estimate.lvm: Estimation of parameters in a Latent Variable Model (lvm)

In lava: Latent Variable Models

Estimation of parameters in a Latent Variable Model (lvm)

Description

Estimate parameters. MLE, IV or user-defined estimator.

Usage

## S3 method for class 'lvm'
estimate(
  x,
  data = parent.frame(),
  estimator = NULL,
  control = list(),
  missing = FALSE,
  weights,
  weightsname,
  data2,
  id,
  fix,
  index = !quick,
  graph = FALSE,
  messages = lava.options()$messages,
  quick = FALSE,
  method,
  param,
  cluster,
  p,
  ...
)

Arguments

x	lvm-object
data	data.frame
estimator	String defining the estimator (see details below)
control	control/optimization parameters (see details below)
missing	Logical variable indiciating how to treat missing data. Setting to FALSE leads to complete case analysis. In the other case likelihood based inference is obtained by integrating out the missing data under assumption the assumption that data is missing at random (MAR).
weights	Optional weights to used by the chosen estimator.
weightsname	Weights names (variable names of the model) in case weights was given as a vector of column names of data
data2	Optional additional dataset used by the chosen estimator.
id	Vector (or name of column in data) that identifies correlated groups of observations in the data leading to variance estimates based on a sandwich estimator
fix	Logical variable indicating whether parameter restriction automatically should be imposed (e.g. intercepts of latent variables set to 0 and at least one regression parameter of each measurement model fixed to ensure identifiability.)
index	For internal use only
graph	For internal use only
messages	Control how much information should be printed during estimation (0: none)
quick	If TRUE the parameter estimates are calculated but all additional information such as standard errors are skipped
method	Optimization method
param	set parametrization (see help(lava.options))
cluster	Obsolete. Alias for 'id'.
p	Evaluate model in parameter 'p' (no optimization)
...	Additional arguments to be passed to lower-level functions

Details

A list of parameters controlling the estimation and optimization procedures is parsed via the control argument. By default Maximum Likelihood is used assuming multivariate normal distributed measurement errors. A list with one or more of the following elements is expected:

start:

Starting value. The order of the parameters can be shown by calling coef (with mean=TRUE) on the lvm-object or with plot(..., labels=TRUE). Note that this requires a check that it is actual the model being estimated, as estimate might add additional restriction to the model, e.g. through the fix and exo.fix arguments. The lvm-object of a fitted model can be extracted with the Model-function.

starterfun:

Starter-function with syntax function(lvm, S, mu). Three builtin functions are available: startvalues, startvalues0, startvalues1, ...

estimator:

String defining which estimator to use (Defaults to “gaussian”)

meanstructure

Logical variable indicating whether to fit model with meanstructure.

method:

String pointing to alternative optimizer (e.g. optim to use simulated annealing).

control:

Parameters passed to the optimizer (default stats::nlminb).

tol:

Tolerance of optimization constraints on lower limit of variance parameters.

Value

A lvmfit-object.

Author(s)

Klaus K. Holst

See Also

estimate.default score, information

Examples

dd <- read.table(header=TRUE,
text="x1 x2 x3
 0.0 -0.5 -2.5
-0.5 -2.0  0.0
 1.0  1.5  1.0
 0.0  0.5  0.0
-2.5 -1.5 -1.0")
e <- estimate(lvm(c(x1,x2,x3)~u),dd)

## Simulation example
m <- lvm(list(y~v1+v2+v3+v4,c(v1,v2,v3,v4)~x))
covariance(m) <- v1~v2+v3+v4
dd <- sim(m,10000) ## Simulate 10000 observations from model
e <- estimate(m, dd) ## Estimate parameters
e

## Using just sufficient statistics
n <- nrow(dd)
e0 <- estimate(m,data=list(S=cov(dd)*(n-1)/n,mu=colMeans(dd),n=n))
rm(dd)

## Multiple group analysis
m <- lvm()
regression(m) <- c(y1,y2,y3)~u
regression(m) <- u~x
d1 <- sim(m,100,p=c("u,u"=1,"u~x"=1))
d2 <- sim(m,100,p=c("u,u"=2,"u~x"=-1))

mm <- baptize(m)
regression(mm,u~x) <- NA
covariance(mm,~u) <- NA
intercept(mm,~u) <- NA
ee <- estimate(list(mm,mm),list(d1,d2))

## Missing data
d0 <- makemissing(d1,cols=1:2)
e0 <- estimate(m,d0,missing=TRUE)
e0

lava documentation built on Nov. 5, 2023, 1:10 a.m.