topic Re: multivariate mixed model issues - Y variables with and without residual variance in Statistical Procedures

multivariate mixed model issues - Y variables with and without residual variance

fishhead — Mon, 27 Oct 2014 03:28:14 GMT

Hi,

i have a rather complex mulitvariate mixed model that has Y variables (traits) that do and do not have repeated measures. the aim is to look for across-individual correlations between traits.

I have repeated measures of metabolism in relation to temperature, so that trait i wish to model as random intercepts and slopes. but, the other traits have only a single estimate (mass of internal organs, like liver, heart etc). i am interested mainly in whether intercepts and/or slopes of metabolism (smr) are correlated across individuals to growth (grow), and organ masses. i have standardised all variables to mean 0, variance 1.

i understand i must fix residual variance to zero for those traits without repeated measures (see final line of parms parameters). i am able to do this for a bivariate situation, but the residual variances i request be held to zero are not all held at that ... SAS seems to fit something anyways! and for any model, even the bivariate models that converge and make sense, i get non positive definate errors.

The Model:

proc mixed maxiter=100 method=reml covtest;

class id trait sex;

where trait in ('smr' 'grow' 'stomach''liver''heart' ) ;

model score = trait trait*mass trait*temp trait*sex / noint solution ;

random trait trait*temp / subject=id type=un g gcorr ;

repeated / subject=id group=trait type=vc ;

parms

0.4

0.1 0.3

0.1 0.1 0.2

0.1 0.1 0.1 0.1

0.1 0.1 0.1 0.1 0.1

0 0 0 0 0 0

0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0.1 0.1 0.1 0.1 0.1 0 0 0 0.2

0 0 0 0 0 0 0 0 0 0

0 0 0 0.2 0

/ hold=16-36,42-44,46-55,56-58,60;

run;

any help would be MUCH appreciated.

Here is the output:

