100.
order.by.original	Logical. Should the residuals in the the processes $W^m$ be ordered by the original fitted values? Defaults to TRUE. Makes sense only for type="sign.flip" and type="permutation" since when type="simulation" the ordering is always based on the original predictions. It is programmed such that J_i is reestimated at each iteration $m$.
force.permutation.with.O	Logical. Should the permutations be used also for the O process? Defaults to FALSE.
verbose	Logical. Print the current status of the test. Can slow down the algorithm, but it can make it feel faster. Defaults to FALSE.
flip.cluster	Logical. Should entire cluster be flipped (i.e. should all subjects within the cluster be multiplied with the same random number). Defaults to TRUE.
use.normal	Lolgical. Use normal random variables instead of sign-flip. Defaultes to FALSE.
use.mammen	Logical. Use Mammen's 2 point dostribution instead of sign-flip. Defaultes to FALSE. Not in use when use.normal=TRUE
use.sigmoid	Logical. Use sigmoid function instead of the indicator, i.e. smooth the process. Defaults to FALSE.
lambda	Smoothing parameter. Not used when use.sigmoid=FALSE. Defaults to 0.5.
transform	Logical. Should the predictions be transformed to 0,1? Defaults to TRUE.

Value

An object of class "gofLMM" for which plot and summary functions are available.

Author(s)

Rok Blagus, [e-mail]

See Also

gof.lmm.pan, plot.gofLMM and summary.gofLMM

Examples

# simulate some data:
N=50
set.seed(1)
n<-floor(runif(N,min=1,max=15)) #imbalanced
betas<-c(1,1,1,15) #don't change! #the last one is only used whe omit.important.predictor=TRUE
norm.eps<-FALSE
shape=0.5
scale=1
norm.re.intercept<-FALSE
shape.re.intercept=0.5
scale.re.intercept=1
norm.re.slope<-FALSE
shape.re.slope=0.5
scale.re.slope=1
sim.re.slope=FALSE
over.parameterized.model=FALSE #i.e. fit a variable which is not used when generating the data
omit.important.predictor=FALSE
yy<-NA
x22<-NA
id<-NA
x1<-NA
for (gg in 1:N){

  id<-c(id,rep(gg,each=n[gg]))
  x11<-rep(rbinom(1,size=1,prob=0.4),each=n[gg])
  x1<-c(x1,x11)

  if (norm.re.intercept==TRUE) re.int<-rnorm(1,sd=sqrt(2)) else re.int<-rgamma(1,shape=shape.re.intercept,scale=scale.re.intercept)-shape.re.intercept*scale.re.intercept

  b<-rep(re.int,each=n[gg])

  if (norm.re.slope==TRUE) re.slope<-rnorm(1,sd=sqrt(1)) else re.slope<-rgamma(1,shape=shape.re.slope,scale=scale.re.slope)-shape.re.slope*scale.re.slope

  b2<-rep(re.slope,each=n[gg])
  x2<-1:n[gg]
  x4<-runif(n[gg])

  if (norm.eps==TRUE) eps<-rnorm(n[gg]) else eps<-rgamma(n[gg],shape=shape,scale=scale)-shape*scale

  if (sim.re.slope==TRUE) {
    if (omit.important.predictor==FALSE) y<-betas[1]+betas[2]*x2+betas[3]*(x11*x2)+b+b2*x2+eps else y<-betas[1]+betas[2]*x2+betas[3]*(x11*x2)+b+b2*x2+eps+betas[4]*x4
  } else {
    if (omit.important.predictor==FALSE) y<-betas[1]+betas[2]*x2+betas[3]*(x11*x2)+b+eps else y<-betas[1]+betas[2]*x2+betas[3]*(x11*x2)+b+eps+betas[4]*x4
  }
  yy<-c(yy,y)
 x22<-c(x22,x2)
}
yy<-yy[-1]
x22<-x22[-1]
x1<-x1[-1]
id<-id[-1]
x4<-runif(sum(n))
aids.art<-data.frame(ptnt=id,outcome=yy,x1=x1,x2=x22,x4=x4)
library(nlme)
fit<-lme(fixed=outcome~ x2+x1:x2, data=aids.art, random=~x2|ptnt,control=lmeControl( returnObject = TRUE),method="REML" )
fit.gof<-gof.lmm(fit,residuals= "individual" ,std.type=2,use.correction.for.imbalance=FALSE,subset.fix=outcome~x2,type= "simulation" ,M=25,order.by.original=FALSE,force.permutation.with=FALSE,verbose=TRUE)
plot.gofLMM(fit.gof,type=2,subset.M=NULL,xlab="",main="Example")
summary.gofLMM(fit.gof)

library(nlme)
data(Orthodont)
Orthodont$Subject<- rep(1:27,each=4)
fm1<-lme(distance~age,random=~1|Subject,data=Orthodont,control=lmeControl( returnObject = TRUE),method="REML")
gof.fm1<-gof.lmm(fm1,residuals= "individual" ,std.type=2,use.correction.for.imbalance=FALSE,subset.fix=NULL,type= "sign.flip" ,M=500,order.by.original=FALSE,force.permutation.with.O=FALSE,verbose=TRUE)
plot.gofLMM(gof.fm1,type=2,subset.M=NULL,xlab="",main="Orthodont, model 1")
summary.gofLMM(gof.fm1)

fm1.1<-lme(distance~age,random=~age|Subject,data=Orthodont,control=lmeControl( returnObject = TRUE),method="REML")
gof.fm1.1<-gof.lmm(fm1.1,residuals= "individual" ,std.type=2,use.correction.for.imbalance=FALSE,subset.fix=NULL,type= "sign.flip" ,M=500,order.by.original=FALSE,force.permutation.with.O=FALSE,verbose=TRUE)
plot.gofLMM(gof.fm1.1 ,type=2,subset.M=NULL,xlab="",main="Orthodont, model 1.1")
summary.gofLMM(gof.fm1.1)

fm2<-lme(distance~age+Sex,random=~1|Subject,data=Orthodont,control=lmeControl( returnObject = TRUE),method="REML")
gof.fm2<-gof.lmm(fm2,residuals= "individual" ,std.type=2,use.correction.for.imbalance=FALSE,subset.fix=distance~age,type= "sign.flip" ,M=500,order.by.original=FALSE,force.permutation.with=FALSE,verbose=TRUE)
plot.gofLMM(gof.fm2,type=2,subset.M=NULL,xlab="",main="Orthodont, model 2")
summary.gofLMM(gof.fm2)

fm2.1<-lme(distance~age*Sex,random=~1|Subject,data=Orthodont,control=lmeControl( returnObject = TRUE),method="REML")
gof.fm2.1<-gof.lmm(fm2.1,residuals= "individual" ,std.type=2,use.correction.for.imbalance=FALSE,subset.fix=NULL,type= "sign.flip" ,M=500,order.by.original=FALSE,force.permutation.with.O=FALSE,verbose=TRUE)
plot.gofLMM(gof.fm2.1,type=2,subset.M=NULL,xlab="",main="Orthodont, model 2.1")
summary.gofLMM(gof.fm2.1)

rokblagus/gofLMM documentation built on April 4, 2022, 8:41 p.m.