Finite Mixtures of Beta Regression for Rates and Proportions
Description
Fit finite mixtures of beta regression models for rates and proportions via maximum likelihood with the EM algorithm using a parametrization with mean (depending through a link function on the covariates) and precision parameter (called phi).
Usage
1 2 3 4 5 6 7 8 9 10  betamix(formula, data, k, subset, na.action, weights, offset,
link = c("logit", "probit", "cloglog", "cauchit", "log",
"loglog"), link.phi = "log",
control = betareg.control(...), cluster = NULL,
FLXconcomitant = NULL, FLXcontrol = list(), verbose = FALSE,
nstart = if (is.null(cluster)) 3 else 1, which = "BIC",
ID, fixed, extra_components, ...)
extraComponent(type = c("uniform", "betareg"), coef, delta,
link = "logit", link.phi = "log")

Arguments
formula 
symbolic description of the model (of type 
data, subset, na.action 
arguments controlling formula processing
via 
weights 
optional numeric vector of integer case weights. 
offset 
optional numeric vector with an a priori known component to be included in the linear predictor for the mean. 
k 
a vector of integers indicating the number of components of
the finite mixture; passed in turn to the 
link 
character specification of the link function in
the mean model (mu). Currently, 
link.phi 
character specification of the link function in
the precision model (phi). Currently, 
control 
a list of control arguments specified via

cluster 
Either a matrix with 
FLXconcomitant 
concomitant variable model; object of class

FLXcontrol 
object of class 
verbose 
a logical; if 
nstart 
for each value of 
which 
number of model to get if 
ID 
grouping variable indicating if observations are from the same individual, i.e. the component membership is restricted to be the same for these observations. 
fixed 
symbolic description of the model for the parameters
fixed over components (of type 
extra_components 
a list containing objects returned by

... 
arguments passed to 
type 
specifies if the component follows a uniform distribution or a beta regression model. 
coef 
a vector with the coefficients to determine the midpoint of the uniform distribution or names list with the coefficients for the mean and precision of the beta regression model. 
delta 
numeric; halflength of the interval of the uniform distribution. 
Details
The arguments and the model specification are similar to
betareg
. Internally stepFlexmix
is called with suitable arguments to fit the finite mixture model with
the EM algorithm. See Grün et al. (2012) for more details.
extra_components
is a list where each element corresponds to a
component where the parameters are fixed apriori.
Value
An object of class "flexmix"
containing the best model with
respect to the log likelihood or the one selected according to
which
if k
is a vector of integers longer than 1.
Author(s)
Bettina Grün and Achim Zeileis
References
CribariNeto, F., and Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1–24. http://www.jstatsoft.org/v34/i02/.
Grün, B., Kosmidis, I., and Zeileis, A. (2012). Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned. Journal of Statistical Software, 48(11), 1–25. http://www.jstatsoft.org/v48/i11/.
Grün, B., and Leisch, F. (2008). FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters. Journal of Statistical Software, 28(4), 1–35. http://www.jstatsoft.org/v28/i04/.
Leisch, F. (2004). FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R. Journal of Statistical Software, 11(8), 1–18. http://www.jstatsoft.org/v11/i08/.
See Also
betareg
, flexmix
,
stepFlexmix
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52  options(digits = 4)
## data with two groups of dyslexic and nondyslexic children
data("ReadingSkills", package = "betareg")
set.seed(4040)
## try to capture accuracy ~ iq relationship (without using dyslexia
## information) using two beta regression components and one additional
## extra component for a perfect reading score
rs_mix < betamix(accuracy ~ iq, data = ReadingSkills, k = 3,
nstart = 10, extra_components = extraComponent(type = "uniform",
coef = 0.99, delta = 0.01))
## visualize result
## intensities based on posterior probabilities
prob < 2 * (posterior(rs_mix)[cbind(1:nrow(ReadingSkills),
clusters(rs_mix))]  0.5)
## associated HCL colors
col0 < hcl(c(260, 0, 130), 65, 45, fixup = FALSE)
col1 < col0[clusters(rs_mix)]
col2 < hcl(c(260, 0, 130)[clusters(rs_mix)], 65 * abs(prob)^1.5,
95  50 * abs(prob)^1.5, fixup = FALSE)
## scatter plot
plot(accuracy ~ iq, data = ReadingSkills, col = col2, pch = 19,
cex = 1.5, xlim = c(2, 2))
points(accuracy ~ iq, data = ReadingSkills, cex = 1.5, pch = 1,
col = col1)
## fitted lines
iq < 30:30/10
cf < rbind(coef(rs_mix, model = "mean", component = 1:2),
c(qlogis(0.99), 0))
for(i in 1:3)
lines(iq, plogis(cf[i, 1] + cf[i, 2] * iq), lwd = 2,
col = col0[i])
## refit the model including a concomitant variable model
## using the dyslexia information
w < rnorm(nrow(ReadingSkills),
c(1, 1)[as.integer(ReadingSkills$dyslexia)])
## The argument FLXconcomitant can be omitted when specifying
## the model via a three part formula given by
## accuracy ~ iq  1  w
## The posteriors from the previously fitted model are used
## for initialization.
library("flexmix")
rs_mix2 < betamix(accuracy ~ iq, data = ReadingSkills,
extra_components = extraComponent(type = "uniform",
coef = 0.99, delta = 0.01), cluster = posterior(rs_mix),
FLXconcomitant = FLXPmultinom(~w))
coef(rs_mix2, which = "concomitant")
summary(rs_mix2, which = "concomitant")