Model Information

Data Set WORK.SNAKE

Dependent Variable score

Covariance Structures Unstructured, Variance

Components

Subject Effects id, id

Group Effect trait

Estimation Method REML

Residual Variance Method None

Fixed Effects SE Method Model-Based

Degrees of Freedom Method Containment

Class Level Information

Class Levels Values

id 78 1 2 3 4 5 6 7 8 9 10 11 12 13

14 15 16 17 18 19 20 21 22 23

24 25 26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43

44 45 46 47 48 49 50 51 52 53

54 55 56 57 58 59 60 61 62 63

64 65 66 67 68 69 70 71 72 73

74 75 76 77 78

trait 5 grow heart liver smr stomach

sex 2 f m

Dimensions

Covariance Parameters 60

Columns in X 25

Columns in Z Per Subject 10

Subjects 78

Max Obs Per Subject 7

Number of Observations

Number of Observations Read 546

Number of Observations Used 543

Number of Observations Not Used 3

SNAKE gifford multivariate 993

14:02 Sunday, January 22, 2012

The Mixed Procedure

Parameter Search

CovP1 CovP2 CovP3 CovP4 CovP5 CovP6 CovP7 CovP8 CovP9 CovP10

0.4000 0.1000 0.3000 0.1000 0.1000 0.2000 0.1000 0.1000 0.1000 0.1000

Parameter Search

CovP11 CovP12 CovP13 CovP14 CovP15 CovP16 CovP17 CovP18 CovP19 CovP20

0.1000 0.1000 0.1000 0.1000 0.1000 0 0 0 0 0

Parameter Search

CovP21 CovP22 CovP23 CovP24 CovP25 CovP26 CovP27 CovP28 CovP29 CovP30

0 0 0 0 0 0 0 0 0 0

Parameter Search

CovP31 CovP32 CovP33 CovP34 CovP35 CovP36 CovP37 CovP38 CovP39 CovP40

0 0 0 0 0 0 0.1000 0.1000 0.1000 0.1000

Parameter Search

CovP41 CovP42 CovP43 CovP44 CovP45 CovP46 CovP47 CovP48 CovP49 CovP50

0.1000 0 0 0 0.2000 0 0 0 0 0

Parameter Search

CovP51 CovP52 CovP53 CovP54 CovP55 CovP56 CovP57 CovP58 CovP59 CovP60

0 0 0 0 0 0 0 0 0.2000 0

Parameter Search

Res Log Like -2 Res Log Like

-1646.0444 3292.0888

Iteration History

Iteration Evaluations -2 Res Log Like Criterion

1 2 3052.77234298 5076446.9586

2 1 3020.53129601 5396314.6003

SNAKE gifford multivariate 994

14:02 Sunday, January 22, 2012

The Mixed Procedure

Iteration History

Iteration Evaluations -2 Res Log Like Criterion

3 1 2623.03272815 3512091.3947

4 1 2239.29440240 2179422.9738

5 1 1955.97441629 1534676.7519

6 1 1857.64284936 1616514.1840

7 1 1753.59719832 1997053.3055

8 1 1602.83749339 3323477.4337

9 1 1493.10709367 5965459.3658

10 1 1432.24335881 10071334.555

11 3 1263.59574182 .

12 1 955.09012350 .

13 1 756.70827473 .

14 1 636.28480138 .

15 1 570.77910660 .

16 1 537.89890246 505.89610327

17 1 522.91363072 125.67368087

18 1 517.65753686 24.35200327

19 1 516.59637099 1.79963774

20 1 516.52797109 0.01407840

21 1 516.52755520 0.00000074

22 1 516.52755518 0.00000000

Convergence criteria met but final hessian is not positive

definite.

Estimated G Matrix

Row Effect trait id Col1 Col2 Col3 Col4 Col5 Col6

1 trait grow 1 0.000751 -0.00107 -0.00363 -0.02785 0.006168

2 trait heart 1 -0.00107 0.5930 0.1582 -0.3107 0.3585

3 trait liver 1 -0.00363 0.1582 0.3993 -1.7961 0.2958

4 trait smr 1 -0.02785 -0.3107 -1.7961 3.4202 -1.4543

5 trait stomach 1 0.006168 0.3585 0.2958 -1.4543 0.9790

Estimated G Matrix

Row Col7 Col8 Col9 Col10

1 0.01991

2 0.2445

3 1.2976

4 -3.0078

5 1.0739

SNAKE gifford multivariate 995

14:02 Sunday, January 22, 2012

The Mixed Procedure

Estimated G Matrix

Row Effect trait id Col1 Col2 Col3 Col4 Col5 Col6

6 temp*trait grow 1

7 temp*trait heart 1

8 temp*trait liver 1

9 temp*trait smr 1 0.01991 0.2445 1.2976 -3.0078 1.0739

10 temp*trait stomach 1

Estimated G Matrix

Row Col7 Col8 Col9 Col10

9 2.5226

Estimated G Correlation Matrix

Row Effect trait id Col1 Col2 Col3 Col4 Col5 Col6

1 trait grow 1 1.0000 -0.05076 -0.2097 -0.5496 0.2276

2 trait heart 1 -0.05076 1.0000 0.3251 -0.2181 0.4704

3 trait liver 1 -0.2097 0.3251 1.0000 -1.0000 0.4731

4 trait smr 1 -0.5496 -0.2181 -1.0000 1.0000 -0.7948

5 trait stomach 1 0.2276 0.4704 0.4731 -0.7948 1.0000

6 temp*trait grow 1 1.0000

7 temp*trait heart 1

8 temp*trait liver 1

9 temp*trait smr 1 0.4576 0.1999 1.0000 -1.0000 0.6834

Estimated G Correlation Matrix

Row Col7 Col8 Col9 Col10

1 0.4576

2 0.1999

3 1.0000

4 -1.0000

5 0.6834

7 1.0000

8 1.0000

9 1.0000

SNAKE gifford multivariate 996

14:02 Sunday, January 22, 2012

The Mixed Procedure

Estimated G Correlation Matrix

Row Effect trait id Col1 Col2 Col3 Col4 Col5 Col6

10 temp*trait stomach 1

Estimated G Correlation Matrix

Row Col7 Col8 Col9 Col10

10 1.0000

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Group Estimate Error Value Pr Z

