proc mixed between and within factors

[ACF1]

Dear Community,

I have troubles in using PROC MIXED OR PROC GLIMMIXED. My experiment consist of 12 control and 12 diseased animals (group factor). Cultured cells from each animal are treated with 4 compounds (repeated measures factor) and the measure of a signal is replicated 5 times (repeated measures factor).

I would like to test for group effect and compound effect and possibly their interaction taking into account the nested repeated measures nature of the experiment.

I also have a similar experiment where the numeber of animals and the number is variable as regard the group, the compound end the replicates.

Thanks for your help

[SteveDenham]

If your response variable is continuous, you can fit a Kronecker product in the REPEATED statement of PROC MIXED.  See the short example here .

For GLIMMIX, multivariate repeated measures are not so simple.  See my reply in this thread https://communities.sas.com/t5/Statistical-Procedures/repeated-measures-in-glimmix/td-p/128310  or here https://communities.sas.com/t5/Statistical-Procedures/Doubly-repeated-measures-with-GLIMMIX/td-p/116...

The latter is an incomplete version of this fantastic blog by the Ontario Agriculture College's statistical support group:

https://oacstats.blog/2018/04/23/ridgetown-workshop-repeated-measures-adding-year-location/ 

This gives code for a doubly repeated measures analysis in GLIMMIX.

SteveDenham 

[ACF1]

Hi Steve,
thanks for your suggestion. Unfortunately it seems not working.
I tried this model:

PROC GLIMMIX DATA=mydata PLOTS=ALL ;
CLASS animal group compound repeat ;
MODEL signal = groupt|compound ;
RANDOM repeat / SUBJECT=animal ;
RANDOM compound / SUBJECT=animal*repeat TYPE=UN ;
LSMEANS group|compound / CL ;
RUN;

but it doesn't work, this is the log:

WARNING: MIVQUE0 estimate of profiled variance is linearly related to other
covariance parameters.
NOTE: Convergence criterion (FCONV=2.220446E-16) satisfied.
NOTE: At least one element of the gradient is greater than 1e-3.
NOTE: A linear combination of covariance parameters is confounded with the
residual variance.

[SteveDenham]

Well, in some sense, things worked (convergence is good), but the thing to notice here is that you aren't fitting 'repeat' in the model.  Give this a try:

PROC GLIMMIX DATA=mydata PLOTS=ALL ;
CLASS animal group compound repeat ;
MODEL signal = group|compound|repeat ;
RANDOM intercept / SUBJECT=animal group=compound ;
RANDOM repeat / SUBJECT=animal residual TYPE=cs ;
LSMEANS group|compound / CL ;
RUN;

I still feel that this is missing something from the OAC reference, as you don't have a factor equivalent to their 'rep' variable, so I am not sure if the first RANDOM statement will do what is needed.. I might be missing what the experimental unit is in this case.  I think 'animal' is a block equivalent to 'rep' in the OAC, in which case you should have some variable ID'ing what was sampled from the animal.  The more I think about this, that would be 'compound' so you have confounding of compound with the experimental unit.  I definitely feel like I am missing a key element in the design.

SteveDenham

[ACF1]

Here my design and my data: 12 diseased (D) animals and 12 controls (ctrl) are assigned to receive all of 4 compounds (first repeated factor) and there is a signal measured 5 times for each coumpound on each animal (second repeated factor, but I'm not interested in this effect).

