# Flexible Mixture Modeling

### Description

FlexMix implements a general framework for finite
mixtures of regression models. Parameter estimation is performed using
the EM algorithm: the E-step is implemented by `flexmix`

, while
the user can specify the M-step.

### Usage

1 2 3 4 5 |

### Arguments

`formula` |
A symbolic description of the model to be fit. The
general form is |

`data` |
An optional data frame containing the variables in the model. |

`k` |
Number of clusters (not needed if |

`cluster` |
Either a matrix with |

`weights` |
An optional vector of replication weights to be used in
the fitting process. Should be |

`model` |
Object of class |

`concomitant` |
Object of class |

`control` |
Object of class |

`object` |
Object of class |

`eps` |
Probabilities below this threshold are treated as zero in the summary method. |

`...` |
Currently not used. |

### Details

FlexMix models are described by objects of class `FLXM`

,
which in turn are created by driver functions like
`FLXMRglm`

or `FLXMCmvnorm`

. Multivariate
responses with independent components can be specified using a
list of `FLXM`

objects.

The `summary`

method lists for each component the prior
probability, the number of observations assigned to the corresponding
cluster, the number of observations with a posterior probability
larger than `eps`

and the ratio of the latter two numbers (which
indicates how separated the cluster is from the others).

### Value

Returns an object of class `flexmix`

.

### Author(s)

Friedrich Leisch and Bettina Gruen

### References

Friedrich Leisch. FlexMix: A general framework for finite mixture
models and latent class regression in R. *Journal of Statistical
Software*, **11**(8), 2004. http://www.jstatsoft.org/v11/i08/

Bettina Gruen and Friedrich Leisch. Fitting finite mixtures of generalized linear regressions in R. Computational Statistics & Data Analysis, 51(11), 5247-5252, 2007. doi:10.1016/j.csda.2006.08.014

Bettina Gruen and Friedrich Leisch. FlexMix Version 2: Finite mixtures with concomitant variables and varying and constant parameters Journal of Statistical Software, 28(4), 1-35, 2008. URL http://www.jstatsoft.org/v28/i04/

### See Also

`plot-methods`

### 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 | ```
data("NPreg", package = "flexmix")
## mixture of two linear regression models. Note that control parameters
## can be specified as named list and abbreviated if unique.
ex1 <- flexmix(yn ~ x + I(x^2), data = NPreg, k = 2,
control = list(verb = 5, iter = 100))
ex1
summary(ex1)
plot(ex1)
## now we fit a model with one Gaussian response and one Poisson
## response. Note that the formulas inside the call to FLXMRglm are
## relative to the overall model formula.
ex2 <- flexmix(yn ~ x, data = NPreg, k = 2,
model = list(FLXMRglm(yn ~ . + I(x^2)),
FLXMRglm(yp ~ ., family = "poisson")))
plot(ex2)
ex2
table(ex2@cluster, NPreg$class)
## for Gaussian responses we get coefficients and standard deviation
parameters(ex2, component = 1, model = 1)
## for Poisson response we get only coefficients
parameters(ex2, component = 1, model = 2)
## fitting a model only to the Poisson response is of course
## done like this
ex3 <- flexmix(yp ~ x, data = NPreg, k = 2,
model = FLXMRglm(family = "poisson"))
## if observations are grouped, i.e., we have several observations per
## individual, fitting is usually much faster:
ex4 <- flexmix(yp~x|id1, data = NPreg, k = 2,
model = FLXMRglm(family = "poisson"))
## And now a binomial example. Mixtures of binomials are not generically
## identified, here the grouping variable is necessary:
set.seed(1234)
ex5 <- initFlexmix(cbind(yb,1 - yb) ~ x, data = NPreg, k = 2,
model = FLXMRglm(family = "binomial"), nrep = 5)
table(NPreg$class, clusters(ex5))
ex6 <- initFlexmix(cbind(yb, 1 - yb) ~ x | id2, data = NPreg, k = 2,
model = FLXMRglm(family = "binomial"), nrep = 5)
table(NPreg$class, clusters(ex6))
``` |