Within and between factors in regression models in R - r

Question

I'm trying to run a rmANOVA and a corresponding regression model. In the experiment participants were completing a questionnaire which was evaluating how much of a trait X they have (score). Then they were performing a task, in which each participant was exposed to three conditions (COND - nSCM, SCM, SC). Their brain responses were measured (ERP).
This is how it looks like:
> head(df)
code SEX AGE SCORE COND ERP
1 AA1407 male 29 14 nSCM -3.0348373
2 AN0312 male 26 13 nSCM -1.8799240
3 BR1410 male 23 30 nSCM 0.4284033
4 EZ2404 male 23 23 nSCM -0.7615117
5 HA1012 female 27 22 nSCM -2.9301698
6 HS3004 male 30 16 nSCM -0.5468492
Since I am a bit confused about how to use different types of variables in R, maybe someone could also reassure me about the following:
> sapply(df,class)
code SEX AGE SCORE COND ERP
"factor" "factor" "numeric" "numeric" "factor" "numeric"
Based on the experimental design, the ANOVA design has one between-subject IV: SCORE, one within-subject IV: COND and the DV is ERP (right?).
This is the model I used and the summary:
> anERP <- aov(ERP ~ COND*SCORE, data = df)
> summary(anERP)
Df Sum Sq Mean Sq F value Pr(>F)
COND 2 0.21 0.105 0.027 0.9736
SCORE 1 16.87 16.868 4.297 0.0419 *
COND:SCORE 2 0.58 0.289 0.074 0.9291
Residuals 69 270.85 3.925
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
So, IF this is right (please let me know if anything doesn't seem right), I should also find an effect for SCORE when I build a regression model, right? Also, I'm not sure how to interpret this effect, since AQ is an interval variable (scores in range 6-35). I would appreciate a little help here.
Now I'm very confused about how this model should look like for regression. I started with simple lm model with SCORE and COND as fixed effects:
> lmERP <- lm(ERP ~ SCORE*COND, data = df)
> summary(lmERP)
Call:
lm(formula = ERP ~ SCORE * COND, data = df)
Residuals:
Min 1Q Median 3Q Max
-5.2554 -1.0916 0.1975 1.4582 3.3097
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.04269 1.06193 -2.865 0.00552 **
SCORE 0.06458 0.05229 1.235 0.22108
CONDSCM -0.08141 1.50180 -0.054 0.95693
CONDnSCM 0.36646 1.50180 0.244 0.80795
SCORE:CONDSCM 0.01111 0.07396 0.150 0.88104
SCORE:CONDnSCM -0.01707 0.07396 -0.231 0.81814
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.981 on 69 degrees of freedom
Multiple R-squared: 0.0612, Adjusted R-squared: -0.006827
F-statistic: 0.8997 on 5 and 69 DF, p-value: 0.4864
However, here the main effect of SCORE doesn't reach significance. How is it possible? Shouldn't rmANOVA and regression show roughly similar results (or at least the main effects)?
I guess I'm not applying the right linear model here, since it doesn't seem to recognise there are both within and between subject factors in the design.
I have read hundreds of webpages, tutorials and forums and I'm still completely confused about these models. Thank you in advance for any piece of advice!

Answer 1

Repeated-measures or mixed-model designs can be very confusing to specify using R's base aov function. In the code you have written, for example, aov will treat all the specified factors as independent (i.e., between-subject). I highly recommend using a library that makes it easier to specify these types of designs.
The ez library contains ezANOVA, which makes these tests simple to perform, provided that all your cases are complete (all factors are fully crossed, with no missing data). Assuming that your CODE column uniquely identifies each subject and you wanted to include all factors from your data set, the test would look something like this:
my.aov <- ezANOVA(data = df, dv = ERP, wid = CODE, between = .(SEX, AGE, SCORE), within = COND).
It is also possible to implement these designs with the lme4 package (in fact, ezANOVA is a wrapper around lme4's functions). While lme4 allows for more flexible model specifications and can tolerate incomplete data, its syntax is more difficult. Bodo Winter's tutorial on lme4 is a good start, if you want to go really deep.
As an aside, there is usually little point in performing both an ANOVA and a linear regression. Unless the two tests are specified in a way that treats the factors differently, the results will be equivalent.