Add regression association to latent variable model

Define regression association between variables in a lvm-object and define linear constraints between model equations.

Usage

# S3 method for class 'lvm'
regression(object = lvm(), to, from, fn = NA,
messages = lava.options()$messages, additive=TRUE, y, x, value, ...)
# S3 method for class 'lvm'
regression(object, to = NULL, quick = FALSE, ...) <- value

Arguments

object: lvm-object.
...: Additional arguments to be passed to the low level functions
value: A formula specifying the linear constraints or if to=NULL a list of parameter values.
to: Character vector of outcome(s) or formula object.
from: Character vector of predictor(s).
fn: Real function defining the functional form of predictors (for simulation only).
messages: Controls which messages are turned on/off (0: all off)
additive: If FALSE and predictor is categorical a non-additive effect is assumed
y: Alias for 'to'
x: Alias for 'from'
quick: Faster implementation without parameter constraints

Value

A lvm-object

Details

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.

Note

Variables will be added to the model if not already present.

Author

Klaus K. Holst

Examples


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)