Description Usage Arguments Details Value Author(s) References See Also Examples
dmm
creates an object of class dmm
, a
dependent mixture model.
lca
creates an object of class dmm,lca
, a
latent class model or an independent mixture model.
1 2 3 4 5 6 7 8 9 10 11  dmm(nstates, itemtypes, modname = NULL, fixed = NULL,
stval = NULL, conrows = NULL, conpat = NULL, tdfix =
NULL, tdst = NULL, linmat = NULL, snames = NULL,
inames = NULL)
## S3 method for class 'dmm'
summary(object, specs=FALSE, precision=3, se=NULL, ...)
lca(nclasses, itemtypes, modname = NULL, fixed = NULL,
stval = NULL, conrows = NULL, conpat = NULL,
linmat = NULL, snames = NULL, inames = NULL)

nstates 
The number of latent states/classes of the model. 
nclasses 
The number of classes of an lca model, ie the number of
states in a 
itemtypes 
A vector of length 
modname 
A character string with the name of the model, good when fitting many models. Components of mixture models keep their own names. Names are printed in the summary. Boring default names are provided. 
fixed 
A vector of length the number of parameters of the model idicating whether parameters are fixed (0) or not (>0). This may be identical to conpat (see below). 
stval 
Start values of the parameters. These will be random if not specified. Start values must be specified (for all parameters) if there are fixed parameters. 
conrows 
Argument 
conpat 
Argument 
tdfix,tdst 
The first is a logical vector indicating (with 1's) which parameters are dependent on covariates (it should have length npars). tdst provides the starting values for the regression parameters. Using tdcov=TRUE in fitdmm will actually fit the regression parameters. The covariate itself has to be specified in the data as "covariate" (see help on markovdata) and should be scaled to 01. 
linmat 
A complete matrix of linear constraints. This argument
is intended for internal use only, it is used by the fit routine to
recreate the model with the fitted parameter values. Warning: use of
this argument results in complete replacement of the otherwise created
matrix A, which contains e.g. sum contraints for transition matrix
parameters. If 
snames 
Names for the states may be provided in snames. Defaults are State1, State2 etc. These are printed in the summary. 
inames 
Names for items may be provided in inames. Defaults are Item1, Item2 etc. They are printed in the summary. 
dmm 
Object of class 
precision 
Precision sets the number of digits to be printed in the summary functions. 
se 
Vector with standard errors, these are passed on from the summary.fit function if and when ses are available. 
specs,... 
Internal use. 
object 
An object of class 
The function dmm
creates an object of class dmm
and sets
random initial parameter values if these are not provided. Even though
dmm
is not a mixture of Markov models, the mixture parameter is
is included in the parameter vector. This is important when specifying
constraints. Parameters are ordered as follows: the first parameter(s)
are the mixing proportions of the mixture of Markov and/or latent class
models. I.e., when a single latent class model or a single Markov
chain is fitted, this mixture proportion has value 1.0 and is it is
fixed in estimation. After the mixing proportions, the next parameters
in the parameter vector are the transition matrix parameters, the
square of nstates in rowmajor order. That is, first the transition
probabilities from state 1 to all the other states are given, then the
probabilities from state 2 to all the other states etc. Next are the
observation matrix parameters. These are provided consecutively for
each state/class. Ie a trichtomous item model with two states has 6
observation parameters; the first three are the probabilities of
observing category 1, 2 and 3 respectively in state 1 (which sum to
one), and then similarly for state 2. As another example: suppose we
have model for one binary item and one gaussian item, in that order, we
would have 4 observation parameters for each state, first the
probabilities of observing a symbol from category 1 or 2 in state 1,
the two parameters, the mean and standard deviation for state 1, and
then the same state 2 (see the example in fitdmm with data from rudy).
Finally the initial state probabilities are provided, in the order of
the states. In the case of a latent class model or a finite mixture
model, these parameters are usually denote as the mixture proportions.
Linear constraints can be set using arguments conrows
and
conpat
. conrows
must be contain nc by npars values, in
row major order, with nc the number of contraints to be specified.
conrows
is used to define general linear constraints. A row of
conrows
must contain the partial derivatives of a general linear
constraint with respect to each of the parameters. Suppose we want the
constraint x1 2*x2=0, one row of conrows should contain a 1 in
position one and 2 in position and zeroes in the remaining positions.
In the function mixdmm
conrows
is understood to specify
linear constraints on the mixing proportions only. As a consequence,
it is not possible to easily constrain parameters between components of
a mixture model.
conpat
can be used as a shortcut for both fixed and conrows. It
must be a single vector of length npars contaning 0's (zeroes) for
fixed parameters, 1's (ones) for free parameters and higher numbers for
possibly equality constrained parameters. E.g.
conpat=c(1,1,0,2,2,3,3,3)
would indicate that pars 1 and 2 are
freely estimated, par 3 is fixed at its startvalue (which must be
provided in this case), par 4 and 5 are to estimated equal and pars 6,
7 and 8 are also to be estimated equal.
dmm
returns an object of class dmm
which has its own summary
method. This will print the parameter values, itemtypes, number of (free)
parameters, and the number of states. There is no print method. Using
print will print all fields of the model which is a list of the following:
modname 
See above. 
nstates 
See above 
snames 
See above. 
nitems 
The number of items(=length(itemtypes)). 
itemtypes 
See above. 
inames 
See above. 
npars 
The total parameter count of the model. 
nparstotal 
The total number of parameters of when the covariate parameters are included. 
freepars 
The number of freely estimated parameters (it is computed as sum(as.logical(fixed))rank(qr(A)). 
freeparsnotd 
The number of freely estimated parameters (it is computed as sum(as.logical(fixed))rank(qr(A)); this version without the covariate parameters. 
pars 
A vector of length npars containing parameter values. 
fixed 