Group	Compound	Animal	Repeat	Signal
D	1	D1	1	299092
D	1	D1	2	280073
D	1	D1	3	239451
D	1	D1	4	256468
D	1	D1	5	285194
D	1+2	D1	1	348124
D	1+2	D1	2	336914
D	1+2	D1	3	369524
D	1+2	D1	4	307687
D	1+2	D1	5	316932
D	1+2+3	D1	1	358802
D	1+2+3	D1	2	389635
D	1+2+3	D1	3	397721
D	1+2+3	D1	4	418724
D	1+2+3	D1	5	420941
D	1+3	D1	1	415534
D	1+3	D1	2	371207
D	1+3	D1	3	384587
D	1+3	D1	4	428517
D	1+3	D1	5	415308
D	1	D2	1	451305
D	1	D2	2	442801
D	1	D2	3	481227
D	1	D2	4	413664
D	1	D2	5	430914
D	1+2	D2	1	278262
D	1+2	D2	2	286955
D	1+2	D2	3	226982
D	1+2	D2	4	258981
D	1+2	D2	5	268785
D	1+2+3	D2	1	236513
D	1+2+3	D2	2	210532
D	1+2+3	D2	3	156137
D	1+2+3	D2	4	119717
D	1+2+3	D2	5	151279
D	1+3	D2	1	538222
D	1+3	D2	2	529583
D	1+3	D2	3	517925
D	1+3	D2	4	532973
D	1+3	D2	5	530916
D	1	D3	1	496014
D	1	D3	2	419344
D	1	D3	3	468740
D	1	D3	4	470809
D	1	D3	5	484953
D	1+2	D3	1	712583
D	1+2	D3	2	634273
D	1+2	D3	3	654884
D	1+2	D3	4	664783
D	1+2	D3	5	676842
D	1+2+3	D3	1	456312
D	1+2+3	D3	2	424410
D	1+2+3	D3	3	440612
D	1+2+3	D3	4	416622
D	1+2+3	D3	5	438208
D	1+3	D3	1	693942
D	1+3	D3	2	691170
D	1+3	D3	3	629976
D	1+3	D3	4	698913
D	1+3	D3	5	769643
D	1	D4	1	427913
D	1	D4	2	419932
D	1	D4	3	397815
D	1	D4	4	399724
D	1	D4	5	399517
D	1+2	D4	1	511499
D	1+2	D4	2	460973
D	1+2	D4	3	422244
D	1+2	D4	4	559974
D	1+2	D4	5	518275
D	1+2+3	D4	1	448751
D	1+2+3	D4	2	375320
D	1+2+3	D4	3	417325
D	1+2+3	D4	4	327513
D	1+2+3	D4	5	327415
D	1+3	D4	1	598966
D	1+3	D4	2	593115
D	1+3	D4	3	537046
D	1+3	D4	4	588924
D	1+3	D4	5	568589
D	1	D5	1	452302
D	1	D5	2	295407
D	1	D5	3	443580
D	1	D5	4	380202
D	1	D5	5	342135
D	1+2	D5	1	526964
D	1+2	D5	2	513785
D	1+2	D5	3	485871
D	1+2	D5	4	493392
D	1+2	D5	5	428953
D	1+2+3	D5	1	290895
D	1+2+3	D5	2	304773
D	1+2+3	D5	3	233861
D	1+2+3	D5	4	239263
D	1+2+3	D5	5	204572
D	1+3	D5	1	561195
D	1+3	D5	2	563376
D	1+3	D5	3	552295
D	1+3	D5	4	542625
D	1+3	D5	5	550423
D	1	D6	1	151525
D	1	D6	2	140694
D	1	D6	3	151348
D	1	D6	4	140498
D	1	D6	5	132310
D	1+2	D6	1	324575
D	1+2	D6	2	323197
D	1+2	D6	3	316585
D	1+2	D6	4	284173
D	1+2	D6	5	312782
D	1+2+3	D6	1	123533
D	1+2+3	D6	2	121773
D	1+2+3	D6	3	121476
D	1+2+3	D6	4	120766
D	1+2+3	D6	5	121636
D	1+3	D6	1	314985
