How to interpret regression coefficient if predictor itself is on a negative scale?

Question

I'm looking at effects of tree mortality (using "Biomass loss") on forest growth patterns. I incorporate loss into a mixed effects model like so (using lmer in R):

lmer(GrowthRate ~ Year + BiomassLoss + (1 + Year | Plot), data = dat, REML = F)

However, BiomassLoss is negative (i.e., the range of the actual values is -50 to 0).

So when I examine my model estimates, how do I interpret the estimate for Biomassloss?

                               95% Confidence Intervals
                     Estimate        Lower        Upper
(Intercept)        7.97955622   6.44676081   9.51907782
Year               0.02984233   0.01092181   0.04854870
BiomassLoss        0.09893282   0.06394322   0.13372741

Normally (i.e., for a predictor on a positive scale), the estimate can be interpreted as:

For every unit increase of the predictor, the interecpt will increase by the value of the predictor's estimate.

But how does this work for a negatively-scaled predictor?

Does "every unit increase" of a negatively-scaled predictor mean:

• as it becomes less negative (i.e., as it increases in value) or

• as it becomes more negative (i.e., as it increases in magnitude) ?

In other words, do I interpret my results as:

• for every unit less of biomass lost my intercept increases by 0.0989

• for every unit more (i.e., every unit lost) my intercept increases by 0.0989

This is important so I can understand if mortality is having a positive or negative impact on the trend...

Answer 1

It is your first option. That is, "for every unit less of biomass lost my intercept increases by 0.0989". To be more explicit, if the biomass loss went from, say, $-45$ to $-44$, and all else were held constant, you would expect the mean of the growth rate to increase by $0.0989$. The model doesn't 'know' what the numbers mean; as far as the fitting procedure goes, they're just numbers. So it reflects a positive increment no matter what the numbers actually correspond to.

If you reverse the sign on the data, the model will be the same, but the coefficient will be -0.0989 instead.

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Update: It seems I skimmed over your quoted example of the "normal" interpretation. You state that it is for the intercept. That isn't correct (but may have been just a typo). The following formulation has been corrected:

Normally (i.e., for a predictor on a positive scale), the estimate can be interpreted as:

For every unit increase of the predictor, holding all else constant, the interecpt predicted mean value of the response will increase by the value of the predictor's estimate.