A 
The matrix A contains the general linear constraints of the model. nrow(A) is the number of linear constraints. A starts with a number of rows for the sum constraints for the transition, observation and initial state parameters, after which the user provided constraints are added. 
bu,bl 
bu and bl represent the upper and lower bounds of the parameters and the constraints. These vectors are each of length npars + nrow(A). 
bllin,bulin 
The lower and upper bounds of the linear constraints. 
td,tdin,tdtr,tdob,tdfit 
Logicals indicating whehter there covariates, in which parameters they are, and whether they are estimated or not (the latter is used to decide whether to print those values or not). 
st 
Logical indicating whether the model has user specified starting values. 
lca
returns an object of class dmm, lca
, and is otherwise
identical to a dmm
object. The only difference is that the
transition matrix parameters are irrelevant, and
consequently they are not printed in the summary function.
Ingmar Visser [email protected]
On hidden Markov models: Lawrence R. Rabiner (1989). A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of IEEE, 772, p. 267295.
On latent class models: A. L. McCutcheon (1987). Latent class analysis. Sage Publications.
mixdmm
on defining mixtures of dmm
's,
mgdmm
for defining multi group models, and
generate
for generating data from models.
1 2 3 4 5 6 7 8 9 10 11 12 13  # create a 2 state model with one continuous and one binary response
# with start values provided in st
st < c(1,0.9,0.1,0.2,0.8,2,1,0.7,0.3,5,2,0.2,0.8,0.5,0.5)
mod < dmm(nsta=2,itemt=c(1,2), stval=st)
summary(mod)
# 2 class latent class model with equal conditional probabilities in each class
stv=c(1,rep(c(0.9,0.1),5),rep(c(0.1,0.9),5),0.5,0.5)
# here the conditional probs of the first item are set equal to those in
# the subsequent items
conpat=c(1,rep(c(2,3),5),rep(c(4,5),5),1,1)
lc=lca(ncl=2,itemtypes=rep(2,5),conpat=conpat,stv=stv)
summary(lc)

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