Description Usage Arguments Details Value Author(s) See Also Examples
Define covariances between residual terms in a lvm
-object.
1 2 |
object |
|
var1 |
Vector of variables names (or formula) |
var2 |
Vector of variables names (or formula) defining pairwise
covariance between |
constrain |
Define non-linear parameter constraints to ensure positive definite structure |
pairwise |
If TRUE and |
... |
Additional arguments to be passed to the low level functions |
value |
List of parameter values or (if |
The covariance
function is used to specify correlation structure
between residual terms of a latent variable model, using a formula syntax.
For instance, a multivariate model with three response variables,
Y_1 = μ_1 + ε_1
Y_2 = μ_2 + ε_2
Y_3 = μ_3 + ε_3
can be specified as
m <- lvm(~y1+y2+y3)
Pr. default the two variables are assumed to be independent. To add a covariance parameter r = cov(ε_1,ε_2), we execute the following code
covariance(m) <- y1 ~ f(y2,r)
The special function f
and its second argument could be omitted thus
assigning an unique parameter the covariance between y1
and
y2
.
Similarily the marginal variance of the two response variables can be fixed to be identical (var(Y_i)=v) via
covariance(m) <- c(y1,y2,y3) ~ f(v)
To specify a completely unstructured covariance structure, we can call
covariance(m) <- ~y1+y2+y3
All the parameter values of the linear constraints can be given as the right
handside expression of the assigment function covariance<-
if the
first (and possibly second) argument is defined as well. E.g:
covariance(m,y1~y1+y2) <- list("a1","b1")
covariance(m,~y2+y3) <- list("a2",2)
Defines
var(ε_1) = a1
var(ε_2) = a2
var(ε_3) = 2
cov(ε_1,ε_2) = b1
Parameter constraints can be cleared by fixing the relevant parameters to
NA
(see also the regression
method).
The function covariance
(called without additional arguments) can be
used to inspect the covariance constraints of a lvm
-object.
A lvm
-object
Klaus K. Holst
regression<-
, intercept<-
,
constrain<-
parameter<-
, latent<-
,
cancel<-
, kill<-
1 2 3 4 5 | m <- lvm()
### Define covariance between residuals terms of y1 and y2
covariance(m) <- y1~y2
covariance(m) <- c(y1,y2)~f(v) ## Same marginal variance
covariance(m) ## Examine covariance structure
|
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