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LME (Assumptions (Homoscedasticity within each random effect group,…
LME
Assumptions
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plot the residuals, fitted values and predicted random effects to verify the assumptions above.
Key Points to Remember:
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decide whether you need a linear mixed-effects model (LME) or a generalized linear mixed-effects model (GLMM). There are several packages available. e.g. lme4, nlme.
One way to decide whether you need a mixed-effects model or a plain linear regression is to compare the AIC of the LME and the GLS (equivalent to the linear regression). We want to see that the mixed-effects model is an improvement.
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LME/LMER Functions
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LME
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model1 <- lme(y~x, random = ~1|A/B/C)
model1 <- glmer(y~x + (1|A/B/C), family = binomial)
Types of LME
Random Intercept Model
How to code in R
RIKZ<-read.table("D:\yourWD\RIKZ.txt",header=T)
library(nlme)
RIKZ$fBeach <- factor(RIKZ$Beach)
Mlme1 <- lme(Richness ~ NAP, random = ~1 | fBeach, data=RIKZ)
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Intepretation
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The predictions are composed of a fixed component (as usual the intercept plus the slope times the value of NAP)
The random component “shifts” this average fixed prediction for each beach according to the variance estimated (2.9442).
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To compare models, we can observe that AIC
Random Effects Model
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Richness is now modeled as an intercept and a random effect bi that can differ per beach. The AIC for the model is higher, 267. The code is:
Mlme3 <- lme(Richness ~ 1, random = ~1 | fBeach, data = RIKZ)
summary(Mlme3)
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R^2
How can we know the variance explained by the LME and what part of the variance is due to fixed/random effects?
MuMIn Package
r.squaredGLMM()
reports the marginal R2 (the variance explained by the fixed effects of the model) and the conditional R2 (variance explained by both fixed and random effects).
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