# Interpreting interactions of mixed model estimates correctly?

I have data of the following form:

  Plot Period ChangeRate PlotType HurrStat
1    4      1   4.226524     Succ        N
3    4      2   4.465217     Succ        N
2    4      3   4.250807     Succ        N
4    5      1   4.647065     Succ        F
5    5      2   8.437362     Succ        F
6    5      3   1.826346     Succ        F


Where the ChangeRate of biomass (Mg/ha/year) during 3 different sampling Periodswas determined. The data have 3 samples from each of 37 Plots. The plots also experienced differential Hurricane Fran damage between Period 2 and 3, which is captured by the categorical variable HurrStat (where N is no damage and F codes for damage). PlotType is also a 2-level factor not used.

I fit the following model using lmer (in R):

mod <- lmer(ChangeRate ~ factor(Period) * factor(HurrStat) + (1|Plot), data = dat, REML=F)


and followed that up by calculating bootstrapped confidence intervals for each predictor:

confint(mod,method='boot',nsim=10000)


I combined them into the following table showing Estimates and 2.5% and 97.5% confidence intervals:

                                   Estimates       2.5%      97.5%
(Intercept)                        3.4592000  2.2492249  4.6814362
factor(Period)2                    2.5679507  0.7930576  4.2767805
factor(Period)3                    2.9561185  1.2523120  4.6726818
factor(HurrStat)F                  0.3630296 -1.0398981  1.7304300
factor(Period)2:factor(HurrStat)F -1.4151125 -3.3603946  0.5210217
factor(Period)3:factor(HurrStat)F -4.4443273 -6.4183476 -2.4845560


Are the below interpretations correct given these results?

* Period 1: biomass change rate = 3.46 (95% CI 2.45, 4.68) Mg/ha/yr
* Period 2: 2.57 higher --> so 6.12 Mg/ha/yr
* Period 3: 2.96 higher --> so 6.51 Mg/ha/yr
x Period 1 plots w/ Fran damage had 0.36 higher rates vs. Period 1 values above --> so 3.82 Mg/ha/yr
x Fran plots were -1.42 lower in Period 2
* Plots with Hurr damage were -4.44 lower in period 3
(So is this 3.46 + 2.96 + 0.36 -4.44, or do I ignore the non-significant 0.36?)

* = SIGNIFICANT EFFECTS   |   x = INSIGNIFICANT EFFECTS


Ultimately I want to know if plots experienced a slowing down of ChangeRate between periods (with a focus on Period 3).

• Is it safe to say form the results I got that: overall, ChangeRate increased in Period 3, but plots impacted by the hurricane actually decreased??

• 6.51 rate in non-damaged plots vs 1.98 (3.46 + 2.96 + -4.44) rate in hurricane plots in Period 3 (vs. a mean Period 1 ChangeRate of 3.46)
• How did you actually compute ChangeRate in each Period? – Isabella Ghement May 7 '18 at 3:28
• Biomass.year2 - Biomass.year1 / Year.year2 - Year.year1 (change in biomass devided by change in time for that given period) – theforestecologist May 7 '18 at 3:42