Hi Ian, hi Ben,


first of all many thanks for your answers. I tested your proposals and I
will report you the results in a moment. But first let me say that I used
the dataset linked above, in which we have:


DV = Recall

IV1 = Gender (between-factor)

IV2 = Dosage (between-factor)

IV3 = Valence (within-factor)

IV4 = Task (within-factor)


The ANOVA fitted with the aov function is the following:


> aovRecall<-
aov(Recall~(Gender*Dosage*Valence*Task)+Error(Subject/(Valence*Task)))

> summary(aovRecall)


Error: Subject

              Df Sum Sq Mean Sq F value Pr(>F)

Gender         1  542.3   542.3   5.685 0.0345 *

Dosage         2  694.9   347.5   3.643 0.0580 .

Gender:Dosage  2   70.8    35.4   0.371 0.6976

Residuals     12 1144.6    95.4

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Error: Subject:Valence

                      Df Sum Sq Mean Sq F value Pr(>F)

Valence                2  14.69   7.343   2.998 0.0688 .

Gender:Valence         2   3.91   1.954   0.798 0.4619

Dosage:Valence         4  20.26   5.065   2.068 0.1166

Gender:Dosage:Valence  4   1.04   0.259   0.106 0.9793

Residuals             24  58.78   2.449

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Error: Subject:Task

                   Df Sum Sq Mean Sq F value   Pr(>F)

Task                1  96.33   96.33  39.862 3.87e-05 ***

Gender:Task         1   1.33    1.33   0.552    0.472

Dosage:Task         2   8.17    4.08   1.690    0.226

Gender:Dosage:Task  2   3.17    1.58   0.655    0.537

Residuals          12  29.00    2.42

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Error: Subject:Valence:Task

                           Df Sum Sq Mean Sq F value Pr(>F)

Valence:Task                2   5.39  2.6944   1.320  0.286

Gender:Valence:Task         2   2.17  1.0833   0.531  0.595

Dosage:Valence:Task         4   2.78  0.6944   0.340  0.848

Gender:Dosage:Valence:Task  4   2.67  0.6667   0.327  0.857

Residuals                  24  49.00  2.0417


Then I tried with your proposals:


> testIan


Linear mixed model fit by REML

Formula: Recall ~ (Gender * Dosage * Valence * Task) + (1 | Subject)

 AIC   BIC logLik deviance REMLdev

 424 525.9   -174    418.9     348

Random effects:

 Groups   Name        Variance Std.Dev.

 Subject  (Intercept) 15.5167  3.9391

 Residual              2.2796  1.5098

Number of obs: 108, groups: Subject, 18


Fixed effects:

