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?
By request, I'll describe the task and data a little further. The data come from a computer task in which participants are presented a number of stimuli, either two or three, in various locations about the screen. These stimuli can either be "targets" or "distractors". After these stimuli, a probe stimulus is presented; if it appears in a position where a previous target has appeared, participants should respond "yes"; if it appears in the position of a previous distractor or elsewhere, the correct answer is "no." There are 288 trials of this nature; some have two stimuli and some have three, and some lack distractors entirely. The variables in my model, then, can be elaborated as follows:
Number of Stimuli: 2 or 3 (2 levels)
Trial Type: No Distractor (0) or Distractor (1) (2 levels)
Probe Location: Probe at Target (1), Probe at Distractor (2), or Probe Elsewhere (0) (3 levels)
Distance: Total Cartesian distance between stimuli, divided by number of stimuli per trial (Continuous)
Dx: Participant's clinical categorization
Sub ID: Unique subject identifier (random effect)
Trial: Trial number (1:288) (random effect)
Correct: Response classification, either incorrect (0) or correct (1) per trial
Note that the task design makes it inherently imbalanced, as trials without distractors cannot have Probe Location "Probe at Distractor"; this makes R mad when I try to run RM ANOVAs, and it is another reason I opted for a regression.
Below is a sample of my data (with SubID altered, just in case anyone might get mad):
SubID Dx Correct No_of_Stim Trial_Type Probe_Loc Dist Trial 1 99999999 PROBAND 1 3 0 1 0.9217487 1 2 99999999 PROBAND 0 3 0 0 1.2808184 2 3 99999999 PROBAND 1 3 0 0 1.0645292 3 4 99999999 PROBAND 1 3 1 2 0.7838786 4 5 99999999 PROBAND 0 3 0 0 1.0968788 5 6 99999999 PROBAND 1 3 1 1 1.3076598 6
Hopefully, with the above variable descriptions these data should be self-explanatory.
Any assistance that people can provide in this matter is very much appreciated.