I am working with data from a computer task which has 288 total trials, each of which can be categorically classified according to Trial Type, Number of Stimuli, and Probe Location. Because I want to also examine a continuous variable, the total Cartesian Distance between stimuli per trial (divided by number of stimuli to control for varying numbers), I have opted to use a mixed linear model with repeated measures. In addition to each of these task variables, I am also interested in whether folks in various diagnostic groups perform differently on the task, as well as whether or not there is a Dx interaction with any of the above variables. Thus (if I'm not mistaken), I have the following effects in my model:

Trial Type, a fixed effect Number of Stimuli, a fixed effect Probe Location, a fixed effect Dist(ance), a fixed effect Dx, a fixed effect Dx*Trial Type, a fixed effect Dx*Number of Stimuli, a fixed effect Dx*Probe Location, a fixed effect Dx*Dist, a fixed effect Trial, a random effect, nested within SubID, a random effect

Based on my examination of documentation, it seems that the nesting of random effects does not seem to be important to lme4, and so I specify my model as follows:

tab.lmer <- lmer(Correct ~ Dx+No_of_Stim+Trial_Type+Probe_Loc+Dist+Dx*No_of_Stim+Dx*Trial_Type+Dx*Probe_Loc+Dx*Dist+(1|Trial)+(1|SubID),data=bigdf)

This would be my first question: 1) Is the above model specification correct?

Assuming so, I am a bit troubled by my results, but as I read and recall my instruction on such models, I am wondering if interpretation of particular coefficients is bad practice in this case:

Linear mixed model fit by REML ['merModLmerTest']
Formula: Correct ~ Dx + No_of_Stim + Trial_Type + Probe_Loc + Dist + Dx *  
    No_of_Stim + Dx * Trial_Type + Dx * Probe_Loc + Dx * Dist +  
    (1 | Trial) + (1 | SubID)
   Data: bigdf

REML criterion at convergence: 13600.4

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.89810 -0.03306  0.27004  0.55363  2.81656 

Random effects:
 Groups   Name        Variance Std.Dev.
 Trial    (Intercept) 0.013256 0.11513 
 SubID    (Intercept) 0.006299 0.07937 
 Residual             0.131522 0.36266 
Number of obs: 15840, groups:  Trial, 288; SubID, 55

Fixed effects:
                         Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)             4.196e-01  4.229e-02  4.570e+02   9.922  < 2e-16 ***
DxPROBAND               8.662e-02  4.330e-02  2.920e+02   2.000  0.04640 *  
DxRELATIVE              9.917e-02  4.009e-02  2.920e+02   2.474  0.01394 *  
No_of_Stim3            -9.281e-02  1.999e-02  4.520e+02  -4.642 4.53e-06 ***
Trial_Type1             3.656e-02  2.020e-02  4.520e+02   1.810  0.07097 .  
Probe_Loc1              3.502e-01  2.266e-02  4.520e+02  15.456  < 2e-16 ***
Probe_Loc2              3.535e-01  3.110e-02  4.520e+02  11.369  < 2e-16 ***
Dist                    1.817e-01  2.794e-02  4.520e+02   6.505 2.06e-10 ***
DxPROBAND:No_of_Stim3  -1.744e-02  1.759e-02  1.548e+04  -0.992  0.32144    
DxRELATIVE:No_of_Stim3 -2.886e-02  1.628e-02  1.548e+04  -1.773  0.07628 .  
DxPROBAND:Trial_Type1  -9.250e-03  1.777e-02  1.548e+04  -0.521  0.60267    
DxRELATIVE:Trial_Type1  1.336e-02  1.645e-02  1.548e+04   0.812  0.41682    
DxPROBAND:Probe_Loc1   -8.696e-02  1.993e-02  1.548e+04  -4.363 1.29e-05 ***
DxRELATIVE:Probe_Loc1  -4.287e-02  1.845e-02  1.548e+04  -2.323  0.02018 *  
DxPROBAND:Probe_Loc2   -1.389e-01  2.735e-02  1.548e+04  -5.079 3.83e-07 ***
DxRELATIVE:Probe_Loc2  -8.036e-02  2.532e-02  1.548e+04  -3.173  0.00151 ** 
DxPROBAND:Dist         -3.920e-02  2.457e-02  1.548e+04  -1.595  0.11066    
DxRELATIVE:Dist        -1.485e-02  2.275e-02  1.548e+04  -0.653  0.51390    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

In general, these results make sense to me. The troubling portion, however, comes in the positive, significant (yes, I am using LmerTest) p-value for DxProband, particularly in light of the fact that in terms of performance means, Probands are performing worse than Controls. So, this mismatch concerns me. Examining the corresponding ANOVA:

> anova(tab.lmer)
Analysis of Variance Table of type 3  with  Satterthwaite 
approximation for degrees of freedom
               Sum Sq Mean Sq NumDF   DenDF F.value    Pr(>F)    
Dx             0.8615  0.4308     2   159.0   1.412   0.24662    
No_of_Stim     0.6984  0.6984     1   283.5  37.043 3.741e-09 ***
Trial_Type     8.3413  8.3413     1   283.5   4.456   0.03565 *  
Probe_Loc     25.7223 12.8612     2   283.5 116.405 < 2.2e-16 ***
Dist           5.8596  5.8596     1   283.5  43.399 2.166e-10 ***
Dx:No_of_Stim  1.4103  0.7051     2 15483.7   1.590   0.20395    
Dx:Trial_Type  2.0323  1.0162     2 15483.7   0.841   0.43128    
Dx:Probe_Loc   3.5740  0.8935     4 15483.7   7.299 7.224e-06 ***
Dx:Dist        0.3360  0.1680     2 15483.7   1.277   0.27885    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

...the results seem to more or less line up with the regression, with the exception of the Dx variable. So, my second question is 2) Can anyone clarify what is going on with the Dx variable? Is interpreting individual coefficients from the regression model bad practice in this case?

Finally, as a basic (and somewhat embarrassing) afterthought, 3) If I attempt to reduce the model, I should favor the model with the lower REML, yes?

In summation, 1) Is the above model specification correct? 2) Can anyone clarify what is going on with the Dx variable? Is interpreting individual coefficients from the regression model bad practice in this case? 3) If I attempt to reduce the model, I should favor the model with the lower REML, yes?

Any assistance that people can provide in this matter is very much appreciated.

Sincerely, peteralynn