                                   Estimate Std. Error t value

(Intercept)                       1.733e+01  2.435e+00   7.117

GenderM                          -4.667e+00  3.444e+00  -1.355

DosageB                           1.324e-12  3.444e+00   0.000

DosageC                           3.333e+00  3.444e+00   0.968

ValenceNeu                        2.330e-13  1.233e+00   0.000

ValencePos                       -3.333e-01  1.233e+00  -0.270

TaskF                            -1.333e+00  1.233e+00  -1.082

GenderM:DosageB                  -2.667e+00  4.871e+00  -0.547

GenderM:DosageC                   2.000e+00  4.871e+00   0.411

GenderM:ValenceNeu               -2.225e-13  1.743e+00   0.000

GenderM:ValencePos                3.333e-01  1.743e+00   0.191

DosageB:ValenceNeu                6.667e-01  1.743e+00   0.382

DosageC:ValenceNeu                1.000e+00  1.743e+00   0.574

DosageB:ValencePos                2.667e+00  1.743e+00   1.530

DosageC:ValencePos                1.000e+00  1.743e+00   0.574

GenderM:TaskF                    -3.333e-01  1.743e+00  -0.191

DosageB:TaskF                    -1.000e+00  1.743e+00  -0.574

DosageC:TaskF                     3.333e-01  1.743e+00   0.191

ValenceNeu:TaskF                 -6.667e-01  1.743e+00  -0.382

ValencePos:TaskF                  6.667e-01  1.743e+00   0.382

GenderM:DosageB:ValenceNeu        1.000e+00  2.466e+00   0.406

GenderM:DosageC:ValenceNeu        2.372e-13  2.466e+00   0.000

GenderM:DosageB:ValencePos       -3.333e-01  2.466e+00  -0.135

GenderM:DosageC:ValencePos        2.340e-13  2.466e+00   0.000

GenderM:DosageB:TaskF             1.000e+00  2.466e+00   0.406

GenderM:DosageC:TaskF             6.667e-01  2.466e+00   0.270

GenderM:ValenceNeu:TaskF          1.333e+00  2.466e+00   0.541

GenderM:ValencePos:TaskF         -1.333e+00  2.466e+00  -0.541

DosageB:ValenceNeu:TaskF         -1.333e+00  2.466e+00  -0.541

DosageC:ValenceNeu:TaskF         -1.333e+00  2.466e+00  -0.541

DosageB:ValencePos:TaskF         -1.667e+00  2.466e+00  -0.676

DosageC:ValencePos:TaskF         -6.667e-01  2.466e+00  -0.270

GenderM:DosageB:ValenceNeu:TaskF -6.667e-01  3.487e+00  -0.191

GenderM:DosageC:ValenceNeu:TaskF -3.333e-01  3.487e+00  -0.096

GenderM:DosageB:ValencePos:TaskF  2.667e+00  3.487e+00   0.765

GenderM:DosageC:ValencePos:TaskF  3.333e-01  3.487e+00   0.096


> testBen


Linear mixed model fit by REML

Formula: Recall ~ (Gender * Dosage * Valence * Task) + (Valence * Task |
  Subject)

   AIC   BIC logLik deviance REMLdev

 413.5 569.1 -148.8    343.2   297.5

Random effects:

 Groups   Name             Variance Std.Dev. Corr

 Subject  (Intercept)      29.38096 5.4204

          ValenceNeu        6.92965 2.6324   -0.710

          ValencePos       10.70611 3.2720   -0.729  0.915

          TaskF             5.92752 2.4347   -0.820  0.857  0.759

          ValenceNeu:TaskF  3.63960 1.9078    0.832 -0.932 -0.778 -0.930

          ValencePos:TaskF 13.78699 3.7131    0.785 -0.951 -0.950 -0.809

 Residual                   0.17464 0.4179













  0.879



Number of obs: 108, groups: Subject, 18


Fixed effects:

