Design:
I am interested in assessing how the emotional intensity recorded in videos, changes over time (during the video), depending on the type of video (A vs. B).
I have a total of 203 videos.
The dependent variable is emotional intensity, for which I have 5 measurements, taken at regular intervals.
My specific hypothesis is that the emotion intensity will increase from the beginning of the video until about the middle of it, and then decrease. In other words, a quadratic trend. However, I expect this trend to be more pronounced in one type of video than in the other. Thus, the basic syntax is using PROC GLM would be:
proc glm data=wide;
class type;
model intensity1-intensity5= genre;
repeated intervals 5 (1 2 3 4 5) polynomial/summary printm;
means type;
However, I am asked to test the hypothesis treating the variable INTERVALS as a continuous predictor. I have re-organized the data in the long format.
DATA and syntax are attached.
The basic proc mixed model would thus be:
MODEL 1
proc mixed data=datalong;
class id type ;
model intensity= type | intervals | intervals ;
I have received two types of suggestions to add a REPEATED or a RANDOM factor.
MODEL 2
proc mixed data=datalong;
class id type ;
model intensity= type | intervals | intervals ;
REPEATED / TYPE = vc SUB = id;
MODEL 3
proc mixed data=datalong;
class id type ;
model intensity= type | intervals | intervals ;
RANDOM / TYPE = vc SUB = id;
MODEL 1, 2 and 3, however, produce virtually identical results.
Thoughts?
DATA DATALONG;
INPUT ID$ TYPE$ INTERVALS INTENSITY;
CARDS;
1 A -1.413516734 -0.649020828
1 A -0.706758367 -1.22358075
1 A 0 1.352921145
1 A 0.706758367 0.500871969
1 A 1.413516734 0.018808464
2 A -1.413516734 -1.266169712
2 A -0.706758367 0.971700973
2 A 0 -0.112375142
2 A 0.706758367 1.027200532
2 A 1.413516734 -0.620356651
3 A -1.413516734 -1.560937174
3 A -0.706758367 1.031723315
3 A 0 0.663046994
3 A 0.706758367 0.091883888
3 A 1.413516734 -0.225717022
4 B -1.413516734 -1.319423504
4 B -0.706758367 1.140810514
4 B 0 0.059537663
4 B 0.706758367 -0.628589792
4 B 1.413516734 0.747665118
5 B -1.413516734 1.137849518
5 B -0.706758367 -0.669917033
5 B 0 0.050520402
5 B 0.706758367 0.770229877
5 B 1.413516734 -1.288682765
6 A -1.413516734 0.461239549
6 A -0.706758367 0.634366686
6 A 0 0.962105976
6 A 0.706758367 -0.61527461
6 A 1.413516734 -1.442437601
7 B -1.413516734 -1.572540346
7 B -0.706758367 0.774956933
7 B 0 0.216181258
7 B 0.706758367 -0.305457477
7 B 1.413516734 0.886859632
8 A -1.413516734 0.740387309
8 A -0.706758367 -0.896557429
8 A 0 -0.546936403
8 A 0.706758367 -0.673554681
8 A 1.413516734 1.376661204
9 B -1.413516734 -0.145695931
9 B -0.706758367 0.975464197
9 B 0 -1.519329145
9 B 0.706758367 0.835256811
9 B 1.413516734 -0.145695931
10 A -1.413516734 -1.021781313
10 A -0.706758367 -0.905008882
10 A 0 -0.086925578
10 A 0.706758367 0.781203054
10 A 1.413516734 1.232512719
11 B -1.413516734 1.242033793
11 B -0.706758367 -0.875904541
11 B 0 -1.160073879
11 B 0.706758367 0.51779833
11 B 1.413516734 0.276146298
12 A -1.413516734 -0.768500659
12 A -0.706758367 -0.884066505
12 A 0 0.356861469
12 A 0.706758367 1.559186052
12 A 1.413516734 -0.263480356
13 B -1.413516734 -0.89982493
