What is the best way to report the results of a Linear mixed effect model?

I have my results for my LME and am wondering how I should report these:

Linear mixed-effects model fit by REML
Data: anovatuk
AIC       BIC   logLik
-887.2886 -866.0678 448.6443

Random effects:
Formula: ~1 | ID
(Intercept)   Residual
StdDev:   0.0737231 0.09767646

Fixed effects: distance ~ region
Value  Std.Error  DF   t-value p-value
(Intercept)  1.1185789 0.03676021 505 30.429070  0.0000
regionPU    -0.0174890 0.04023870 505 -0.434630  0.6640
regionU     -0.0308177 0.04334312 505 -0.711017  0.4774
Correlation:
(Intr) regnPU
regionPU -0.746
regionU  -0.719  0.876

Standardized Within-Group Residuals:
Min         Q1        Med         Q3        Max
-3.8985706 -0.6273493  0.1357286  0.7493181  1.7777268

Number of Observations: 518
Number of Groups: 11


There is clearly a significant difference between the intercept and the other regions, however, I believe reporting the p-value is not sufficient.

I additionally ran an analysis of deviance and an emmeans, should I be reporting the chi-squared value in addition to the p-value or declare the confidence limits perhaps?:

Anova(lme.odba,type="III")
Analysis of Deviance Table (Type III tests)

Response: distance
Chisq Df Pr(>Chisq)
(Intercept) 925.9283  1     <2e-16 ***
region        0.6589  2     0.7193
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

> #Estimated marginal means - site factor
> #Use emmeans where the factor has levels
> emmeans(object =  lme.odba,
+         specs =  'region',
+         data = anovatuk)
region emmean     SE df lower.CL upper.CL
FO       1.12 0.0368 10     1.04     1.20
PU       1.10 0.0277 10     1.04     1.16
U        1.09 0.0306 10     1.02     1.16


That's true, the intercept is significant (the expected naive value is not 0), but there's no significance in the effect of the region over the intercept. Actually your emmeans is showing values close to 1. {Hint: Make histograms/boxplots/distribution plots with Distance as numerical variable stratified by region. Are you able to see differences between them or they follow similar distribution?}

In brief, the region has no significance over your response variable. Furthermore, the effect of your random effect (ID) is quite low, check the value of the stdev.

Before displaying your conclusions you should check the following things:

1. Check the residuals of the model, the estimations could be wrong because of this. Are the errors normally distributed? Are the errors related with another variable not considered in the model?
2. There are just three regions? Because you treated this variable as a fixed effect.
3. There are more than 11 IDs in reality? Because you treated this variable as a random effect.
4. There are more variables at your disposal that could be used as predictors?

If everything has been checked, your response is brief: there are no evidences to determine that region is affecting distance. Then put these results on an annex in case that someone wants to check it.

• Thank you very much Dave, that's really helpful!
– SamR
Commented Oct 10, 2020 at 9:20