mix2normal1 {VGAM} | R Documentation |
Estimates the five parameters of a mixture of two univariate normal distributions by maximum likelihood estimation.
mix2normal1(lphi="logit", lmu="identity", lsd="loge", ephi=list(), emu1=list(), emu2=list(), esd1=list(), esd2=list(), iphi=0.5, imu1=NULL, imu2=NULL, isd1=NULL, isd2=NULL, qmu=c(0.2, 0.8), ESD=TRUE, nsimEIM=100, zero=1)
lphi |
Link function for the parameter phi.
See Links for more choices.
|
lmu |
Link function applied to each mu parameter.
See Links for more choices.
|
lsd |
Link function applied to each sd parameter.
See Links for more choices.
|
ephi, emu1, emu2, esd1, esd2 |
List. Extra argument for each of the links.
See earg in Links for general information.
If ESD=TRUE then esd1 must equal esd2 .
|
iphi |
Initial value for phi, whose value must lie
between 0 and 1.
|
imu1, imu2 |
Optional initial value for mu1 and mu2.
The default is to compute initial values internally using
the argument qmu .
|
isd1, isd2 |
Optional initial value for sd1 and sd2.
The default is to compute initial values internally based on
the argument qmu .
Currently these are not great, therefore using these arguments
where practical is a good idea.
|
qmu |
Vector with two values giving the probabilities relating to the sample
quantiles for obtaining initial values for mu1
and mu2.
The two values are fed in as the probs argument into
quantile .
|
ESD |
Logical indicating whether the two standard deviations should be
constrained to be equal. If TRUE then the appropriate
constraint matrices will be used.
|
nsimEIM |
See CommonVGAMffArguments .
|
zero |
An integer specifying which linear/additive predictor is modelled as
intercepts only. If given, the value or values must be from the
set 1,2,...,5.
The default is the first one only, meaning phi
is a single parameter even when there are explanatory variables.
Set zero=NULL to model all linear/additive predictors as
functions of the explanatory variables.
See CommonVGAMffArguments for more information.
|
The probability function can be loosely written as
f(y) = phi * N(mu1, sd1) + (1-phi) * N(mu2, sd2)
where phi is the probability an observation belongs
to the first group.
The parameters mu1 and mu2 are the means, and
sd1 and sd2 are the standard deviations.
The parameter phi satisfies 0 < phi < 1.
The mean of Y is
phi*mu1 + (1-phi)*mu2
and this is returned as the fitted values.
By default, the five linear/additive predictors are
(logit(phi),
mu1, log(sd1), mu2, log(sd2))^T.
If ESD=TRUE
then sd1=sd2 is enforced.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
Numerical problems can occur and
half-stepping is not uncommon.
If failure to converge occurs, try inputting better initial values,
e.g., by using iphi
,
qmu
,
imu1
,
imu2
,
isd1
,
isd2
,
etc.
This VGAM family function should be used with care.
Fitting this model successfully to data can be difficult due to numerical problems and ill-conditioned data. It pays to fit the model several times with different initial values and check that the best fit looks reasonable. Plotting the results is recommended. This function works better as mu1 and mu2 become more different.
Convergence can be slow, especially when the two component
distributions are not well separated.
The default control argument trace=TRUE
is to encourage
monitoring convergence.
Having ESD=TRUE
often makes the overall optimization problem
easier.
T. W. Yee
McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models. New York: Wiley.
Everitt, B. S. and Hand, D. J. (1981) Finite Mixture Distributions. London: Chapman & Hall.
n = 1000 mu1 = 99 mu2 = 150 sd1 = sd2 = exp(3) (phi = logit(-1, inverse=TRUE)) y = ifelse(runif(n) < phi, rnorm(n, mu1, sd1), rnorm(n, mu2, sd2)) fit = vglm(y ~ 1, mix2normal1(ESD=TRUE)) # Compare the results cf = coef(fit) round(rbind('Estimated'=c(logit(cf[1], inv=TRUE), cf[2], exp(cf[3]), cf[4]), 'Truth'=c(phi, mu1, sd1, mu2)), dig=2) ## Not run: # Plot the results xx = seq(min(y), max(y), len=200) plot(xx, (1-phi)*dnorm(xx, mu2, sd2), type="l", xlab="y", main="Red=estimate, blue=truth", col="blue") phi.est = logit(coef(fit)[1], inverse=TRUE) sd.est = exp(coef(fit)[3]) lines(xx, phi*dnorm(xx, mu1, sd1), col="blue") lines(xx, phi.est * dnorm(xx, Coef(fit)[2], sd.est), col="red") lines(xx, (1-phi.est) * dnorm(xx, Coef(fit)[4], sd.est), col="red") abline(v=Coef(fit)[c(2,4)], lty=2, col="red") abline(v=c(mu1, mu2), lty=2, col="blue") ## End(Not run)