UN(1,1) id 0.000751 0.000129 5.82 <.0001

UN(2,1) id -0.00107 0.003318 -0.32 0.7469

UN(2,2) id 0.5930 0.1577 3.76 <.0001

UN(3,1) id -0.00363 0.002722 -1.33 0.1823

UN(3,2) id 0.1582 0.09710 1.63 0.1033

UN(3,3) id 0.3993 0.1111 3.59 0.0002

UN(4,1) id -0.02785 0.02200 -1.27 0.2057

UN(4,2) id -0.3107 0.7639 -0.41 0.6842

UN(4,3) id -1.7961 0.6333 -2.84 0.0046

UN(4,4) id 3.4202 7.6157 0.45 0.3267

UN(5,1) id 0.006168 0.004053 1.52 0.1280

UN(5,2) id 0.3585 0.1483 2.42 0.0156

UN(5,3) id 0.2958 0.1174 2.52 0.0118

UN(5,4) id -1.4543 0.6873 -2.12 0.0343

UN(5,5) id 0.9790 0.1587 6.17 <.0001

UN(6,1) id 0 . . .

UN(6,2) id 0 . . .

UN(6,3) id 0 . . .

UN(6,4) id 0 . . .

UN(6,5) id 0 . . .

UN(6,6) id 0 . . .

UN(7,1) id 0 . . .

UN(7,2) id 0 . . .

UN(7,3) id 0 . . .

UN(7,4) id 0 . . .

UN(7,5) id 0 . . .

UN(7,6) id 0 . . .

UN(7,7) id 0 . . .

UN(8,1) id 0 . . .

UN(8,2) id 0 . . .

UN(8,3) id 0 . . .

UN(8,4) id 0 . . .

SNAKE gifford multivariate 997

14:02 Sunday, January 22, 2012

The Mixed Procedure

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Group Estimate Error Value Pr Z

UN(8,5) id 0 . . .

UN(8,6) id 0 . . .

UN(8,7) id 0 . . .

UN(8,8) id 0 . . .

UN(9,1) id 0.01991 0.01563 1.27 0.2026

UN(9,2) id 0.2445 0.5433 0.45 0.6527

UN(9,3) id 1.2976 0.4513 2.88 0.0040

UN(9,4) id -3.0078 5.3254 -0.56 0.5722

UN(9,5) id 1.0739 0.4884 2.20 0.0279

UN(9,6) id 0 . . .

UN(9,7) id 0 . . .

UN(9,8) id 0 . . .

UN(9,9) id 2.5226 3.7309 0.68 0.2495

UN(10,1) id 0 . . .

UN(10,2) id 0 . . .

UN(10,3) id 0 . . .

UN(10,4) id 0 . . .

UN(10,5) id 0 . . .

UN(10,6) id 0 . . .

UN(10,7) id 0 . . .

UN(10,8) id 0 . . .

UN(10,9) id 0 . . .

UN(10,10) id 0 . . .

Residual id trait grow 0 . . .

Residual id trait heart 0.2930 0 . .

Residual id trait liver 0.1993 0 . .

Residual id trait smr 0.2168 0.03502 6.19 <.0001

Residual id trait stomach 0 . . .

Fit Statistics

-2 Res Log Likelihood 516.5

AIC (smaller is better) 618.5

AICC (smaller is better) 629.7

BIC (smaller is better) 738.7

PARMS Model Likelihood Ratio Test

DF Chi-Square Pr > ChiSq

51 2775.56 <.0001

SNAKE gifford multivariate 998

14:02 Sunday, January 22, 2012

The Mixed Procedure

Solution for Fixed Effects

Standard

Effect trait sex Estimate Error DF t Value Pr > |t|

trait grow -0.3277 0.03308 378 -9.91 <.0001

trait heart -2.3197 1.0897 378 -2.13 0.0339

trait liver -4.7063 0.8233 378 -5.72 <.0001

trait smr -19.4215 0.7135 378 -27.22 <.0001

trait stomach -0.1774 0.1558 378 -1.14 0.2553

mass*trait grow 0.2982 0.02101 73 14.20 <.0001

mass*trait heart 1.3864 0.6801 73 2.04 0.0451

mass*trait liver 2.8763 0.5154 73 5.58 <.0001

mass*trait smr 1.8862 0.1671 73 11.29 <.0001

mass*trait stomach 0 . . . .

