emCgm.default(object, margins, gauss, design, optData, subset, prior = 1, start = NULL, control = emCgm.control(), contrasts = NULL) emCgm.preCgm(object, margins, gauss, design, optData, prior = 1, start = NULL, control = emCgm.control(), contrasts = NULL) emCgm.missmodel(object, margins, gauss, design optData, prior = 1, start = NULL, control = emCgm.control(), contrasts = NULL)
emCgm.default
: a data frame or matrix containing the raw data.
When a data frame is input and if the
margins
argument is not
provided, then the loglinear part of the model is assumed to be a
saturated model in which all
factor
variables are used to form the
table. If the
gauss
argument is not provided, then all numeric
variables in the data frame are included in the conditional Gaussian
part of the model.
When a matrix is input, you must provide the
margins
argument,
which identifies the variables to use in the discrete part
of the model. If the
gauss
argument is omitted, then all remaining
variables in the matrix are used in the Gaussian part of the
conditional Gaussian distribution.
emCgm.preCgm
: an object of class
"preCgm"
.
emCgm.missmodel
: an object of class
"missmodel"
containing
the results of a previous analysis. Any of the functions
mdCgm
,
completeCgm
,
emCgm
, or
daCgm
may be used to produce the
missmodel object.
list(1:2, 3:4)
would
indicate fitting the 1,2 margin (summing over variables 3 and 4) and
the 3,4 margin in a four-way table. This same model can be specified
using the names of the variables (e.g.,
list(c("V1", "V2"), c("V3", "V4"))
),
or using formula notation, as in
margins = ~V1:V2 + V3:V4
.
margins
is not specified, a saturated model is fitted.
emLoglin.default
: When a matrix is input as argument
object
,
argument
margins
must be specified. When a data frame is input and
argument
margins
is missing, then a saturated model involving all
factor variables is fitted.
emLoglin.missmodel
: If not given, argument
margins
defaults to
the margins specified in the
call
statement of the input
"missmodel"
object.
c(1, 2, 4)
, as a
vector of variable names, e.g.
c("V1", "V2", "V4")
, and using
formula notation, e.g.
~V1+V2+V4
. If argument
gauss
is
omitted, then all numeric variables (which do not appear in argument
margins
) are used in the multivariate gaussian model.
optData
. Optionally, an
ncell
by
m
matrix may be input directly as the design matrix.
i=1, ..., ncell
denote the cells in the loglinear model, and let
mu(i)
denote the vector of numeric variable means in cell
i
. Then
the formula
design
provides the design matrix for predicting the
cell means. As an example, let
"V1"
and
"V2"
be the names of the
factor variables, and let
"age"
be a vector giving an average age
for the subjects in each cell. Then formula
design=~V1+V2
indicates
a main effect model for the cell means, while
design=~V1 + V2 + age
indicates a main effect model for the cell means, adjusted for average
cell age.
ncell
by
m
matrix may be input. In this case, the regression model is obtained
as a linear function of the columns of the input matrix.
design
is not specified, then the design matrix
is taken to be an identity matrix.
ncell
rows containing predictors to be used in
computing the
design
matrix. In the example given in the description
for argument
design
, the variable
age
would be input in argument
optData
.
object
is a data frame,
this expression may use variables in the data frame.
"priorLoglin"
,
or a vector of hyperparameters.
"ml"
(maximum likelihood),
"noninformative"
, and
"data.dependent"
. String matching is used,
so the characters
"m"
,
"n"
, or
"d"
are sufficient. The values
of the hyperparameters change with the algorithm (see
priorLoglin
for details). E.g.
"noninformative"
means a common value of 1 for
EM, and a common value of 0.5 for DA.
"priorLoglin"
object is created by routine
priorLoglin
.
dataDepPrior
.
See
for details.
"noninformative"
.
emLoglin.missmodel
: If not given, argument
prior
defaults to
the prior probabilities specified in the
call
statement of the input
"missmodel"
object. If these are not specified, then the default
(which depends on the algorithm) is used.
"cgm"
object of starting values of the model
parameters. The parameters estimated by
mdCgm
are the cell means and
variance--covariance matrix of a multivariate Gaussian distribution,
and log-linear model cell probabilities.
start
may be a list with matrix component
mu
giving the
matrix of means in each of its
ncell
columns (where the columns must
be in the same order as the log-linear model cells, and the rows must
be in the same order as the continuous variables), a matrix component
sigma
giving the variance-covariance matrix, and a vector
pi
giving the cell probabilities. If structural zeros appear in the
contingency table,
start$pi
must contain zeros to indicate the
structural zeros; see
for details.
"cgm"
object created as the
paramIter
component of the class
"missmodel"
object may be input for the
starting values. Routines
mdCgm
,
daCgm
, and
emCgm
may be used to
create an appropriate
"missmodel"
object.
1
s for
pi
, and a matrix of means and a diagonal matrix of
variances estimated obtained from the numeric observations with no
missing values.
object
is a class
"missmodel"
object,
start
defaults to the final estimates in the input
"missmodel"
object.
daCgm.missmodel
: if not given, argument
control
defaults to
the control parameters specified in the
call
statement of the input
"missmodel"
object, but only if these are of the correct class. If
these are not given (or are not of the correct class), then the
argument
control
defaults to
daCgm.control
values.
design
formula. The elements of the list should have the same
name as the variable and should be either a contrast matrix
(specifically, any full-rank matrix with as many rows as there are
levels in the factor), or else a function to compute such a matrix
given the number of levels.
"missmodel"
is returned; see
for details.
See the help file for for additional details.
emCgm(object = language) # NOTE: this iterates forever, # suggesting need for restricted model. emCgm.default(object = language) # same # Restricted model # Categorical variables LAN, AGE, PRI, SEX, GRD specify a 5 dimensional # contingency table with 4*5*5*2*5= 1000 cells # Specify loglinear model with all main effects and 2-variable associations: margins.form <- ~ LAN + AGE + PRI + SEX + GRD + LAN:AGE + LAN:PRI + LAN:SEX + LAN:GRD + AGE:PRI + AGE:SEX + AGE:GRD + PRI:SEX + PRI:GRD + SEX:GRD #linear contrast lc <- c(-2,-1,0,1,2) design.form <- ~ LAN + C(AGE,lc,1) + C(PRI,lc,1) + SEX + C(GRD,lc,1) # PreProcess language.pre <- preCgm(language) # Set hyperparameter to 1.05 to ensure a mode in the # interior of the parameter space language.em <- emCgm(language.pre, margins = margins.form, design = design.form, prior = 1.05) # same as: emCgm.preCgm(language.pre, margins = margins.form, design = design.form, prior = 1.05)