Regsem Package

Simulate Data

To test out the regsem package, we will first simulate data

library(lavaan);library(regsem)

## This is lavaan 0.6-18
## lavaan is FREE software! Please report any bugs.

## Loading required package: Rcpp

## Loading required package: Rsolnp

sim.mod <- "
f1 =~ 1*y1 + 1*y2 + 1*y3+ 1*y4 + 1*y5
f1 ~ 0*x1 + 0*x2 + 0*x3 + 0*x4 + 0*x5 + 0.2*x6 + 0.5*x7 + 0.8*x8
f1~~1*f1"
dat.sim = simulateData(sim.mod,sample.nobs=100,seed=12)

Run the Model with Lavaan

And then run the model with lavaan so we can better see the structure.

run.mod <- "
f1 =~ NA*y1 + y2 + y3+ y4 + y5
f1 ~ c1*x1 + c2*x2 + c3*x3 + c4*x4 + c5*x5 + c6*x6 + c7*x7 + c8*x8
f1~~1*f1
"
lav.out <- sem(run.mod,dat.sim,fixed.x=FALSE)
#summary(lav.out)
parameterestimates(lav.out)[6:13,] # just look at regressions

##    lhs op rhs label    est    se      z pvalue ci.lower ci.upper
## 6   f1  ~  x1    c1  0.068 0.118  0.582  0.561   -0.162    0.299
## 7   f1  ~  x2    c2  0.099 0.112  0.883  0.377   -0.120    0.318
## 8   f1  ~  x3    c3 -0.077 0.132 -0.583  0.560   -0.334    0.181
## 9   f1  ~  x4    c4  0.049 0.120  0.407  0.684   -0.186    0.284
## 10  f1  ~  x5    c5 -0.017 0.133 -0.129  0.897   -0.278    0.243
## 11  f1  ~  x6    c6  0.165 0.107  1.544  0.123   -0.044    0.373
## 12  f1  ~  x7    c7  0.443 0.129  3.438  0.001    0.191    0.696
## 13  f1  ~  x8    c8  0.668 0.144  4.631  0.000    0.385    0.951

Plot the Model

semPlot::semPaths(lav.out)

One of the difficult pieces in using the cv_regsem function is that the penalty has to be calibrated for each particular problem. In running this code, I first tested the default, but this was too small given that there were some parameters > 0.4. After plotting this initial run, I saw that some parameters weren’t penalized enough, therefore, I increased the penalty jump to 0.05 and with 30 different values this tested a model (at a high penalty) that had all estimates as zero. In some cases it isn’t necessary to test a sequence of penalties that would set “large” parameters to zero, as either the model could fail to converge then, or there is not uncertainty about those parameters inclusion.

reg.out <- cv_regsem(lav.out,n.lambda=30,type="lasso",jump=0.04,
                     pars_pen=c("c1","c2","c3","c4","c5","c6","c7","c8"))

In specifying this model, we use the parameter labels to tell cv_regsem which of the parameters to penalize. Equivalently, we could have used the extractMatrices function to identify which parameters to penalize.

# not run
extractMatrices(lav.out)["A"]

Additionally, we can specify which parameters are penalized by type: “regressions”, “loadings”, or both c(“regressions”,“loadings”). Note though that this penalizes all parameters of this type. If you desire to penalize a subset of parameters, use either the parameter name or number format for pars_pen.

Next, we can get a summary of the models tested.

summary(reg.out)

## CV regsem Object
##  Number of parameters regularized: 8
##  Lambda ranging from 0 to 0.88
##  Lowest Fit Lambda: 0.2
##  Metric: BIC
##  Number Converged: 23

Plot the parameter trajectories

plot(reg.out)

Here we can see that we used a large enough penalty to set all parameter estimates to zero. However, the best fitting model came early on, when only a couple parameters were zero.

regsem defaults to using the BIC to choose a final model. This shows up in the final_pars object as well as the lines in the plot. This can be changed with the metric argument.

Understand better what went on with the fit

head(reg.out$fits,10)

##       lambda conv   rmsea      BIC    chisq
##  [1,]   0.00    0 0.07885 3969.101 59.77295
##  [2,]   0.04    0 0.07688 3964.960 60.23719
##  [3,]   0.08    0 0.07599 3961.415 61.29751
##  [4,]   0.12    0 0.07570 3958.203 62.69114
##  [5,]   0.16    0 0.07570 3955.167 64.26013
##  [6,]   0.20    0 0.07634 3952.532 66.23046
##  [7,]   0.24    0 0.07868 3954.042 67.74022
##  [8,]   0.28    0 0.08178 3956.110 69.80762
##  [9,]   0.32    0 0.08543 3958.650 72.34768
## [10,]   0.36    0 0.08915 3961.348 75.04648

One thing to check is the “conv” column. This refers to convergence, with 0 meaning the model converged.

And see what the best fitting parameter estimates are.

reg.out$final_pars[1:13] # don't show variances/covariances

## f1 -> y1 f1 -> y2 f1 -> y3 f1 -> y4 f1 -> y5 x1 -> f1 x2 -> f1 x3 -> f1 
##    1.035    0.948    1.021    1.137    0.948    0.000    0.001    0.000 
## x4 -> f1 x5 -> f1 x6 -> f1 x7 -> f1 x8 -> f1 
##    0.000    0.000    0.057    0.255    0.493

In this final model, we set the regression paths for x2,x3, x4, and x5 to zero. We make a mistake for x1, but we also correctly identify x6, x7, and x8 as true paths .Maximum likelihood estimation with lavaan had p-values > 0.05 for the parameters simulated as zero, but also did not identify the true path of 0.2 as significant (< 0.05).

- Plot the parameter trajectories