Styjun

I'm running a lme in nlme and when I try to plot the results (using the code from one of the answered questions here), I'm getting different results than the resulting model coefficients, namely the intercept. Is this plotting the random effects intercept and not the fixed effects intercept?

model<-lme(Y~A+ Group + A*Group, random=~1|Subject, data.in2)

 > summary(model)
 Linear mixed-effects model fit by REML
 Data: data.in2 
 AIC BIC logLik
 3203.191 3227.229 -1595.596

Random effects:
 Formula: ~1 | Subject
 (Intercept) Residual
StdDev: 17.6086 10.03305

Fixed effects: Y ~ A + Group + A * Group 
 Value Std.Error DF t-value p-value
(Intercept) 42.36244 7.122246 360 5.947905 0.0000
A -1.05472 0.144155 360 -7.316565 0.0000
Group1 -7.49777 12.920964 46 -0.580279 0.5646
A:Group1 0.00180 0.291035 360 0.006195 0.9951
 Correlation: 
 (Intr) A Group1
A -0.902 
Group1 -0.551 0.497 
A:Group1 0.447 -0.495 -0.888

Standardized Within-Group Residuals:
 Min Q1 Med Q3 Max 
-2.99649773 -0.50936511 -0.01409361 0.55007319 4.11784199 

Number of Observations: 410
Number of Groups: 48

And the graph code is:

newdata<-expand.grid(Group=unique(data.in2$Group), A=c(min(data.in2$A), max(data.in2$A)))

[![ggplot(data.in2, aes(x=A, y=Y, colour=Group)) + geom_point(size=1) +
 geom_line(aes(y=predict(model), group=Subject, size="Subjects"))+
 geom_line(data=newdata, aes(y=predict(model, level=0, newdata=newdata), size="Population")) +
 scale_size_manual(name="Predictions", values=c("Subjects"=0.5, "Population"=3), guide="none")][2]][2]

I'm also trying to attach the image but I'm not sure how. https://i.stack.imgur.com/rfNwP.png

Your model formula does not match your output notation. The correct model formula for the output you provided is:

model<-lme(Y ~ A + Group + A:Group, random=~1|Subject, data.in2)

which is equivalent with:

model<-lme(Y ~ A*Group, random=~1|Subject, data.in2)

If you tell us more about your A and Group variables, we can comment on the model output you provided.

Addendum:

Not clear from your post what you mean by "getting different intercepts". In your model, the relationship between Y and A for each subject in each group is assumed to be linear (e.g., the value of Y tends to decrease as A increases); the intercept of the straight line capturing that relationship is allowed to be different across subjects within a group but the slope is presumed to be the same across subjects in that group. The slope captures the rate of change in the expected value of Y per 1-unit increase in the value of A for a given subject in a given group.

Because your model includes an intercept between A and Group, there is a further assumption that the slopes of subjects in the first group are different than the slopes of subjects in the second group. The p-value for the interaction between A and Group is quite large, so your data don't seem to support this assumption. This is why, in your plot, you see slopes for subjects in the two groups to be more or less the same.

The 'typical' subject in your first group (Group = 0) has an intercept given by 42.36244 and a slope given by -1.05472. Other subjects in the first group have the same slope but intercepts that vary randomly across the 'typical' intercept value of 42.36244. You can extract the deviations from this 'typical' intercept with the ranef() command. Adding these deviations to the 'typical' intercept in the first group will give you the subject-specific intercepts for the first group subjects.

The 'typical' subject in your second group (Group = 1) has an intercept given by 42.36244 + (-7.49777) a slope given by -1.05472 + (0.00180). Other subjects in the second group have the same slope of -1.05472 + (0.00180) but intercepts that vary randomly across the 'typical' intercept value of 42.36244 + (-7.49777). You can extract the deviations from this 'typical' intercept with the ranef() command - just make sure to match each deviation with the appropriate subject in group 2. Adding these deviations to the 'typical' intercept for the second group will give you the subject-specific intercepts for the second group subjects.

You have enough information in your summary model and the ranef() command to actually build your plot from scratch and see if it matches the plot you showed here.