D	1+3	D6	2	309984
D	1+3	D6	3	288682
D	1+3	D6	4	295393
D	1+3	D6	5	285891
D	1	D7	1	231758
D	1	D7	2	238973
D	1	D7	3	252995
D	1	D7	4	184888
D	1	D7	5	203697
D	1+2	D7	1	150338
D	1+2	D7	2	143496
D	1+2	D7	3	143558
D	1+2	D7	4	140278
D	1+2	D7	5	140189
D	1+2+3	D7	1	237055
D	1+2+3	D7	2	260468
D	1+2+3	D7	3	247947
D	1+2+3	D7	4	241240
D	1+2+3	D7	5	217081
D	1+3	D7	1	229403
D	1+3	D7	2	216481
D	1+3	D7	3	198361
D	1+3	D7	4	207942
D	1+3	D7	5	217733
D	1	D8	1	528971
D	1	D8	2	493396
D	1	D8	3	498951
D	1	D8	4	480924
D	1	D8	5	497756
D	1+2	D8	1	500988
D	1+2	D8	2	352342
D	1+2	D8	3	434887
D	1+2	D8	4	402875
D	1+2	D8	5	370769
D	1+2+3	D8	1	418733
D	1+2+3	D8	2	539952
D	1+2+3	D8	3	482380
D	1+2+3	D8	4	526684
D	1+2+3	D8	5	504143
D	1+3	D8	1	513150
D	1+3	D8	2	571970
D	1+3	D8	3	550684
D	1+3	D8	4	511224
D	1+3	D8	5	518795
D	1	D9	1	254832
D	1	D9	2	234697
D	1	D9	3	211593
D	1	D9	4	242894
D	1	D9	5	225680
D	1+2	D9	1	69043
D	1+2	D9	2	75423
D	1+2	D9	3	70081
D	1+2	D9	4	70284
D	1+2	D9	5	71052
D	1+2+3	D9	1	49326
D	1+2+3	D9	2	51262
D	1+2+3	D9	3	43746
D	1+2+3	D9	4	45299
D	1+2+3	D9	5	46240
D	1+3	D9	1	168523
D	1+3	D9	2	172344
D	1+3	D9	3	167297
D	1+3	D9	4	169445
D	1+3	D9	5	167032
D	1	D10	1	152369
D	1	D10	2	148473
D	1	D10	3	136721
D	1	D10	4	150212
D	1	D10	5	145133
D	1+2	D10	1	223495
D	1+2	D10	2	256362
D	1+2	D10	3	313593
D	1+2	D10	4	226295
D	1+2	D10	5	219989
D	1+2+3	D10	1	338262
D	1+2+3	D10	2	293914
D	1+2+3	D10	3	247747
D	1+2+3	D10	4	285989
D	1+2+3	D10	5	269962
D	1+3	D10	1	223514
D	1+3	D10	2	192321
D	1+3	D10	3	225333
D	1+3	D10	4	221425
D	1+3	D10	5	166638
D	1	D11	1	258947
D	1	D11	2	238768
D	1	D11	3	210975
D	1	D11	4	248985
D	1	D11	5	231799
D	1+2	D11	1	274832
D	1+2	D11	2	282496
D	1+2	D11	3	253349
D	1+2	D11	4	249934
D	1+2	D11	5	269321
D	1+2+3	D11	1	649398
D	1+2+3	D11	2	558776
D	1+2+3	D11	3	572953
D	1+2+3	D11	4	613874
D	1+2+3	D11	5	649631
D	1+3	D11	1	355945
D	1+3	D11	2	387984
D	1+3	D11	3	326617
D	1+3	D11	4	328583
D	1+3	D11	5	331750
D	1	D12	1	325151
D	1	D12	2	296417
D	1	D12	3	250726
D	1	D12	4	308349
D	1	D12	5	248071
D	1+2	D12	1	163460
D	1+2	D12	2	148729
D	1+2	D12	3	159533
D	1+2	D12	4	139568
D	1+2	D12	5	151676
D	1+2+3	D12	1	79323
D	1+2+3	D12	2	76269