temp*trait grow 0 . . . .

temp*trait heart 0 . . . .

temp*trait liver 0 . . . .

temp*trait smr 11.3638 0.4747 77 23.94 <.0001

temp*trait stomach 0 . . . .

trait*sex grow f -0.00298 0.006210 73 -0.48 0.6324

trait*sex grow m 0 . . . .

trait*sex heart f 0.1831 0.2149 73 0.85 0.3971

trait*sex heart m 0 . . . .

trait*sex liver f 0.2231 0.1625 73 1.37 0.1739

trait*sex liver m 0 . . . .

trait*sex smr f -0.04568 0.04914 73 -0.93 0.3557

trait*sex smr m 0 . . . .

trait*sex stomach f 0.3549 0.2164 73 1.64 0.1053

trait*sex stomach m 0 . . . .

Type 3 Tests of Fixed Effects

Num Den

Effect DF DF F Value Pr > F

trait 5 378 193.39 <.0001

mass*trait 4 73 105.26 <.0001

temp*trait 1 77 573.02 <.0001

trait*sex 5 73 1.27 0.2850

Re: multivariate mixed model issues - Y variables with and without residual variance

SteveDenham — Mon, 27 Oct 2014 15:27:57 GMT

Before I get into modeling, I am going to ask some physiological questions.

First, you have repeated measures of metabolic rate, but the organ weight data is only available at the final point, as near as I can understand. If I am missing something on this, then my next question (and most of the rest) can be ignored.

1. I assume mass is organ weight, or body weight change. What is mass for metabolic rate?

2. How can organ mass at the end of the trial be associated with smr at earlier timepoints? I would think the two may be related, but it would be hard for me to consider the two together as a repeated measure.

3. Given that organ mass is a single timepoint, why not have two analyses--one a repeated measures analysis of metabolic rate, and one a multivariate of organ masses and smr at the final time point? In the repeated measure analysis of metabolic rate, you might include the various organ masses as covariates. Will an approach like that address your research questions?

Steve Denham

Re: multivariate mixed model issues - Y variables with and without residual variance

fishhead — Mon, 27 Oct 2014 23:28:56 GMT

First, thanks so much for quick reply!

Yes, one measure of metabolism at each of three different temperatures. Mass was measured at time of each metabolism measurement. So, "mass" is the mass at time of metabolism. After conditioning on mass, the aim is to see if the individual intercepts and slopes of metabolic response to temperature covary with internal organs that are implicated in energy metabolism (e.g. liver mass, also conditioned on the final mass to remove the allometry). So, it is mass-independent metabolism and mass-independent organ sizes that we're interested in relating to one another. Of course, organ masses are taken at end of experiment after metabolism work is done.

I'm intrigued by your idea of a multivariate analysis at the final time point. Perhaps metabolism at each of the temperatures (3) should be treated as separate traits, with a single measure each of course, and relate that to the organ masses etc. if so, how do i do this so that mass effects, and sex, are also accounted for? just use proc Mixed, but omit all random effects?

proc mixed;

class trait sex;

model score = trait trait*mass trait*sex ;

run;

thanks mate!

Pete

Re: multivariate mixed model issues - Y variables with and without residual variance

SteveDenham — Tue, 28 Oct 2014 13:26:14 GMT

I managed to confuse myself a lot here.

There is body mass, and there is organ weight (or mass), and I think I confused the two. See if the following is correct:

For any record, the following are available:

trait (several organs, plus metabolic rate)

temp (temperature)

sex

mass

score

Metabolic rate is measured at all temperatures. Organ wt is measured at the end of the trial, after the animals have undergone all temperatures.

