https://github.com/bozenne/lavareduce

Latent variable models with linear predictors

https://github.com/bozenne/lavareduce

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Latent variable models with linear predictors

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* lavaReduce


** example

First define a standard =lvm= model:
#+BEGIN_SRC R :exports both :results output
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)
#+END_SRC

#+RESULTS:
#+begin_example
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
#+end_example

Since the number of covariate can be large, we would like to consider only the linear predictor for each outcome:
#+BEGIN_SRC R :exports both :results output
mr <- reduce(m, simplify = TRUE)
mr
#+END_SRC

#+RESULTS:
#+begin_example
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
#+end_example

The parameters associated to the covariates in the linear predictor
are now considered as external parameters:
#+BEGIN_SRC R :exports both :results output
coef(mr)
#+END_SRC

#+RESULTS:
:       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:
#+BEGIN_SRC R :exports both :results output graphics :file inst/lava1.png  
   plot(mr)
#+END_SRC

#+RESULTS:
[[file:inst/lava1.png]]


Then we can estimate the model:
#+BEGIN_SRC R :exports both :results output
  e.mr <- estimate(mr, data = df.data, control = list(constrain = TRUE))
  coef(e.mr)
#+END_SRC

#+RESULTS:
:          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=
#+BEGIN_SRC R :exports both :results output
  e.m <- estimate(m, data = df.data)
  coef(e.m)
#+END_SRC

#+RESULTS:
:          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

#+BEGIN_SRC R :exports both :results output
  ls(getNamespace("lavaReduce"), all.names=TRUE)
#+END_SRC

 [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"         


#+TITLE: Plugin for =lava= allowing LVM with linear predictors (=lavaReduce=)
#+AUTHOR: Brice Ozenne
#+PROPERTY: header-args:R  :session *R* :cache no :width 550 :height 450
#+PROPERTY: header-args  :eval never-export :exports results :results output :tangle yes :comments yes 
#+PROPERTY: header-args:R+ :colnames yes :rownames no :hlines yes
#+OPTIONS: timestamp:t title:t date:t author:t creator:nil toc:nil 
#+OPTIONS: h:4 num:t tags:nil d:t
#+PROPERTY: comments yes 
#+STARTUP: hideall 
#+OPTIONS: toc:t h:4 num:nil tags:nil

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