13 B -0.706758367 -0.923825546
13 B 0 0.799374645
13 B 0.706758367 1.278065831
13 B 1.413516734 -0.25379
14 B -1.413516734 -1.776132654
14 B -0.706758367 0.408899645
14 B 0 0.501799066
14 B 0.706758367 0.593750534
14 B 1.413516734 0.271683409
15 A -1.413516734 1.539220225
15 A -0.706758367 -0.458170414
15 A 0 -0.964716892
15 A 0.706758367 -0.549814512
15 A 1.413516734 0.433481594
16 B -1.413516734 0.321052768
16 B -0.706758367 -0.642683252
16 B 0 1.43604545
16 B 0.706758367 0.075523291
16 B 1.413516734 -1.189938257
17 A -1.413516734 -1.134751647
17 A -0.706758367 -0.485262609
17 A 0 -0.246074762
17 A 0.706758367 1.514061721
17 A 1.413516734 0.352027297
18 B -1.413516734 -1.409270477
18 B -0.706758367 -0.680288709
18 B 0 0.947605593
18 B 0.706758367 0.546700973
18 B 1.413516734 0.59525262
19 B -1.413516734 -0.091435218
19 B -0.706758367 0.166472909
19 B 0 1.54723158
19 B 0.706758367 -0.454678455
19 B 1.413516734 -1.167590816
20 B -1.413516734 0.266057064
20 B -0.706758367 0.836500601
20 B 0 -0.113988761
20 B 0.706758367 0.673588124
20 B 1.413516734 -1.662157028
21 B -1.413516734 -1.337532168
21 B -0.706758367 -0.385549218
21 B 0 1.247270846
21 B 0.706758367 -0.205646928
21 B 1.413516734 0.681457467
22 B -1.413516734 -0.822686691
22 B -0.706758367 -1.292686346
22 B 0 0.381949087
22 B 0.706758367 0.822642622
22 B 1.413516734 0.910781329
23 A -1.413516734 -1.657960629
23 A -0.706758367 0.024777839
23 A 0 0.298950016
23 A 0.706758367 1.035282758
23 A 1.413516734 0.298950016
24 B -1.413516734 -0.247658323
24 B -0.706758367 -1.614057502
24 B 0 0.752020732
24 B 0.706758367 0.278951774
24 B 1.413516734 0.830743319
25 A -1.413516734 -0.241190546
25 A -0.706758367 -0.102269521
25 A 0 -1.445799746
25 A 0.706758367 1.241260705
25 A 1.413516734 0.547999108
26 A -1.413516734 -1.122265459
26 A -0.706758367 -0.675375759
26 A 0 -0.228242522
26 A 0.706758367 0.712782984
26 A 1.413516734 1.313100756
27 B -1.413516734 -0.8079403
27 B -0.706758367 1.490871229
27 B 0 0.57571436
27 B 0.706758367 -0.607024172
27 B 1.413516734 -0.651621116
28 A -1.413516734 -0.674973988
28 A -0.706758367 -0.085728935
28 A 0 0.977400336
28 A 0.706758367 1.02263988
28 A 1.413516734 -1.239337293
29 B -1.413516734 -1.191021761
29 B -0.706758367 0.51427148
29 B 0 1.340589345
29 B 0.706758367 -0.71887629
29 B 1.413516734 0.055037226
30 B -1.413516734 0.347520833
30 B -0.706758367 0.60946281
30 B 0 0.347520833
30 B 0.706758367 0.473835606
30 B 1.413516734 -1.778340081
31 A -1.413516734 -1.044811468
31 A -0.706758367 -0.487717758
31 A 0 -0.119174727
31 A 0.706758367 1.629666257
31 A 1.413516734 0.022037697
32 B -1.413516734 0.377497667
32 B -0.706758367 1.199257881
32 B 0 0.444011551
32 B 0.706758367 -1.310700011
32 B 1.413516734 -0.710067088
33 B -1.413516734 -1.651339211
33 B -0.706758367 0.597787457
33 B 0 -0.127175749
33 B 0.706758367 0.27216839
33 B 1.413516734 0.908559113
34 B -1.413516734 0.061473535
34 B -0.706758367 1.67256508
34 B 0 -0.236801918
34 B 0.706758367 -0.644184056
34 B 1.413516734 -0.853052642
35 B -1.413516734 -1.354204425
35 B -0.706758367 -0.017152506
35 B 0 0.093354624
35 B 0.706758367 1.45768184
35 B 1.413516734 -0.179679532
36 B -1.413516734 -0.99842569
36 B -0.706758367 -1.180087379