Does that accurately capture the experimental design? If not, what am I missing?

Given that, consider the example in the PROC MIXED documentation in the REPEATED statement for the Kronecker product TYPE= option. Would something like the following work (and of course it ignores all of the variance components you are trying to fix at zero currently, but hey, it's something different).

proc mixed maxiter=100 method=reml covtest;

class id trait sex;

where trait in ('smr' 'grow' 'stomach''liver''heart' ) ;

model score = trait trait*mass trait*temp trait*sex / noint solution ;

;

repeated trait temp/ subject=id type=un@un ;

You may need to consider temp as a classification variable for this to work well (or at all). Now if the temperatures were applied sequentially, you might be able to change to un@ar(1) as a type.

Steve Denham

Re: multivariate mixed model issues - Y variables with and without residual variance

fishhead — Tue, 28 Oct 2014 23:30:40 GMT

your take on the data is basically correct. here it is for individual 1 (of78 total):

id	trait$	score	obs	julienday	temp	pop$	sex$	litter	mass
1	gro_len	0.080916	1	0	0	mal	f	229	38.3
1	grow	0.166412	1	0	0	mal	f	229	38.3
1	heart	0.0136	1	0	0	mal	f	229	41.1
1	intesti	0.3158	1	0	0	mal	f	229	41.1
1	liver	0.2724	1	0	0	mal	f	229	41.1
1	smr	1131.02	1	48	22	mal	f	229	38.3
1	smr	1916.27	2	76	27	mal	f	229	46.2
1	smr	2854.82	3	62	33	mal	f	229	41.1

Note that temp was set to zero for all traits other than SMR (standard metabolic rate) to prevent SAS from trying to fit fixed/random effects of temp to them.

temperatures were applied randomly, not sequentially from 22 to 33C.

i'll try your suggested coding!! thx!

Pete

Re: multivariate mixed model issues - Y variables with and without residual variance

fishhead — Wed, 29 Oct 2014 04:21:06 GMT

Trying your model, and making temp a categorical variable:

proc mixed maxiter=100 method=reml covtest ;

class id trait sex temp;

where trait in ('smr' 'grow' 'liver' 'heart' ) ;

model score = trait trait*mass trait*temp trait*sex / noint solution ;

repeated trait temp / subject=id type=un@un rcorr ;

run;

Yields this result - the covariance structure of which i cannot interpret at all!

Data Set WORK.SNAKE

Dependent Variable score

Covariance Structure Unstructured @

Unstructured

Subject Effect id

Estimation Method REML

Residual Variance Method None

Fixed Effects SE Method Model-Based

Degrees of Freedom Method Between-Within

Class Level Information

Class Levels Values

id 78 1 2 3 4 5 6 7 8 9 10 11 12 13

14 15 16 17 18 19 20 21 22 23

24 25 26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43

44 45 46 47 48 49 50 51 52 53

54 55 56 57 58 59 60 61 62 63

64 65 66 67 68 69 70 71 72 73

74 75 76 77 78

trait 4 grow heart liver smr

sex 2 f m

temp 4 0 22 27 33

Dimensions

Covariance Parameters 20

Columns in X 22

Columns in Z 0

Subjects 78

Max Obs Per Subject 6

Number of Observations

Number of Observations Read 468

Number of Observations Used 465

Number of Observations Not Used 3

SNAKE gifford multivariate 1031

14:02 Sunday, January 22, 2012

The Mixed Procedure

Iteration History

Iteration Evaluations -2 Res Log Like Criterion

0 1 817.36095618

1 2 1793.83609030 431151.14982

2 1 1073.84990331 323311.68917

3 1 652.23471322 75931.666262

4 1 440.01937907 5345.0261541

5 1 344.60561121 634.83797490

6 1 309.62726924 68.97791911

7 1 301.26778524 4.46781833

8 1 300.39610532 0.07755390

9 1 300.37671696 0.00006424

10 1 300.37669985 0.00000000

Convergence criteria met but final hessian is not positive

definite.

