gof.lmm.O.type2: 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 for O and John's idea. Not well tested!

Usage

gof.lmm.O.type2(
  fit,
  residuals = c("individual", "cluster"),
  std.type = c(1, 2),
  use.correction.for.imbalance = FALSE,
  type = c("sign.flip", "permutation"),
  M = 100,
  order.by.original = FALSE,
  verbose = FALSE
)

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.
type	How to obtain the processes $W^m$. Possible values are "sign.flip" for the sign-flipping approach and "permutation" for the permutation approach.
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 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.

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, gof.lmm.sim

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=TRUE
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=~1|ptnt,control=lmeControl( returnObject = TRUE),method="REML" )
fit.gof<-gof.lmm.O.type2(fit,residuals= "individual" ,std.type=2,use.correction.for.imbalance=FALSE,type= "permutation" ,M=100,order.by.original=FALSE,verbose=TRUE)
fit.gof$KS
fit2<-lme(fixed=outcome~ x2+x1:x2, data=aids.art, random=~x2|ptnt,control=lmeControl( returnObject = TRUE),method="REML" )
fit.gof2<-gof.lmm.O.type2(fit2,residuals= "individual" ,std.type=2,use.correction.for.imbalance=FALSE,type= "permutation" ,M=100,order.by.original=FALSE,verbose=TRUE)
fit.gof2$KS
fit3<-lme(fixed=outcome~ x2+x1:x2, data=aids.art, random=~x1|ptnt,control=lmeControl( returnObject = TRUE),method="REML" )
fit.gof3<-gof.lmm.O.type2(fit3,residuals= "individual" ,std.type=2,use.correction.for.imbalance=FALSE,type= "permutation" ,M=100,order.by.original=FALSE,verbose=TRUE)
fit.gof3$KS

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