Interpreting a linear mixed effect model's interaction term I am a biologist and am attempting to analyze the effects of time and location on depth. I was told I needed to use a mixed effects model to account for the random variables of Individual and tracking type, but am unfamiliar with the outputs and am having difficulty interpreting it. I am not sure if there is something wrong with my model, or if I do not correctly understand how to read the output. 
I am attempting to analyze data that looks like this:
Name Seconds Depth Time Location  Place Tracking
8601   29422    19  Day      Off Hawaii   Active
8601   29434    29  Day      Off Hawaii   Active
8601   29444    36  Day      Off Hawaii   Active
8601   29455    44  Day      Off Hawaii   Active
8601   29466    50  Day      Off Hawaii   Active
8601   29480    55  Day      Off Hawaii   Active

and I built a model using R package lme4, function lmer. My model is 
Depth~Time*Location+(1|Name)+(1|Tracking)

With output: 
Fixed effects:
                     Estimate Std. Error t value
(Intercept)            28.577      4.263   6.703
TimeNight              26.021      6.341   4.104
LocationOn            -22.835      1.181 -19.327
TimeNight:LocationOn  -33.049      1.567 -21.088

Systematically removing terms revealed that Location, Time, and their interaction were all significant. 
I am mostly interested in the differences between On/Night and On/Day, as well as Off/Night and Off/Day. I know that Off/Day is 28.577, with Off/Night at (28.577+26.021), and On/Day at (28.577-22.835). My trouble comes in interpreting Night/On, since the answer cannot be negative (can't have negative depth). Does the negative value mean this type of model isn't appropriate for my situation?
Also, is there a way to determine if the values for On/Night are significantly different from On/Day? Can I use a glht?
 A: If you're interested in those particular comparisons, the easiest thing to do would be to split the data into On and Off subsets, and run Day/Night comparisons separately in each one.  (This would involve a few extra comparisons, but if you aren't doing something like an all-pairwise-comparisons analysis you can probably get away without a formal correction for multiple comparisons.)
The negative value is more problematic.  It's hard for me to see circumstances where a model like this (a 2x2 interaction of categorical fixed predictors) would give you predicted results that were significantly different from the group means.  I would look at model diagnostics and plots of your data: are there observations or individuals that are outliers?
I'm also a little surprised that you're treating Tracking as a random effect -- you don't say how many levels it has, but I'm guessing that it's either Active or Inactive (i.e., only two levels).  If you want to control for it you would be better off treating it as a fixed effect ...