36 B 0 0.693005702
36 B 0.706758367 0.626743021
36 B 1.413516734 0.858764347
37 B -1.413516734 0.048336135
37 B -0.706758367 1.497872157
37 B 0 0.134924676
37 B 0.706758367 -0.438861416
37 B 1.413516734 -1.242271552
38 B -1.413516734 0.035400547
38 B -0.706758367 0.974537095
38 B 0 0.935280584
38 B 0.706758367 -0.596884807
38 B 1.413516734 -1.348333419
39 B -1.413516734 0.087620348
39 B -0.706758367 -0.483005168
39 B 0 1.30593249
39 B 0.706758367 0.449994216
39 B 1.413516734 -1.360541885
40 A -1.413516734 -0.784073
40 A -0.706758367 -1.223691138
40 A 0 0.730061411
40 A 0.706758367 0.119930495
40 A 1.413516734 1.157772232
41 B -1.413516734 -0.350360014
41 B -0.706758367 -1.027540304
41 B 0 1.331151055
41 B 0.706758367 0.747374944
41 B 1.413516734 -0.700625681
42 B -1.413516734 -0.951051299
42 B -0.706758367 1.390401503
42 B 0 -0.786447167
42 B 0.706758367 0.66525357
42 B 1.413516734 -0.318156607
43 B -1.413516734 0.557778933
43 B -0.706758367 -0.619332194
43 B 0 1.413445252
43 B 0.706758367 -0.232281236
43 B 1.413516734 -1.119610755
44 B -1.413516734 -1.644533236
44 B -0.706758367 -0.119318781
44 B 0 0.409288717
44 B 0.706758367 0.990598856
44 B 1.413516734 0.363964445
45 A -1.413516734 1.047673592
45 A -0.706758367 0.822666805
45 A 0 0.181876683
45 A 0.706758367 -1.234342509
45 A 1.413516734 -0.817874571
46 B -1.413516734 -0.11204195
46 B -0.706758367 -0.238523675
46 B 0 -1.449058065
46 B 0.706758367 1.224974164
46 B 1.413516734 0.574649526
47 B -1.413516734 0.767099888
47 B -0.706758367 1.036673856
47 B 0 -0.186993031
47 B 0.706758367 -0.103085902
47 B 1.413516734 -1.513694811
48 A -1.413516734 1.344705303
48 A -0.706758367 -0.423005157
48 A 0 -0.717508256
48 A 0.706758367 -0.961505342
48 A 1.413516734 0.757313452
49 A -1.413516734 -1.704177562
49 A -0.706758367 0.792346949
49 A 0 0.311266676
49 A 0.706758367 0.60910205
49 A 1.413516734 -0.008538114
50 A -1.413516734 -0.434706336
50 A -0.706758367 0.987221013
50 A 0 0.763697404
50 A 0.706758367 0.174655698
50 A 1.413516734 -1.490867779
51 A -1.413516734 -0.764773019
51 A -0.706758367 0.353237072
51 A 0 1.180736729
51 A 0.706758367 -1.279131457
51 A 1.413516734 0.509930675
52 A -1.413516734 -0.390557847
52 A -0.706758367 -0.983770116
52 A 0 -0.347732362
52 A 0.706758367 0.062282001
52 A 1.413516734 1.659778324
53 A -1.413516734 -1.086147455
53 A -0.706758367 1.241344627
53 A 0 -0.848976012
53 A 0.706758367 -0.051809974
53 A 1.413516734 0.745588814
54 B -1.413516734 -0.407976115
54 B -0.706758367 0.540762297
54 B 0 1.252515365
54 B 0.706758367 0.018969455
54 B 1.413516734 -1.404271002
55 B -1.413516734 -0.295718846
55 B -0.706758367 1.737756778
55 B 0 -0.147884565
55 B 0.706758367 -0.517721687
55 B 1.413516734 -0.77643168
56 A -1.413516734 -0.601017706
56 A -0.706758367 0.797676563
56 A 0 -0.601017706
56 A 0.706758367 -0.929084139
56 A 1.413516734 1.333442987
57 B -1.413516734 0.495833311
57 B -0.706758367 0.711015579
57 B 0 0.272004223
57 B 0.706758367 0.280651042
57 B 1.413516734 -1.759504154
58 A -1.413516734 -1.636577989
58 A -0.706758367 0.547101144
58 A 0 0.988667422
58 A 0.706758367 0.19138039
58 A 1.413516734 -0.090570967
59 B -1.413516734 -0.516802394
59 B -0.706758367 -1.327088346
