mix2poisson {VGAM} | R Documentation |
Estimates the three parameters of a mixture of two Poisson distributions by maximum likelihood estimation.
mix2poisson(lphi = "logit", llambda = "loge", ephi=list(), el1=list(), el2=list(), iphi = 0.5, il1 = NULL, il2 = NULL, qmu = c(0.2, 0.8), zero = 1)
lphi |
Link function for the parameter phi.
See below for more details.
See Links for more choices.
|
llambda |
Link function applied to each lambda parameter.
See Links for more choices.
|
ephi, el1, el2 |
List. Extra argument for each of the links.
See earg in Links for general information.
|
iphi |
Initial value for phi, whose value must lie
between 0 and 1.
|
il1, il2 |
Optional initial value for lambda1 and
lambda2. These values must be positive.
The default is to compute initial values internally using
the argument qmu .
|
qmu |
Vector with two values giving the probabilities relating to the sample
quantiles for obtaining initial values for lambda1
and lambda2.
The two values are fed in as the probs argument into
quantile .
|
zero |
An integer specifying which linear/additive predictor is modelled as
intercepts only. If given, the value must be either 1 and/or 2 and/or
3, and 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.
|
The probability function can be loosely written as
P(Y=y) = phi * Poisson(lambda1) + (1-phi) * Poisson(lambda2)
where phi is the probability an observation belongs to the first group, and y=0,1,2,.... The parameter phi satisfies 0 < phi < 1. The mean of Y is phi*lambda1 + (1-phi)*lambda2 and this is returned as the fitted values. By default, the three linear/additive predictors are (logit(phi), log(lambda1), log(lambda2))^T.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
and vgam
.
Numerical problems can occur.
Half-stepping is not uncommon.
If failure to converge occurs, try obtaining better initial values,
e.g., by using iphi
and qmu
etc.
This function uses a quasi-Newton update for the working weight matrices
(BFGS variant). It builds up approximations to the weight matrices,
and currently the code is not fully tested.
In particular, results based on the weight matrices (e.g., from
vcov
and summary
) may be quite incorrect, especially when
the arguments weights
is used to input prior weights.
This VGAM family function should be used with caution.
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 lambda1 and lambda2 become more different.
Convergence is often slow, especially when the two component
distributions are not well separated. The control argument maxit
should be set to a higher value, e.g., 200, and use trace=TRUE
to monitor convergence.
T. W. Yee
n = 3000 mu1 = exp(2.4) # also known as lambda1 mu2 = exp(3.1) phi = 0.3 y = ifelse(runif(n) < phi, rpois(n, mu1), rpois(n, mu2)) fit = vglm(y ~ 1, mix2poisson, maxit=200) # good idea to have trace=TRUE coef(fit, matrix=TRUE) Coef(fit) # the estimates c(phi, mu1, mu2) # the truth ## Not run: # Plot the results ty = table(y) plot(names(ty), ty, type="h", main="Red=estimate, blue=truth") abline(v=Coef(fit)[-1], lty=2, col="red") abline(v=c(mu1, mu2), lty=2, col="blue") ## End(Not run)