[R-sig-ME] dyads nested: confused on interpretation

[Dexter Locke]

Greetings mixed modelers,

I'm fitting a three-level mixed model with lme4::lmer and struggling with
the interpretation.

The dependent variable is species richness. There are zeros, and its not
normal, so I've added one and then logged it. Observations are collected as
pairs at sites, and therefore not independent. As Wickham (2014) notes -
referencing Bolker - there is an equivalence between a t-test a mixed model
in this type of case. Sites are also uniquely nested within one of two
cities, hence the third level. My syntax is:

AAA <- lmer(log(richness + 1) ~fb*City + (1 | Site / City),
data=wy_GardenC, REML = F)

"fb" indicates the location of the observation within the site: either
front (Front) or back (Back).

Using sjPlot::sjt.lmer the p-values are calculated and formatted neatly in
a table (I do understand the controversies and assumptions around using
t-stats as Walk Z-stats..)

The estimated intercept is 2.77 (or 15.96 once back-transformed), the fb
variable becomes "fbBack", its beta is 0.42 (or 1.52 once
back-transformed). The City and fb*City interaction terms are not
significant.

Can I conclude that back yards are on average ~10% (1.52/ 15.92 =  0.095)
more species-rich? My confusion is that I'd think R takes b as in Back
first as the base case and makes f as in Front the contrast. Plotting the
data suggests that indeed back yards in Los Angeles (one of the two cities
is higher):

http://dexterlocke.com/wp-content/uploads/2017/07/unnamed-1.png


I'm not interested in if all backs (on average) are greater than all fronts
(on average). I'm interested in if at each site, the back is generally
greater than the front. Am I specifying a corresponding model to this
question? Is the front being taken as the referent, and back as reference?
Given the factors, what is being contrasted with what base-case?

Thank you for your consideration,
Dexter


Wickham, H. (2014). Tidy Data. Journal Of Statistical Software, 59(10).
Retrieved from https://www.jstatsoft.org/article/view/v059i10/v59i10.pdf

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