View source: R/family.mixture.R
mix2poisson | R Documentation |
Estimates the three parameters of a mixture of two Poisson distributions by maximum likelihood estimation.
mix2poisson(lphi = "logitlink", llambda = "loglink", iphi = 0.5, il1 = NULL, il2 = NULL, qmu = c(0.2, 0.8), nsimEIM = 100, zero = "phi")
lphi, llambda |
Link functions for the parameter phi and
lambda.
See |
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 |
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 |
nsimEIM, zero |
See |
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
.
This VGAM family function requires care for a successful
application.
In particular, good initial values are required because
of the presence of local solutions. Therefore running
this function with several different combinations of
arguments such as iphi
, il1
, il2
,
qmu
is highly recommended. Graphical methods such as
hist
can be used as an aid.
With grouped data (i.e., using the weights
argument)
one has to use a large value of nsimEIM
;
see the example below.
This VGAM family function is experimental and should be used with care.
The response must be integer-valued since
dpois
is invoked.
Fitting this model successfully to data can be difficult
due to local solutions 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. The default control argument trace =
TRUE
is to encourage monitoring convergence.
T. W. Yee
rpois
,
poissonff
,
mix2normal
.
## Not run: # Example 1: simulated data nn <- 1000 mu1 <- exp(2.5) # Also known as lambda1 mu2 <- exp(3) (phi <- logitlink(-0.5, inverse = TRUE)) mdata <- data.frame(y = rpois(nn, ifelse(runif(nn) < phi, mu1, mu2))) mfit <- vglm(y ~ 1, mix2poisson, data = mdata) coef(mfit, matrix = TRUE) # Compare the results with the truth round(rbind('Estimated' = Coef(mfit), 'Truth' = c(phi, mu1, mu2)), 2) ty <- with(mdata, table(y)) plot(names(ty), ty, type = "h", main = "Orange=estimate, blue=truth", ylab = "Frequency", xlab = "y") abline(v = Coef(mfit)[-1], lty = 2, col = "orange", lwd = 2) abline(v = c(mu1, mu2), lty = 2, col = "blue", lwd = 2) # Example 2: London Times data (Lange, 1997, p.31) ltdata1 <- data.frame(deaths = 0:9, freq = c(162,267,271, 185,111,61,27,8,3,1)) ltdata2 <- data.frame(y = with(ltdata1, rep(deaths, freq))) # Usually this does not work well unless nsimEIM is large Mfit <- vglm(deaths ~ 1, weight = freq, data = ltdata1, mix2poisson(iphi=0.3, il1=1, il2=2.5, nsimEIM=5000)) # This works better in general Mfit = vglm(y ~ 1, mix2poisson(iphi=0.3, il1=1, il2=2.5), ltdata2) coef(Mfit, matrix = TRUE) Coef(Mfit) ## End(Not run)
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