Define regression association between variables in a lvm-object and
define linear constraints between model equations.
# S3 method for lvm
regression(object = lvm(), to, from, fn = NA,
messages = lava.options()$messages, additive=TRUE, y, x, value, ...)
# S3 method for lvm
regression(object, to=NULL, quick=FALSE, ...) <- valuelvm-object.
Additional arguments to be passed to the low level functions
A formula specifying the linear constraints or if
to=NULL a list of parameter values.
Character vector of outcome(s) or formula object.
Character vector of predictor(s).
Real function defining the functional form of predictors (for simulation only).
Controls which messages are turned on/off (0: all off)
If FALSE and predictor is categorical a non-additive effect is assumed
Alias for 'to'
Alias for 'from'
Faster implementation without parameter constraints
A lvm-object
The regression function is used to specify linear associations
between variables of a latent variable model, and offers formula syntax
resembling the model specification of e.g. lm.
For instance, to add the following linear regression model, to the
lvm-object, m:
$$ E(Y|X_1,X_2) = \beta_1 X_1 + \beta_2 X_2$$
We can write
regression(m) <- y ~ x1 + x2
Multivariate models can be specified by successive calls with
regression, but multivariate formulas are also supported, e.g.
regression(m) <- c(y1,y2) ~ x1 + x2
defines $$ E(Y_i|X_1,X_2) = \beta_{1i} X_1 + \beta_{2i} X_2 $$
The special function, f, can be used in the model specification to
specify linear constraints. E.g. to fix \(\beta_1=\beta_2\)
, we could write
regression(m) <- y ~ f(x1,beta) + f(x2,beta)
The second argument of f can also be a number (e.g. defining an
offset) or be set to NA in order to clear any previously defined
linear constraints.
Alternatively, a more straight forward notation can be used:
regression(m) <- y ~ beta*x1 + beta*x2
All the parameter values of the linear constraints can be given as the right
handside expression of the assigment function regression<- (or
regfix<-) if the first (and possibly second) argument is defined as
well. E.g:
regression(m,y1~x1+x2) <- list("a1","b1")
defines \(E(Y_1|X_1,X_2) = a1 X_1 + b1 X_2\). The rhs argument can be a mixture of character and numeric values (and NA's to remove constraints).
The function regression (called without additional arguments) can be
used to inspect the linear constraints of a lvm-object.
Variables will be added to the model if not already present.
intercept<-, covariance<-,
constrain<-, parameter<-,
latent<-, cancel<-, kill<-
m <- lvm() ## Initialize empty lvm-object
### E(y1|z,v) = beta1*z + beta2*v
regression(m) <- y1 ~ z + v
### E(y2|x,z,v) = beta*x + beta*z + 2*v + beta3*u
regression(m) <- y2 ~ f(x,beta) + f(z,beta) + f(v,2) + u
### Clear restriction on association between y and
### fix slope coefficient of u to beta
regression(m, y2 ~ v+u) <- list(NA,"beta")
regression(m) ## Examine current linear parameter constraints
#> Regression parameters:
#> y1 z v y2 x u
#> y1 * *
#> y2 beta * beta beta
## ## A multivariate model, E(yi|x1,x2) = beta[1i]*x1 + beta[2i]*x2:
m2 <- lvm(c(y1,y2) ~ x1+x2)