How to correctly specify random part of linear mixed model when testing the relationships between dependent variables

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will74lsn
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Joined: Wed Apr 24, 2013 11:57 am

How to correctly specify random part of linear mixed model when testing the relationships between dependent variables

Postby will74lsn » Tue Nov 08, 2016 5:34 pm

The study is about how people look at affective pictures and how their eye gaze behavior relates to their self-reported feelings.
205 participants tested in individual sessions watched 14 series of pictures expected to induce different emotional reactions. Each series consisted of the same 6 thematically similar pictures. So, for instance 6 pictures showing pleasant landscapes formed the series “Pleasant landscapes” and 6 pictures showing violent acts formed the series “Violence”. The same picture was shown only once (no repetition of the same picture) and could be shown as first, second, etc. within its series.
After each series participants reported how they felt while watching the series by filling in 2 scales ranging from 1 to 9: valence (pleasantness) and arousal. Importantly, they gave only 1 valence and 1 arousal rating per series and did not rate each picture.
During the series presentation, eye gaze behavior was recorded with an eye tracker. Several outcome variables can be defined, but my focus is on fixation frequency. Importantly, and contrary to valence and arousal, for fixation number, there is a value for each picture (max. 84 values per subjects). Because of quality criteria and recording problems, the majority of participants do not have all 84 values for fixation number. On the contrary for valence and arousal ratings there are very few missing values.
Furthermore, each picture has certain “physical” properties such as luminosity (i.e., each picture has a “luminosity value”) that should be taken into account.
Main research questions:
Is there a significant relationship between self-reported valence and self-reported arousal on the one side and fixation frequency on the other side, when taking also into account the physical properties of the pictures as well as their position within each series? Moreover, do men and women differ in their fixation frequency? In a further step I would like to test interactions (but this is not essential here to define the model in terms of random part).
So the “basic” model would be something like this:
Fixation frequency = valence ratings + arousal ratings + sex + luminosity + picturePosition
Predicted effects: 1) Arousal is a significant predictor of Fixation frequency: Fixation frequency increases with increasing arousal. 2) Fixation frequency decreases with increasing picture position (e.g., fixation frequency is higher when the same picture is shown first than last within a series); 4) there are no effects of valence ratings, luminosity, and sex.
I have tried different model specifications with all predictors and subsets of the predictors to see how results may differ. The critical question is about the random part.
1) Random intercept for ID and random intercept for Pictures given that ID and Pictures (called Stimulus) are random factors. This seems to work fine if I only include sex and Luminosity:

MIXED FixationFrequency_left_w1st BY Sex WITH Luminosity
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0,
ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED= Sex Luminosity| SSTYPE(3)
/METHOD=REML
/PRINT=G R SOLUTION TESTCOV
/RANDOM=INTERCEPT | SUBJECT(ID) COVTYPE(VC)
/RANDOM=INTERCEPT | SUBJECT(Stimulus) COVTYPE(VC).

Type III Tests of Fixed Effects
Source Numerator df Denominator df F Sig.
Intercept 1 104.052 1024.377 .000
sex 1 204.000 2.839 .094
Luminosity 1 82.000 1.000 .320

2) Same random part; I also include valence ratings, arousal ratings, and Picture Position The denominator df for arousal ratings, and Picture Position are very high (close to number of subjects 205 x number of pictures 84); valence ratings has a much lower denominator (I wonder why arousal and valence would have so different dfs). The p values of valence and PicturePosition are ridiculously low (<. 00000000001) which is not plausible at all; these effects are clearly overestimated.

MIXED FixationFrequency_left_w1st BY Sex PicturePosition WITH valence_demeaned arousal_demeaned Luminosity
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0,
ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED= Sex valence_demeaned arousal_demeaned Luminosity PicturePosition| SSTYPE(3)
/METHOD=REML
/PRINT=G R SOLUTION TESTCOV
/RANDOM=INTERCEPT | SUBJECT(ID) COVTYPE(VC)
/RANDOM=INTERCEPT | SUBJECT(Stimulus) COVTYPE(VC).

Type III Tests of Fixed Effects
Source Numerator df Denominator df F Sig.
Intercept 1 95.843 859.965 .000
sex 1 203.976 3.059 .082
valence_demeaned 1 6239.098 49.649 .000
arousal_demeaned 1 16959.881 1.497 .221
Luminosity 1 78.529 .701 .405
PicturePosition 5 16987.278 28.404 .000

3) I tried another specification of the random part: random intercept for ID with SeriesNumber nested within ID. This seems to give something reasonable if I enter only sex, valence ratings and arousal ratings. The denominator df of valence and arousal are similar to each other and close to the number of subjects (205) multiplied by the number of series (14). The ps are reasonable with the expected significant arousal effect, whereas valence is not significant. This is very different from the results of model 2.

MIXED FixationFrequency_left_w1st BY Sex WITH valence_demeaned arousal_demeaned
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0,
ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED= Sex valence_demeaned arousal_demeaned | SSTYPE(3)
/METHOD=REML
/PRINT=G R SOLUTION TESTCOV
/RANDOM=INTERCEPT | SUBJECT(ID) COVTYPE(VC)
/RANDOM=INTERCEPT | SUBJECT(ID*SeriesNumber) COVTYPE(VC).

Type III Tests of Fixed Effects
Source Numerator df Denominator df F Sig.
Intercept 1 203.943 8271.620 .000
sex 1 203.944 2.928 .089
valence_demeaned 1 2690.274 2.375 .123
arousal_demeaned 1 2734.198 5.062 .025

4) The same as above but I also include Luminosity and PicturePosition. The Denominator dfs for Luminosity and PicturePosition are very high and the ps are extremely low (p < .000000001), which again is not plausible. With model 1, Luminosity had 82 df and p = .320.

MIXED FixationFrequency_left_w1st BY Sex PicturePosition WITH valence_demeaned arousal_demeaned Luminosity
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0,
ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED= Sex valence_demeaned arousal_demeaned Luminosity PicturePosition | SSTYPE(3)
/METHOD=REML
/PRINT=G R SOLUTION TESTCOV
/RANDOM=INTERCEPT | SUBJECT(ID) COVTYPE(VC)
/RANDOM=INTERCEPT | SUBJECT(ID*SeriesNumber) COVTYPE(VC).

Type III Tests of Fixed Effects
Source Numerator df Denominator df F Sig.
Intercept 1 327.678 6974.165 .000
sex 1 203.943 2.927 .089
valence_demeaned 1 2690.263 2.508 .113
arousal_demeaned 1 2735.551 5.520 .019
Luminosity 1 14786.270 35.844 .000
PicturePosition 5 14398.710 31.485 .000

any ideas on how to specify the random part correctly with all fixed effects?
Thank you

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