A simple DAG

According to a discussion on SEMNET, the model below 'lacks any testable implications' or one 'cannot detect any testable implications', URL.

I like to 'see' things before deciding, so I submitted it to daggityR, simple task in fact, see code below, but 1st the visual ('plot', called in R), and its 'implications' (called 'impliedConditionalIndependencies' in R); this happens to be the simplest' mediation (called Barron-Kenny, BK, see Frontiers commentary for clarifications).

impliedConditionalIndependencies(NoImplic)

M _||_ UX | X
M _||_ UY
UM _||_ UX
UM _||_ UY
UM _||_ X
UM _||_ Y | M, X
UX _||_ UY
UX _||_ Y | X
UY _||_ X

adjustmentSets( NoImplic, "X", "Y", type="all" )

 {}
 { UM }
 { UX }
 { UM, UX }
 { UY }
 { UM, UY }
 { UX, UY }
 { UM, UX, UY }

adjustmentSets( NoImplic, "M", "Y", type="all" )

 { X }
 { UM, X }
 { UX, X }
 { UM, UX, X }
 { UY, X }
 { UM, UY, X }
 { UX, UY, X }
 { UM, UX, UY, X }

# how to build it:
library(dagitty)

NoImplic <- dagitty('dag {
UX [pos="0,1"]
X [pos="1,1"]
UM [pos="1,0"]
M [pos="2,0"]
UY [pos="2.5,1.5"]
Y [pos="3,1"]
UX-> X -> M ->Y <- X
UM -> M
UY -> Y
}')
plot(NoImplic)

~~~~~~~~
Coman, E. N., F. Thoemmes and J. Fifield (2017). Commentary: Causal Effects in Mediation Modeling: An Introduction with Applications to Latent Variables. Frontiers in Psychology 8(151). http://journal.frontiersin.org/article/10.3389/fpsyg.2017.00151/full