D	1+2+3	D12	3	78035
D	1+2+3	D12	4	75395
D	1+2+3	D12	5	78143
D	1+3	D12	1	626971
D	1+3	D12	2	553892
D	1+3	D12	3	594874
D	1+3	D12	4	570093
D	1+3	D12	5	586996
ctrl	1	C1	1	86962
ctrl	1	C1	2	78238
ctrl	1	C1	3	73522
ctrl	1	C1	4	73355
ctrl	1	C1	5	69748
ctrl	1+2	C1	1	98594
ctrl	1+2	C1	2	137487
ctrl	1+2	C1	3	124254
ctrl	1+2	C1	4	158471
ctrl	1+2	C1	5	92564
ctrl	1+2+3	C1	1	66288
ctrl	1+2+3	C1	2	59785
ctrl	1+2+3	C1	3	52898
ctrl	1+2+3	C1	4	47599
ctrl	1+2+3	C1	5	49859
ctrl	1+3	C1	1	62148
ctrl	1+3	C1	2	71232
ctrl	1+3	C1	3	65424
ctrl	1+3	C1	4	59534
ctrl	1+3	C1	5	62532
ctrl	1	C2	1	91041
ctrl	1	C2	2	93555
ctrl	1	C2	3	93478
ctrl	1	C2	4	89325
ctrl	1	C2	5	92847
ctrl	1+2	C2	1	60630
ctrl	1+2	C2	2	59552
ctrl	1+2	C2	3	60105
ctrl	1+2	C2	4	61149
ctrl	1+2	C2	5	58308
ctrl	1+2+3	C2	1	83505
ctrl	1+2+3	C2	2	84301
ctrl	1+2+3	C2	3	83447
ctrl	1+2+3	C2	4	82376
ctrl	1+2+3	C2	5	84744
ctrl	1+3	C2	1	83488
ctrl	1+3	C2	2	80861
ctrl	1+3	C2	3	83690
ctrl	1+3	C2	4	83577
ctrl	1+3	C2	5	82614
ctrl	1	C3	1	130417
ctrl	1	C3	2	124647
ctrl	1	C3	3	130866
ctrl	1	C3	4	131894
ctrl	1	C3	5	129993
ctrl	1+2	C3	1	131093
ctrl	1+2	C3	2	128174
ctrl	1+2	C3	3	130239
ctrl	1+2	C3	4	130141
ctrl	1+2	C3	5	129516
ctrl	1+2+3	C3	1	127552
ctrl	1+2+3	C3	2	125519
ctrl	1+2+3	C3	3	126711
ctrl	1+2+3	C3	4	129848
ctrl	1+2+3	C3	5	129213
ctrl	1+3	C3	1	113537
ctrl	1+3	C3	2	121609
ctrl	1+3	C3	3	111941
ctrl	1+3	C3	4	111000
ctrl	1+3	C3	5	114276
ctrl	1	C4	1	22301
ctrl	1	C4	2	24102
ctrl	1	C4	3	19101
ctrl	1	C4	4	38211
ctrl	1	C4	5	37794
ctrl	1+2	C4	1	71477
ctrl	1+2	C4	2	67638
ctrl	1+2	C4	3	81357
ctrl	1+2	C4	4	47137
ctrl	1+2	C4	5	54535
ctrl	1+2+3	C4	1	42178
ctrl	1+2+3	C4	2	51847
ctrl	1+2+3	C4	3	39032
ctrl	1+2+3	C4	4	37201
ctrl	1+2+3	C4	5	37153
ctrl	1+3	C4	1	83592
ctrl	1+3	C4	2	77168
ctrl	1+3	C4	3	65752
ctrl	1+3	C4	4	73187
ctrl	1+3	C4	5	54966
ctrl	1	C5	1	12983
ctrl	1	C5	2	340907
ctrl	1	C5	3	114244
ctrl	1	C5	4	128359
ctrl	1	C5	5	18443
ctrl	1+2	C5	1	72999
ctrl	1+2	C5	2	54537
ctrl	1+2	C5	3	59254
ctrl	1+2	C5	4	38272
ctrl	1+2	C5	5	38254
ctrl	1+2+3	C5	1	82657
ctrl	1+2+3	C5	2	71214
ctrl	1+2+3	C5	3	52381
ctrl	1+2+3	C5	4	32244
ctrl	1+2+3	C5	5	48865
ctrl	1+3	C5	1	71562
ctrl	1+3	C5	2	64598
ctrl	1+3	C5	3	79327