59 B 0 1.322636808
59 B 0.706758367 0.052623542
59 B 1.413516734 0.468630391
60 A -1.413516734 -0.910062825
60 A -0.706758367 -0.673758758
60 A 0 0.656415769
60 A 0.706758367 1.427267217
60 A 1.413516734 -0.499861403
61 B -1.413516734 -1.027894298
61 B -0.706758367 -0.961514298
61 B 0 1.342819983
61 B 0.706758367 0.381258271
61 B 1.413516734 0.265330342
62 B -1.413516734 0.107103769
62 B -0.706758367 1.475482651
62 B 0 -1.063724775
62 B 0.706758367 -0.78161883
62 B 1.413516734 0.262757184
63 A -1.413516734 -0.515915497
63 A -0.706758367 -0.213734385
63 A 0 0.923064784
63 A 0.706758367 -1.283593198
63 A 1.413516734 1.090178297
64 B -1.413516734 -1.329655805
64 B -0.706758367 -0.742270609
64 B 0 0.803819364
64 B 0.706758367 0.97381555
64 B 1.413516734 0.2942915
65 A -1.413516734 1.295806273
65 A -0.706758367 -0.809967287
65 A 0 -0.913356085
65 A 0.706758367 -0.394202931
65 A 1.413516734 0.821720031
66 B -1.413516734 -1.170440296
66 B -0.706758367 -0.305096136
66 B 0 1.027195569
66 B 0.706758367 -0.606898266
66 B 1.413516734 1.055239129
67 B -1.413516734 -1.323346074
67 B -0.706758367 0.485373944
67 B 0 -0.210246217
67 B 0.706758367 1.366600414
67 B 1.413516734 -0.318382066
68 B -1.413516734 -0.748945997
68 B -0.706758367 -0.698681165
68 B 0 0.871584014
68 B 0.706758367 1.294339857
68 B 1.413516734 -0.718296709
69 B -1.413516734 -0.704016665
69 B -0.706758367 -1.330556878
69 B 0 0.266267401
69 B 0.706758367 1.107342785
69 B 1.413516734 0.660963357
70 A -1.413516734 -1.28102959
70 A -0.706758367 -0.403708608
70 A 0 1.329267888
70 A 0.706758367 -0.249962086
70 A 1.413516734 0.605432397
71 B -1.413516734 0.678357874
71 B -0.706758367 0.25848688
71 B 0 0.224206735
71 B 0.706758367 0.591806586
71 B 1.413516734 -1.752858075
72 A -1.413516734 -1.258277415
72 A -0.706758367 0.513227048
72 A 0 1.326728368
72 A 0.706758367 -0.625467999
72 A 1.413516734 0.043789998
73 B -1.413516734 -0.987053622
73 B -0.706758367 1.023156944
73 B 0 -1.128411681
73 B 0.706758367 0.312708984
73 B 1.413516734 0.779599375
74 B -1.413516734 0.215585249
74 B -0.706758367 0.850073553
74 B 0 -0.077777607
74 B 0.706758367 0.67586579
74 B 1.413516734 -1.663746985
75 B -1.413516734 -1.348105226
75 B -0.706758367 -0.194776828
75 B 0 0.90244501
75 B 0.706758367 1.070281015
75 B 1.413516734 -0.429843971
76 B -1.413516734 -0.550179642
76 B -0.706758367 0.674123938
76 B 0 -0.365777137
76 B 0.706758367 1.36184849
76 B 1.413516734 -1.120015649
77 B -1.413516734 0.443103875
77 B -0.706758367 0.63596529
77 B 0 -1.388602188
77 B 0.706758367 -0.688763489
77 B 1.413516734 0.998296512
78 A -1.413516734 -0.86076395
78 A -0.706758367 0.958138475
78 A 0 1.167906948
78 A 0.706758367 -0.929777778
78 A 1.413516734 -0.335503695
79 B -1.413516734 -1.406755519
79 B -0.706758367 -0.553891567
79 B 0 0.204971891
79 B 0.706758367 1.133798406
79 B 1.413516734 0.62187679
80 B -1.413516734 -0.090091966
80 B -0.706758367 1.230988733
80 B 0 -0.248557298
80 B 0.706758367 0.557980299
80 B 1.413516734 -1.450319769
81 B -1.413516734 1.379448423
81 B -0.706758367 -1.029479391
81 B 0 -0.75052555
81 B 0.706758367 0.644002762
81 B 1.413516734 -0.243446245
82 B -1.413516734 -0.560544241
82 B -0.706758367 -0.129863047
82 B 0 -1.260527852
