Solved – Investigating covariates in mixed effect model

mixed modelpanel datarregression

Having read through a few posts, I still couldn't find an answer to my question.

I'm trying to investigate for the effect of covariate C on a longitudinal dataset. I have two linear mixed effect models given below:

A.lme <- lme( A ~ B + C, data = data1, random = ~ 1 | id)

B.lme <- lme( A ~ B*C, data = data1, random = ~ 1 | id)

I just want to be sure that I'm interpreting these two the right way. I believe in order to investigate for covariate C, I should be analysing B.lme.

B represents time whilst A represents immune cells in the body whilst C represents a viral infection status.

The summary and anova for B.lme suggests that C has no significant effect on both intercept and slope as given below:

>summary(B.lme)
Linear mixed-effects model fit by REML
Data: data1 
   AIC      BIC    logLik
4238.806 4270.106 -2113.403

Random effects:
Formula: ~1 | id
         (Intercept)  Residual
StdDev:   0.9242001 0.9692625

Fixed effects: A ~ C + B + C:B 
              Value     Std.Error   DF   t-value p-value
(Intercept)  -3.0675750 0.6212136 1118 -4.938036  0.0000
C             0.7364624 0.6264595  244  1.175595  0.2409
B             0.2200117 0.1988966 1118  1.106161  0.2689
C:B           0.0131436 0.2000672 1118  0.065696  0.9476
Correlation: 
             (Intr)    C       B   
C            -0.992              
B            -0.849  0.842       
C:B           0.844 -0.844 -0.994

Standardized Within-Group Residuals:
    Min          Q1         Med          Q3         Max 
-8.51192452 -0.38169972  0.05365992  0.47695927  7.43457534 

Number of Observations: 1366
Number of Groups: 246 
anova(B.lme)
              numDF denDF  F-value p-value
(Intercept)     1  1118 811.5700  <.0001
C               1   244   3.7171  0.0550
B               1  1118 117.6260  <.0001
B:C             1  1118   0.0043  0.9476

When I had a closer look at A.lme, the summary/anova suggests that variable C is significant.

>summary(A.lme)
Linear mixed-effects model fit by REML
Data: data1 
   AIC      BIC    logLik
4235.429 4261.517 -2112.715

Random effects:
Formula: ~1 | id
         (Intercept)  Residual
StdDev:   0.9228998 0.9690801

Fixed effects: A ~ B + C 
             Value      Std.Error  DF   t-value   p-value
(Intercept) -3.1021904 0.3332309  1119  -9.309431 0.0000
B            0.2330059 0.0214786  1119  10.848303 0.0000
C            0.7713974 0.3352298  244   2.301100  0.0222
Correlation: 
          (Intr)   B   
B         -0.171       
C         -0.971  0.034

Standardized Within-Group Residuals:
    Min          Q1         Med          Q3         Max 
-8.51328019 -0.38179254  0.05385169  0.47724088  7.43658227 

Number of Observations: 1366
Number of Groups: 246 

anova(A.lme)
              numDF denDF F-value p-value
(Intercept)     1  1119 813.4873   <.0001
B               1  1119 116.1162   <.0001
C               1   244   5.2951   0.0222

My question is which of the two models is more suitable for investigating C as a covariate? My second question is how important is the significance of the p-value of C in A.lme-this seems to suggest to me that C has a significant impact on the slope and intercept but not when combined with B (C:B). Can I safely conclude that C is not significant in B.lme? I'm using the nlme package in R.

Any help would be highly appreciated.

Best Answer

Your model B.lme shows that $C$ is not a significant predictor of the slope--this is what the interaction $B \cdot C$ tells you. In other words, the effect of $B$ on the dependent variable is constant across the values of $C$, or conversely, the effect of $C$ on the dependent variable is constant across the values of $B$. Because $B$ and $C$ are involved in an interaction in B.lme, the "main effects" are actually not main effects, but merely the effect of the variable when the other variable is 0. For example, $0.736$ in B.lme is the effect of $C$ on the dependent variable when $B=0$.

For this reason, having determined that $C$ is not a significant predictor of the slope, it's a good idea to remove the non-significant interaction so that the effects are truly interpretable as main effects. The model A.lme shows that $C$ is a significant predictor of the dependent variable controlling for (holding constant) $B$, and similarly, that $B$ is a significant predictor of the DV controlling for $C$.

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