ctrl	1+3	C5	4	38258
ctrl	1+3	C5	5	48368
ctrl	1	C6	1	63305
ctrl	1	C6	2	63293
ctrl	1	C6	3	64925
ctrl	1	C6	4	64381
ctrl	1	C6	5	66729
ctrl	1+2	C6	1	86144
ctrl	1+2	C6	2	83301
ctrl	1+2	C6	3	84701
ctrl	1+2	C6	4	87144
ctrl	1+2	C6	5	82177
ctrl	1+2+3	C6	1	98863
ctrl	1+2+3	C6	2	98377
ctrl	1+2+3	C6	3	100403
ctrl	1+2+3	C6	4	100291
ctrl	1+2+3	C6	5	100793
ctrl	1+3	C6	1	94011
ctrl	1+3	C6	2	86967
ctrl	1+3	C6	3	93922
ctrl	1+3	C6	4	92021
ctrl	1+3	C6	5	89911
ctrl	1	C7	1	119105
ctrl	1	C7	2	121940
ctrl	1	C7	3	116700
ctrl	1	C7	4	122114
ctrl	1	C7	5	115009
ctrl	1+2	C7	1	110396
ctrl	1+2	C7	2	115510
ctrl	1+2	C7	3	111504
ctrl	1+2	C7	4	110784
ctrl	1+2	C7	5	109219
ctrl	1+2+3	C7	1	196448
ctrl	1+2+3	C7	2	196720
ctrl	1+2+3	C7	3	197428
ctrl	1+2+3	C7	4	199719
ctrl	1+2+3	C7	5	192063
ctrl	1+3	C7	1	224785
ctrl	1+3	C7	2	225851
ctrl	1+3	C7	3	221603
ctrl	1+3	C7	4	220562
ctrl	1+3	C7	5	221109
ctrl	1	C8	1	89047
ctrl	1	C8	2	87179
ctrl	1	C8	3	87487
ctrl	1	C8	4	90849
ctrl	1	C8	5	88516
ctrl	1+2	C8	1	162359
ctrl	1+2	C8	2	156512
ctrl	1+2	C8	3	162665
ctrl	1+2	C8	4	168540
ctrl	1+2	C8	5	169213
ctrl	1+2+3	C8	1	79459
ctrl	1+2+3	C8	2	78650
ctrl	1+2+3	C8	3	79524
ctrl	1+2+3	C8	4	78989
ctrl	1+2+3	C8	5	79703
ctrl	1+3	C8	1	104540
ctrl	1+3	C8	2	99693
ctrl	1+3	C8	3	102779
ctrl	1+3	C8	4	101869
ctrl	1+3	C8	5	103001
ctrl	1	C9	1	82848
ctrl	1	C9	2	84812
ctrl	1	C9	3	83114
ctrl	1	C9	4	85284
ctrl	1	C9	5	82324
ctrl	1+2	C9	1	68911
ctrl	1+2	C9	2	67781
ctrl	1+2	C9	3	69592
ctrl	1+2	C9	4	67487
ctrl	1+2	C9	5	68789
ctrl	1+2+3	C9	1	73284
ctrl	1+2+3	C9	2	75162
ctrl	1+2+3	C9	3	73766
ctrl	1+2+3	C9	4	74591
ctrl	1+2+3	C9	5	75591
ctrl	1+3	C9	1	50998
ctrl	1+3	C9	2	49504
ctrl	1+3	C9	3	51023
ctrl	1+3	C9	4	50558
ctrl	1+3	C9	5	50159
ctrl	1	C10	1	92934
ctrl	1	C10	2	96397
ctrl	1	C10	3	100353
ctrl	1	C10	4	97318
ctrl	1	C10	5	92684
ctrl	1+2	C10	1	175796
ctrl	1+2	C10	2	175960
ctrl	1+2	C10	3	177130
ctrl	1+2	C10	4	176969
ctrl	1+2	C10	5	172057
ctrl	1+2+3	C10	1	299139
ctrl	1+2+3	C10	2	295258
ctrl	1+2+3	C10	3	292623
ctrl	1+2+3	C10	4	296571
ctrl	1+2+3	C10	5	301145
ctrl	1+3	C10	1	130747
ctrl	1+3	C10	2	135256
ctrl	1+3	C10	3	130535
ctrl	1+3	C10	4	131637
ctrl	1+3	C10	5	134188
ctrl	1	C11	1	94395