Estimated R Correlation Matrix for id 1

Row Col1 Col2 Col3 Col4 Col5 Col6

1 1.0000 -0.1260 -0.2866

2 -0.1260 1.0000 0.1576

3 -0.2866 0.1576 1.0000

4 1.0000 0.07351 -0.2243

5 0.07351 1.0000 0.03751

6 -0.2243 0.03751 1.0000

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Estimate Error Value Pr Z

trait UN(1,1) id 0.000727 0.000119 6.13 <.0001

UN(2,1) id -0.00312 0.002902 -1.08 0.2823

UN(2,2) id 0.8440 0.1388 6.08 <.0001

UN(3,1) id -0.00569 0.002415 -2.36 0.0184

UN(3,2) id 0.1067 0.08001 1.33 0.1824

UN(3,3) id 0.5430 0.08941 6.07 <.0001

UN(4,1) id 0 . . .

UN(4,2) id 0 . . .

UN(4,3) id 0 . . .

UN(4,4) id 0.4886 65.4912 0.01 0.4970

temp UN(1,1) id 1.0000 0 . .

UN(2,1) id 0 . . .

The Mixed Procedure

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Estimate Error Value Pr Z

UN(2,2) id 0.1519 20.3599 0.01 0.4970

UN(3,1) id 0 . . .

UN(3,2) id 0.01702 2.2813 0.01 0.9940

UN(3,3) id 0.3529 47.3006 0.01 0.4970

UN(4,1) id 0 . . .

UN(4,2) id -0.07503 10.0572 -0.01 0.9940

UN(4,3) id 0.01912 2.5639 0.01 0.9940

UN(4,4) id 0.7365 98.7178 0.01 0.4970

Fit Statistics

-2 Res Log Likelihood 300.4

AIC (smaller is better) 338.4

AICC (smaller is better) 340.1

BIC (smaller is better) 383.2

Null Model Likelihood Ratio Test

DF Chi-Square Pr > ChiSq

18 516.98 <.0001

Solution for Fixed Effects

Standard

Effect trait sex temp Estimate Error DF t Value Pr > |t|

trait grow -0.3846 0.03389 224 -11.35 <.0001

trait heart -4.7222 1.1527 224 -4.10 <.0001

trait liver -7.5913 0.9056 224 -8.38 <.0001

trait smr -2.2962 0.2683 224 -8.56 <.0001

mass*trait grow 0.3347 0.02153 373 15.54 <.0001

mass*trait heart 2.9054 0.7204 373 4.03 <.0001

mass*trait liver 4.6960 0.5679 373 8.27 <.0001

mass*trait smr 2.1312 0.1640 373 13.00 <.0001

trait*temp grow 0 0 . . . .

trait*temp heart 0 0 . . . .

trait*temp liver 0 0 . . . .

trait*temp smr 22 -1.9272 0.08068 153 -23.89 <.0001

trait*temp smr 27 -1.2366 0.08134 153 -15.20 <.0001

trait*temp smr 33 0 . . . .

trait*sex grow f -0.00481 0.006209 224 -0.77 0.4394

Solution for Fixed Effects

Standard

Effect trait sex temp Estimate Error DF t Value Pr > |t|

trait*sex grow m 0 . . . .

trait*sex heart f 0.1293 0.2105 224 0.61 0.5399

trait*sex heart m 0 . . . .

trait*sex liver f 0.1684 0.1692 224 1.00 0.3205

trait*sex liver m 0 . . . .

trait*sex smr f -0.08404 0.04686 224 -1.79 0.0743

trait*sex smr m 0 . . . .

