Not getting a smooth curve using ggplot2 - r

Question

I am trying to fitting a mixed effects models using lme4 package. Unfortunately I cannot share the data that i am working with. Also i couldn't find a toy data set is relevant to my problem . So here i have showed the steps that i followed so far :
First i plotted the overall trend of the data as follows :
p21 <- ggplot(data = sub_data, aes(x = age_cent, y = y))
p21+ geom_point() + geom_smooth()
Based on this , there seems to be a some nonlinear trend in the data. Hence I tried to fit the quadratic model as follows :
sub_data$age_cent=sub_data$age-mean((sub_data)$age)
sub_data$age_centsqr=(sub_data$age-mean((sub_data)$age))^2
m1= lmer(y ~ 1 + age_cent + age_centsqr +(1 | id) , sub_data, REML = TRUE)
In the above model i only included a random intercept because i don't have enough data to include both random slope and intercept.Then i extracted the predictions of these model at population level as follows :
pred1=predict(m1,re.form=NA)
Next I plotted these predictions along with a smooth quadratic function like this
p21+ geom_point() + geom_smooth(method = "lm", formula = y ~ I(x) + I(x^2)
,col="red")+geom_line(aes(y=pred1,group = id) ,col="blue", lwd = 0.5)
In the above plot , the curve corresponds to predictions are not smooth. Can any one helps me to figure out the reason for that ?
I am doing anything wrong here ?
Update :
As eipi10 pointed out , this may due to fitting different curves for different people.
But when i tried the same thing using a toy data set which is in the lme4 package , i got the same curve for each person as follows :
m1 <- lmer(Reaction ~ 1+I(Days) + (1+ Days| Subject) , data = sleepstudy)
pred1new1=predict(m1,re.form=NA)
p21 <- ggplot(data = sleepstudy, aes(x = Days, y = Reaction))
p21+ geom_point() + geom_smooth()
p21+ geom_point() + geom_smooth()+ geom_line(aes(y=pred1new1,group = Subject) ,col="red", lwd = 0.5)
What may be the reason the for different results ? Is this due to unbalance of the data ?
The data i used collected in 3 time steps and some people didn't have it for all 3 time steps. But the toy data set is a balanced data set.
Thank you

Answer 1

tl;dr use expand.grid() or something like it to generate a balanced/evenly spaced sample for every group (if you have a strongly nonlinear curve you may want to generate a larger/more finely spaced set of x values than in the original data)
You could also take a look at the sjPlot package, which does a lot of this stuff automatically ...
You need both an unbalanced data set and a non-linear (e.g. polynomial) model for the fixed effects to see this effect.
if the model is linear, then you don't notice missing values because the linear interpolation done by geom_line() works perfectly
if the data are balanced then there are no gaps to get weirdly filled by linear interpolation
Generate an example with quadratic effects and an unbalanced data set; fit the model
library(lme4)
set.seed(101)
dd <- expand.grid(id=factor(1:10),x=1:10)
dd$y <- simulate(~poly(x,2)+(poly(x,2)|id),
newdata=dd,
family=gaussian,
newparams=list(beta=c(0,0,0.1),
theta=rep(0.1,6),
sigma=1))[[1]]
## subsample randomly (missing values)
dd <- dd[sort(sample(nrow(dd),size=round(0.7*nrow(dd)))),]
m1 <- lmer(y ~ poly(x,2) + (poly(x,2)|id) , data = dd)
Naive prediction and plot:
dd$pred1 <- predict(m1,re.form=NA)
library(ggplot2)
p11 <- (ggplot(data = dd, aes(x = x, y = y))
+ geom_point() + geom_smooth(method="lm",formula=y~poly(x,2))
)
p11 + geom_line(aes(y=pred1,group = id) ,col="red", lwd = 0.5)
Now generate a balanced data set. This version generates 51 evenly spaced points between the min and max - this will be useful if the original data are unevenly spaced. If you have NA values in your x variable, don't forget na.rm=TRUE ...
pframe <- with(dd,expand.grid(id=levels(id),x=seq(min(x),max(x),length.out=51)
Make predictions, and overlay them on the original plot:
pframe$pred1 <- predict(m1,newdata=pframe,re.form=NA)
p11 + geom_line(data=pframe,aes(y=pred1,group = id) ,col="red", lwd = 0.5)