ctrl	1	C11	2	93207
ctrl	1	C11	3	95727
ctrl	1	C11	4	91878
ctrl	1	C11	5	92932
ctrl	1+2	C11	1	29672904
ctrl	1+2	C11	2	41261021
ctrl	1+2	C11	3	54014275
ctrl	1+2	C11	4	25077474
ctrl	1+2	C11	5	73583123
ctrl	1+2+3	C11	1	81872
ctrl	1+2+3	C11	2	82734
ctrl	1+2+3	C11	3	84131
ctrl	1+2+3	C11	4	84768
ctrl	1+2+3	C11	5	83909
ctrl	1+3	C11	1	43734
ctrl	1+3	C11	2	46370
ctrl	1+3	C11	3	43888
ctrl	1+3	C11	4	44855
ctrl	1+3	C11	5	43269
ctrl	1	C12	1	85789
ctrl	1	C12	2	84396
ctrl	1	C12	3	90814
ctrl	1	C12	4	87896
ctrl	1	C12	5	86842
ctrl	1+2	C12	1	34059
ctrl	1+2	C12	2	34206
ctrl	1+2	C12	3	34647
ctrl	1+2	C12	4	34310
ctrl	1+2	C12	5	35210
ctrl	1+2+3	C12	1	145572
ctrl	1+2+3	C12	2	143967
ctrl	1+2+3	C12	3	138577
ctrl	1+2+3	C12	4	144353
ctrl	1+2+3	C12	5	142404
ctrl	1+3	C12	1	83488
ctrl	1+3	C12	2	80861
ctrl	1+3	C12	3	83690
ctrl	1+3	C12	4	83577
ctrl	1+3	C12	5	82614

[SteveDenham]

I tried a couple versions of this, but this code ran without error or warning, and gave the smallest AICC:

proc glimmix data=one;
class Group Compound Animal Repeat;
value=signal/1000;
model value = group|compound|repeat/ddfm=bw;
random intercept/subject=animal;
random repeat/residual subject=animal type=cs group=group*compound;
covtest homogeneity;
run;

 This split plot analysis with heterogeneous variances by group*compound is the best I came up with.  Comparisons of interest regarding group and compound can be obtained with an LSMEANS or LSMESTIMATE statement.

SteveDenham

[ACF1]

Thank you Steve, PROC GLIMMIX is very complicated and the model so! Is it possible to omit the "repeat" factor in the MODEL statement?

[SteveDenham · Accepted solution]

You can, but be sure to include the random statements as in the current model, especially the group=group*compound option to deal with the heterogeneity of variance issue.  I don't know why you would drop it, though. It is a known design factor, the F tests, lsmeans and lsmean difference p values for tests of group, compound and group by compound are no different, and you get some insight into which whole plot factors have the largest effect on the repeat to repeat variability.

SteveDenham