                                   Estimate Std. Error t value

(Intercept)                       1.733e+01  3.139e+00   5.522

GenderM                          -4.667e+00  4.439e+00  -1.051

DosageB                           1.562e-11  4.439e+00   0.000

DosageC                           3.333e+00  4.439e+00   0.751

ValenceNeu                        5.690e-12  1.558e+00   0.000

ValencePos                       -3.333e-01  1.920e+00  -0.174

TaskF                            -1.333e+00  1.446e+00  -0.922

GenderM:DosageB                  -2.667e+00  6.278e+00  -0.425

GenderM:DosageC                   2.000e+00  6.278e+00   0.319

GenderM:ValenceNeu               -5.003e-12  2.203e+00   0.000

GenderM:ValencePos                3.333e-01  2.715e+00   0.123

DosageB:ValenceNeu                6.667e-01  2.203e+00   0.303

DosageC:ValenceNeu                1.000e+00  2.203e+00   0.454

DosageB:ValencePos                2.667e+00  2.715e+00   0.982

DosageC:ValencePos                1.000e+00  2.715e+00   0.368

GenderM:TaskF                    -3.333e-01  2.046e+00  -0.163

DosageB:TaskF                    -1.000e+00  2.046e+00  -0.489

DosageC:TaskF                     3.333e-01  2.046e+00   0.163

ValenceNeu:TaskF                 -6.667e-01  1.203e+00  -0.554

ValencePos:TaskF                  6.667e-01  2.197e+00   0.303

GenderM:DosageB:ValenceNeu        1.000e+00  3.115e+00   0.321

GenderM:DosageC:ValenceNeu        5.803e-12  3.115e+00   0.000

GenderM:DosageB:ValencePos       -3.333e-01  3.839e+00  -0.087

GenderM:DosageC:ValencePos        6.274e-12  3.839e+00   0.000

GenderM:DosageB:TaskF             1.000e+00  2.893e+00   0.346

GenderM:DosageC:TaskF             6.667e-01  2.893e+00   0.230

GenderM:ValenceNeu:TaskF          1.333e+00  1.701e+00   0.784

GenderM:ValencePos:TaskF         -1.333e+00  3.108e+00  -0.429

DosageB:ValenceNeu:TaskF         -1.333e+00  1.701e+00  -0.784

DosageC:ValenceNeu:TaskF         -1.333e+00  1.701e+00  -0.784

DosageB:ValencePos:TaskF         -1.667e+00  3.108e+00  -0.536

DosageC:ValencePos:TaskF         -6.667e-01  3.108e+00  -0.215

GenderM:DosageB:ValenceNeu:TaskF -6.667e-01  2.405e+00  -0.277

GenderM:DosageC:ValenceNeu:TaskF -3.333e-01  2.405e+00  -0.139

GenderM:DosageB:ValencePos:TaskF  2.667e+00  4.395e+00   0.607

GenderM:DosageC:ValencePos:TaskF  3.333e-01  4.395e+00   0.076


First of all, I have some difficulties in matching these two models with
the aov one, since these two obtained with lmer function display the
estimates for the levels of each factor, whereas the aov one displays the
estimates for the factors themselves.


Anyway, the main problem is that none of the two lmer models seems to
distinguish from between and within factors. The solutions you suggested me
seems to deal only with the concepts of fixed and random effects. Moreover
the aov function doesn't make this distinction. I'm beginning to think that
lmer can't perform an ANOVA.


I need to think more about this.




On Sun, Mar 24, 2013 at 6:12 PM, ian m s white <i.m.s.white@ed.ac.uk> wrote:

> I reckon lmer can figure out for itself what is between and what is within
> subjects, so
>
> lmer(DV ~ IV1*IV2*IV3*IV4 + (1|Subject))
>
> should fit the same model as your ANOVA.
>
>
> On 24 Mar 2013, at 08:56, Vanni Rovera <vanni.rovera@gmail.com> wrote:
>
> > Hi there,
> >
> > I'm trying to understand how to use the function lmer in order to do a
> > 'between-and-within-factors' ANOVA, but without any success. I know about
> > the usage of the function aov, but this holds only for balanced designs;
> > its documentation say to use lme function (package nlme) for unbalanced
> > designs. Furthermore I found the lmer function (package lme4) is an
> > evolution of lme, so I wish to use this last function in order to perform
> > my ANOVA. But I'm not able to understand how to do this.
> >
> > More precisely, imagine you have a dependent variable DV and four
> > independent variables IV1, IV2, IV3, IV4, where IV1, IV2 are
> > between-factors and IV3, IV4 are within-factors. Moreover you have a
> > variable called Subject in order to identify the subject on which
> > measurements are done (like for example this dataset:
> > http://personality-project.org/r/datasets/R.appendix5.data). If I use
> the
> > aov function, my 'between-and-within-factors' ANOVA would stand as
> follows:
> >
> > aov(DV~(IV1*IV2*IV3*IV4)+Error(Subject/(IV3*IV4))).
> >
> > Now can you write me the precise syntax in order to obtain the same
> result
> > with the lmer function?
> >
> > Thanks a lot in advance!
> > Vanni Rovera
> >
> >
> >
> > *Additional details:* The problem is that no one seems to be interested
> in
> > explain the relations of 'within-factor' and 'between-factor' concepts
> with
> > those of 'fixed-effect' and 'random-effect'. Textbooks and papers about
> > ANOVA talk about between and within factors, while documentations and
> > papers about lmer function talk about mixed-effects models, i.e. they
> talk
> > about fixed and random effects, without mentioning between and within
> > factors. *Thus I am not able to understand the relations between the two,
> > since I think they are completely uncorrelated each others, and hence I
> am
> > not able to use the syntax in lmer in order to distinguish between
> factors
> > from within factors.*
> >
> >       [[alternative HTML version deleted]]
> >
> > _______________________________________________
> > R-sig-mixed-models@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
>
>
> --
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