Description Usage Arguments Details Value Author(s) References See Also Examples
Produces nsim
simulated realizations of the likelihood
ratio statistic, either parametrically or semiparametrically,
and calculates the corresponding pvalue of the test.
1 2 3 
x 
Either a formula specifying the regression model to be fitted
or a predictor or matrix of predictors for the regression model.
If 
y 
The vector of responses for the regression models. Ignored if

data 
A list or data frame containing the variables in the regression
model. Such variables will be looked for first in 
ncomp 
The nullhypothesized number of components in the mixture. 
ncincr 
The increment from the nullhypothesized number of components in the mixture
to the number under the alternative hypothesis; i.e. the number
of components under the alternative hypothesis is 
intercept 
Logical argument indicating whether the regression models in the mixture
should have intercept terms. Ignored if 
nsim 
The number of simulated replicates of the log likelihood ratio statistic to be produced. 
seed 
Positive integer scalar. The seed for random number generation.
If left 
ts1 
Starting values for fitting the 
ts2 
Starting values for fitting the 
semiPar 
Logical scalar; should semiparametric bootstrapping should be used? 
conditional 
Logical scalar; should the componentselection probabilities be determined conditionally upon the observations? 
verb 
Logical argument indicating whether the fitting processes should be verbose (i.e. whether details should be printed out at each step of the EM algorithm). If TRUE a huge amount of screen output is produced. 
progRep 
Logical argument indicating whether the index, of the simulated statistic just constructed, should be printed out, to give an idea of how the process is progressing. 
... 
Further arguments to be passed to 
In this context the “parametric” procedure is to
simulate data sets by generating data from the fitted
ncomp
model parameters, using Gaussian errors. In contrast,
under the
semiparametric bootstrapping procedure, the errors are generated by
resampling from the residuals. Since at each predictor value there
are ncomp
residuals, one for each component of the model,
the errors are selected at random from these ncomp
possibilities.
If the argument conditional
is TRUE
then the selection
probabilities at this step are the conditional probabilities, of
the observation being generated by each component of the model,
given that observation. If conditional
is FALSE
then
these probabilities are the corresponding entries of lambda
(see Value. The residuals are sampled independently in
either case. The procedure is termed semiparametric since
the sampling probabilities depend on the parameters of the model.
Note that it makes no sense to specify conditional=TRUE
if semiPar
is FALSE
. Doing so will generate an error.
It is important to be aware that the test conducted by this function is a Monte Carlo test and that the pvalue produced is a Monte Carlo pvalue. It is consequently an exact pvalue in a sense which must be carefully understood. See for example Baddeley et al. 2015 (section 10.6) and Turner and Jeffs 2017 for explanation of the interpretation of Monte Carlo pvalues and for some general discussion of Monte Carlo tests and of their advantages. Such tests effect substantial savings on computational costs with only marginal diminishment of power.
A list with components:
lrs 
the likelihood ratio statistic for the test 
pval 
the (Monte Carlo) pvalue of the test 
simStats 
a vector of the values of the likelihood ratio statistics of the simulated data sets 
aic.ncomp 
a vector of the aic values for the

aic.ncomp+nincr 
a vector of the aic values for the

df 
the degrees of freedom that would be appropriate if the
test statistic actually had a chisquared distribution.
Explicitly 
screwUps 
a data frame with columns

The returned value has an attribute "seed"
which is the
(initial) value of the random number generation seed that was used.
This is either the value of the argument seed
, or, if this
was NULL
, a randomly generated value.
Rolf Turner r.turner@auckland.ac.nz
T. Rolf Turner (2000). Estimating the rate of spread of a viral infection of potato plants via mixtures of regressions. Applied Statistics 49 Part 3, pp. 371 – 384.
Adrian Baddeley, Ege Rubak and Rolf Turner (2015). Spatial Point Patterns: Methodology and Applications with R. London: Chapman and Hall/CRC Press.
Rolf Turner and Celeste Jeffs (2017). A note on exact Monte Carlo hypothesis tests. Communications in Statistics: Simulation and Computation 46, pp. 6545 – 6558.
cband()
, covMix()
,
mixreg()
, plot.cband()
,
plot.mixresid()
, qqMix()
,
residuals.mixreg()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  ## Not run:
tst12 < ncMcTest(plntsInf ~ aphRel,ncomp=1,data=aphids,seed=42)
## End(Not run) # Monte Carlo pvalue is 0.01; mixture model is called for.
TS1 < list(list(beta=c(3.0,0.1),sigsq=16,lambda=0.5),
list(beta=c(0.0,0.0),sigsq=16,lambda=0.5))
TS2 < list(list(beta=c(3.0,0.1),sigsq=9,lambda=1/3),
list(beta=c(1.5,0.05),sigsq=9,lambda=1/3),
list(beta=c(0.0,0.0),sigsq=9,lambda=1/3))
x < aphids$aphRel
y < aphids$plntsInf
## Not run:
nsim < 999
## End(Not run)
tst23 < ncMcTest(x,y,nsim=nsim,ts1=TS1,ts2=TS2)

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