Plugin for lava allowing LVM with linear predictors (lavaReduce)

lavaReduce

example

First define a standard lvm model:

library(lavaReduce)

m <- lvm()
m <- regression(m, x=paste0("x",1:10),y="y1")
m <- regression(m, x=paste0("z",1:10),y="y2")
covariance(m) <- y1~y2
m

set.seed(10)
df.data <- sim(m, 1e2)

Latent Variable Model
                                                
  y1 ~ x1+x2+x3+x4+x5+x6+x7+x8+x9+x10   gaussian
  y2 ~ z1+z2+z3+z4+z5+z6+z7+z8+z9+z10   gaussian

Exogenous variables:                     
  x1         gaussian
  x2         gaussian
  x3         gaussian
  x4         gaussian
  x5         gaussian
  x6         gaussian
  x7         gaussian
  x8         gaussian
  x9         gaussian
  x10        gaussian
  z1         gaussian
  z2         gaussian
  z3         gaussian
  z4         gaussian
  z5         gaussian
  z6         gaussian
  z7         gaussian
  z8         gaussian
  z9         gaussian
  z10        gaussian

Since the number of covariate can be large, we would like to consider only the linear predictor for each outcome:

mr <- reduce(m, simplify = TRUE)
mr

Latent Variable Model
                      
  y1 ~ LPy1   gaussian
  y2 ~ LPy2   gaussian

Exogenous variables:                      
  x1          gaussian
  x2          gaussian
  x3          gaussian
  x4          gaussian
  x5          gaussian
  x6          gaussian
  x7          gaussian
  x8          gaussian
  x9          gaussian
  x10         gaussian
  z1          gaussian
  z2          gaussian
  z3          gaussian
  z4          gaussian
  z5          gaussian
  z6          gaussian
  z7          gaussian
  z8          gaussian
  z9          gaussian
  z10         gaussian
  LPy1        gaussian
  LPy2        gaussian

The parameters associated to the covariates in the linear predictor are now considered as external parameters:

coef(mr)

      m1       m2       p1       p2       p3       e1       e2       e3       e4       e5       e6       e7       e8       e9      e10      e11      e12      e13      e14      e15 
    "y1"     "y2" "y1~~y1" "y2~~y2" "y1~~y2"  "y1~x1"  "y1~x2"  "y1~x3"  "y1~x4"  "y1~x5"  "y1~x6"  "y1~x7"  "y1~x8"  "y1~x9" "y1~x10"  "y2~z1"  "y2~z2"  "y2~z3"  "y2~z4"  "y2~z5" 
     e16      e17      e18      e19      e20 
 "y2~z6"  "y2~z7"  "y2~z8"  "y2~z9" "y2~z10"

This will also simplify the graphical display of the model:

plot(mr)

Then we can estimate the model:

e.mr <- estimate(mr, data = df.data, control = list(constrain = TRUE))
coef(e.mr)

         y1          y2      y1~~y1      y2~~y2      y1~~y2       y1~x1       y1~x2       y1~x3       y1~x4       y1~x5       y1~x6       y1~x7       y1~x8       y1~x9      y1~x10 
-0.13074998 -0.01754805  0.85586891  1.05513881  0.54344053  0.93672592  1.00944399  1.07045250  0.99182468  0.92266665  1.07494053  1.06341229  1.00513021  0.90690769  0.91347176 
      y2~z1       y2~z2       y2~z3       y2~z4       y2~z5       y2~z6       y2~z7       y2~z8       y2~z9      y2~z10 
 0.96586425  0.89987012  0.90914748  1.04065111  0.97182091  1.03423191  1.15779342  0.95841344  0.96804614  1.00299685

and check that the estimates match with the one of the standard lvm

e.m <- estimate(m, data = df.data)
coef(e.m)

         y1          y2       y1~x1       y1~x2       y1~x3       y1~x4       y1~x5       y1~x6       y1~x7       y1~x8       y1~x9      y1~x10       y2~z1       y2~z2       y2~z3 
-0.13074458 -0.01754648  0.93672381  1.00944610  1.07045206  0.99182646  0.92266858  1.07494250  1.06341339  1.00513184  0.90690349  0.91347119  0.96586967  0.89987524  0.90914869 
      y2~z4       y2~z5       y2~z6       y2~z7       y2~z8       y2~z9      y2~z10      y1~~y1      y2~~y2      y1~~y2 
 1.04065149  0.97182159  1.03422860  1.15778470  0.95840259  0.96804775  1.00299526  0.85585971  1.05512772  0.54343103

all functions

ls(getNamespace("lavaReduce"), all.names=TRUE)

[1] “.__DEVTOOLS__” “.__NAMESPACE__.” “.__S3MethodsTable__.” “.onAttach” “.onLoad” “.packageName” “calcLP” [8] “callS3methodParent” “cancel.lvm.reduced” “character2formula” “clean” “clean.lvm” “clean.lvm.reduced” “combine.formula” [15] “endogenous.lvm.reduced” “estimate.lvm.reduced” “exogenous.lvm.reduced” “formula2character” “gaussian1LP_gradient.lvm” “gaussian1LP_hessian.lvm” “gaussian1LP_logLik.lvm” [22] “gaussian1LP_method.lvm” “gaussian1LP_objective.lvm” “gaussian1LP_score.lvm” “gaussian2LP_gradient.lvm” “gaussian2LP_hessian.lvm” “gaussian2LP_logLik.lvm” “gaussian2LP_method.lvm” [29] “gaussian2LP_objective.lvm” “gaussian2LP_score.lvm” “gaussianLP_gradient.lvm” “gaussianLP_hessian.lvm” “gaussianLP_logLik.lvm” “gaussianLP_method.lvm” “gaussianLP_objective.lvm” [36] “gaussianLP_score.lvm” “getS3methodParent” “initializer.lavaReduce” “initLP” “initVar_link” “initVar_links” “kill.lvm.reduced” [43] “latent<-.lvm.reduced” “lavaReduce.estimate.hook” “lavaReduce.post.hook” “lp” “lp.lvm.reduced” “lp<-” “lp<-.lvm.reduced” [50] “lvm.reduced” “lvm2reduce” “manifest.lvm.reduced” “procdata.lvm” “reduce” “reduce.lvm” “regression.lvm.reduced” [57] “regression<-.lvm.reduced” “scoreLVM” “select.regressor” “select.regressor.formula” “select.response” “select.response.formula” “vars.lvm.reduced”