How to interpret a GLMM

Question

I am new to stats and have run a GLMM in R using the lme4 package. The model includes marine litter collected in KG, with fixed variables of population (all), wind direction, wave strength. Random variables of Date (year). I want to find out what effects marine litter abundance on the coastline just do not know how to interpret the GLMM.. Here is the results below

Linear mixed model fit by REML ['lmerMod']
Formula: LitterKG ~ All + SurveyWindow + WindDirection + WaveStrength +      (1 | Date)
Data: all.beaches

REML criterion at convergence: 39700

Scaled residuals: 
Min      1Q  Median      3Q     Max 
-0.5254 -0.3101 -0.2122 -0.0110 26.6041 

Random effects:
 Groups   Name        Variance Std.Dev.
 Date     (Intercept)   30.66   5.537  
 Residual             5438.59  73.747  
Number of obs: 3472, groups:  Date, 11

Fixed effects:
                        Estimate Std. Error t value
(Intercept)            3.200e+01  3.532e+00   9.060
All                   -8.038e-07  3.330e-06  -0.241
SurveyWindowSpring    -2.241e+00  3.425e+00  -0.654
SurveyWindowSummer    -8.193e+00  3.668e+00  -2.234
SurveyWindowWinter    -7.108e+00  3.963e+00  -1.794
WindDirectionOffshore -1.120e+01  8.873e+00  -1.263
WindDirectionOnshore  -8.974e+00  7.815e+00  -1.148
WindDirectionStrong    2.330e+00  3.739e+00   0.623
WaveStrengthModerate  -1.716e+00  3.107e+00  -0.552
WaveStrengthStrong    -8.135e-01  4.951e+00  -0.164

    Correlation of Fixed Effects:
            (Intr) All    SrvyWndwSp SrvyWndwSm SrvyWW WndDrctnOf WndDrctnOn WndDrS WvStrM
All         -0.630                                                                        
SrvyWndwSpr -0.251  0.017                                                                 
SrvyWndwSmm -0.238  0.019  0.233                                                          
SrvyWndwWnt -0.176  0.003  0.222      0.196                                               
WndDrctnOff -0.193  0.012  0.004     -0.013     -0.012                                    
WndDrctnOns -0.222  0.013  0.017     -0.011      0.020  0.539                             
WndDrctnStr -0.048 -0.021 -0.043     -0.015     -0.022  0.089      0.118                  
WvStrngthMd -0.269  0.017  0.015      0.014     -0.063  0.060      0.053     -0.403       
WvStrngthSt -0.156  0.073  0.014      0.035     -0.093 -0.067     -0.112     -0.526  0.396
> confint(littereffects)
Computing profile confidence intervals ...
                              2.5 %        97.5 %
.sig01                 1.280327e+00  9.233787e+00
.sigma                 7.196028e+01  7.543197e+01
(Intercept)            2.527790e+01  3.875861e+01
All                   -7.360716e-06  5.679117e-06
SurveyWindowSpring    -8.977767e+00  4.431734e+00
SurveyWindowSummer    -1.543544e+01 -1.065308e+00
SurveyWindowWinter    -1.494666e+01  5.804198e-01
WindDirectionOffshore -2.809227e+01  5.684548e+00
WindDirectionOnshore  -2.394814e+01  6.003506e+00
WindDirectionStrong   -5.063842e+00  9.583612e+00
WaveStrengthModerate  -7.764628e+00  4.405360e+00
WaveStrengthStrong    -1.048129e+01  8.901831e+00

Answer 1

In this example, you have fitted a linear mixed-effects model, which is a special case of a Generalized Linear Mixed Model (GLMM) with normal error terms and an identity link function.

This model can be seen as an extension of simple linear regression to account for the clustering Date. That is, with this model you postulate that measurements of your outcome variable LitterKG on the same year are correlated.

The interpretation of the coefficients you receive in the output is the same as in simple linear regression. I.e., in this particular model the inclusion of the random effects does not complicate the interpretation of the coefficients in any way.