Cross Validated Asked by lazylarry on January 7, 2022

So I’m not too familiar with mixed models, but wondering about the following:

```
library(reshape2)
library(lme4)
library(lmerTest)
#Simulate longitudinal data
N <- 25
t <- 2
x <- rep(1:t,N)
#task1
beta1 <- 4
e1 <- rnorm(N*t, mean = 0, sd = 1.5)
y1 <- 1 + x * beta1 + e1
data1 <- data.frame(id=factor(rep(1:N, each=t)), day = x, y = y1, task=rep(c("task1"),length(y1)))
fakescore <- runif(50)
data1 <- cbind(data1, fakescore)
#temp <- reshape(data1, idvar=c("id"), varying=list(c(2,3),c(4,5), c(6,7), c(8,9), c(10,11), c(12,13),c(14,15)), v.names = varnames.lme, direction = "long")
model <- lmer(fakescore ~ y*day + (1|id), data = data1)
summary(model)
```

The above is an example of how I generated my model. however, my real results are below.

pp_aml, bmi, qsd, and time are continous (time is 0 and another timepoint). sex is male/female. But, I don’t understand – what does it mean that qsd is significant and that qsd:time is at a trend level. I would like to know if qsd trajectory mirrors pp_aml trajectory but also want to know what is signficant down there, if somebody can explain the output to me? My actual stats knowlegde is limited so any help would be great.

Thanks!

```
model <- lmer(pp_aml ~ bmi +sex+ qsd*time + (1|ID), data = temp)
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 1.920e+00 1.133e-01 3.743e+01 16.949 < 2e-16 ***
bmi 4.529e-03 3.676e-03 3.272e+01 1.232 0.226708
sex -1.851e-01 4.863e-02 3.184e+01 -3.808 0.000603 ***
qsd 1.483e-02 5.556e-03 6.595e+01 2.669 0.009573 **
time 6.535e-04 2.253e-04 3.690e+01 2.901 0.006237 **
qsd:time -8.642e-05 4.284e-05 3.576e+01 -2.017 0.051229 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) bmi sex qsd time
bmi -0.890
sex -0.422 0.097
qsd -0.438 0.205 0.118
time -0.189 0.022 -0.020 0.516
qsd:time 0.064 0.039 0.011 -0.439 -0.701
```

This question is about interpreting main effects and interactions.

The principle is that:

main effects that are not involved in an interaction can be interpreted as the association between a 1 unit change in that variable and the outcome, leaving all other fixed effects constant.

main effects that are involved in an interaction can be intepreted as the association between a 1 unit change in that variable and the outcome, when the other variable that it is interacted with is zero (or at it's reference level in the case of a categorical variable), and with other fixed effects held constant.

the interaction can be interpreted as the association between a 1 unit change in one variable and the outcome, when the other variable also changes by 1 unit.

Try not to be too bothered by statistical significance - it is practical significance that matters. The interaction term in your model is 3 orders of magnitude less than one of the main effects and 1 order of magnitude less than the other.

Answered by Robert Long on January 7, 2022

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