82 B 0.706758367 0.678044204
82 B 1.413516734 1.272890936
83 A -1.413516734 1.080286927
83 A -0.706758367 -1.640838833
83 A 0 0.3137458
83 A 0.706758367 0.046803363
83 A 1.413516734 0.200002743
84 B -1.413516734 -1.212655624
84 B -0.706758367 1.156182523
84 B 0 0.513753617
84 B 0.706758367 0.41331488
84 B 1.413516734 -0.870595396
85 A -1.413516734 -0.638935123
85 A -0.706758367 -1.436867091
85 A 0 0.446515382
85 A 0.706758367 0.830629265
85 A 1.413516734 0.798657567
86 A -1.413516734 -0.636744316
86 A -0.706758367 0.726426614
86 A 0 -0.847946128
86 A 0.706758367 1.394111323
86 A 1.413516734 -0.635847493
87 B -1.413516734 -0.493203747
87 B -0.706758367 0.244787922
87 B 0 0.825729618
87 B 0.706758367 0.90473196
87 B 1.413516734 -1.482045754
88 B -1.413516734 -1.516677871
88 B -0.706758367 -0.535490729
88 B 0 0.757747585
88 B 0.706758367 0.624921138
88 B 1.413516734 0.669499877
89 A -1.413516734 -0.958674158
89 A -0.706758367 0.453207714
89 A 0 -1.050881576
89 A 0.706758367 1.30736441
89 A 1.413516734 0.248983611
90 B -1.413516734 -1.133484495
90 B -0.706758367 0.413278144
90 B 0 1.153610934
90 B 0.706758367 -0.964925561
90 B 1.413516734 0.531520978
91 B -1.413516734 -1.191967603
91 B -0.706758367 1.367660474
91 B 0 0.584414283
91 B 0.706758367 -0.577912827
91 B 1.413516734 -0.182194327
92 B -1.413516734 -0.440378229
92 B -0.706758367 -0.376889886
92 B 0 1.586788799
92 B 0.706758367 0.267175735
92 B 1.413516734 -1.036696418
93 A -1.413516734 -0.549930303
93 A -0.706758367 0.597367599
93 A 0 0.965128905
93 A 0.706758367 0.467526341
93 A 1.413516734 -1.480092541
94 A -1.413516734 1.112948445
94 A -0.706758367 0.066000305
94 A 0 -1.598649949
94 A 0.706758367 0.447793359
94 A 1.413516734 -0.028092159
95 A -1.413516734 0.404534353
95 A -0.706758367 1.180764574
95 A 0 -0.47300049
95 A 0.706758367 0.338225873
95 A 1.413516734 -1.45052431
96 A -1.413516734 -0.713855147
96 A -0.706758367 -0.377876811
96 A 0 -0.18913604
96 A 0.706758367 1.756573795
96 A 1.413516734 -0.475705797
97 A -1.413516734 -0.846463825
97 A -0.706758367 -0.773664276
97 A 0 -0.556657971
97 A 0.706758367 1.142594886
97 A 1.413516734 1.034191186
98 B -1.413516734 0.526122568
98 B -0.706758367 1.304819893
98 B 0 -1.336622864
98 B 0.706758367 -0.0106186
98 B 1.413516734 -0.483700998
99 A -1.413516734 -0.196889714
99 A -0.706758367 1.431960964
99 A 0 0.053789168
99 A 0.706758367 0.089479996
99 A 1.413516734 -1.378340413
100 B -1.413516734 0.621378184
100 B -0.706758367 0.054566404
100 B 0 -1.439090988
100 B 0.706758367 -0.408595319
100 B 1.413516734 1.171741719
101 B -1.413516734 -1.551472906
101 B -0.706758367 1.109624323
101 B 0 -0.163178482
101 B 0.706758367 0.02682386
101 B 1.413516734 0.578203206
102 B -1.413516734 -1.160215278
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203 A 1.413516734 -0.530764799
;
proc mixed data=datalong;
TITLE 'MODEL 1';
class id type ;
model intensity= type | intervals | intervals ;
proc mixed data=datalong;
TITLE 'MODEL 2';
class id type ;
model intensity= type | intervals | intervals ;
REPEATED / TYPE = vc SUB = id;
proc mixed data=datalong;
TITLE 'MODEL 3';
class id type ;
model intensity= type | intervals | intervals ;
Random intercept /SUB=id;
