Update vignette.Rmd

vignettes/vignette.Rmd

@@ -31,6 +31,34 @@ library(phylopath)
 
 `dsem` is an R package for fitting dynamic structural equation models (DSEMs) with a simple user-interface and generic specification of simultaneous and lagged effects in a non-recursive structure.   We here highlight a few features in particular.
 
+## Comparison with linear models
+
+We first show that `dsem` is identical to a linear model.  To do so, we simulate data with a single response and single predictor:
+
+```{r, echo=TRUE, message=FALSE, fig.width=7, fig.height=7}
+# simulate normal distribution
+x = rnorm(100)
+y = 1 + 0.5 * x + rnorm(100)
+data = data.frame(x=x, y=y)
+
+# Fit as linear model
+Lm = lm( y ~ x, data=data )
+
+# Fit as DSEM
+fit = dsem( sem = "x -> y, 0, beta",
+            tsdata = ts(data),
+            control = dsem_control(quiet=TRUE) )
+
+# Display output
+m1 = rbind(
+  "lm" = summary(Lm)$coef[2,1:2],
+  "dsem" = summary(fit)[1,9:10]
+)
+knitr::kable( m1, digits=3)
+```
+
+This shows that linear and dynamic structural equation models give identical estimates of the single path coefficient.
+
 ## Comparison with dynamic linear models
 
 We first demonstrate that `dsem` gives identical results to `dynlm` for a well-known econometric model, the Klein-1 model.