Type 3 Tests of Fixed Effects

Num Den

Effect DF DF F Value Pr > F

trait 4 224 109.90 <.0001

mass*trait 4 373 146.49 <.0001

trait*temp 2 153 298.59 <.0001

trait*sex 4 224 1.16 0.3283

Re: multivariate mixed model issues - Y variables with and without residual variance

SteveDenham — Wed, 29 Oct 2014 19:20:18 GMT

I knew I was missing a design issue. Temperature is a treatment effect applied randomly at sequential times. That's important. It means that temp is not a repeated factor. It also means that you may not be capturing within subject correlation correctly for metabolic rate. And last, and most importantly (at least to me), it is hard to wrap my head around metabolic rate and organ weights in a multivariate approach without defining "Sequence of applied temperatures" as a variable of interest. With three temperatures, there are at most 6 sequences. Now I would define trait as heart, liver, grow, etc, plus smr1, smr2 and smr3, all as an undefined R side matrix. The hard part is fitting body mass in. A separate analysis of smr with body mass as a covariate in a repeated measures in time design might be appropriate.

Anyway, throw out the code I suggested earlier with the Kronecker product, and try:

proc mixed data=yetanotherdataset;

class sequence sex trait id;

model score=sequence|sex|trait/solution noint;

repeated trait/subject=id type=un; /* you may have to go to a factor analytic covariance matrix to get this to work with this amount of data */

run;

Maybe this will run without the final Hessian problem, which I notice shows up in every output so far. Estimating 15 coefficients with 78 data points should be doable though.

Then for the body mass and smr problem;

proc mixed data=stillanotherdataset;

where trait='smr';

class julienday sex temp id;

model sex|julienday|temp mass/solution /* You may need to examine the equal slopes assumption made here, especially with regard to sex */

random id;

repeated julienday/subject=id type=<this depends on the spacing of the days. With only 3 timepoints, equally spaced, I would look at AR(1) and ARH(1)>;

lsmeans sex|julienday|temp;

run;

Steve Denham

Re: multivariate mixed model issues - Y variables with and without residual variance

fishhead — Thu, 30 Oct 2014 05:33:52 GMT

If i understand you correctly, u suggest we treat the across individual differences as r-side residuals, instead of gside, and treat each metabolism measures at each temp as a separate trait.

So, if i use this model:

proc mixed maxiter=100 method=reml covtest ;

class id trait2 sex ;

where trait2 in ('zsmr22' 'zsmr27' 'zsmr33' 'grow' 'intesti' 'liver' 'stomach' 'heart' ) ;

model score = trait2 trait2*mass trait2*sex / noint solution ;

repeated trait2 / subject=id type=un rcorr ;

run;

Then i get this (edited down) output:

Dimensions

Covariance Parameters 36

Columns in X 32

Columns in Z 0

Subjects 78

Max Obs Per Subject 8

Iteration Evaluations -2 Res Log Like Criterion

0 1 1236.65651524

1 4 580.46562888 0.00230689

2 1 579.79580628 0.00012298

3 1 579.76255875 0.00000053

4 1 579.76242042 0.00000000

Convergence criteria met.

Estimated R Correlation Matrix for id 1

Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8

1 1.0000 -0.03288 0.05073 -0.2411 0.1108 -0.1745 0.09822 0.2226

2 -0.03288 1.0000 0.3456 0.1806 0.2789 -0.03436 0.02908 0.4050

3 0.05073 0.3456 1.0000 0.4840 0.1841 0.1865 0.1581 0.4525

4 -0.2411 0.1806 0.4840 1.0000 -0.01047 0.1267 0.3301 0.2697

5 0.1108 0.2789 0.1841 -0.01047 1.0000 0.1202 -0.1200 0.3658

6 -0.1745 -0.03436 0.1865 0.1267 0.1202 1.0000 -0.02654 0.01060

7 0.09822 0.02908 0.1581 0.3301 -0.1200 -0.02654 1.0000 0.04925

8 0.2226 0.4050 0.4525 0.2697 0.3658 0.01060 0.04925 1.0000

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Estimate Error Value Pr Z

UN(1,1) id 0.000748 0.000127 5.88 <.0001

UN(2,1) id -0.00085 0.003318 -0.26 0.7968

UN(2,2) id 0.9022 0.1619 5.57 <.0001

UN(3,1) id 0.000960 0.002463 0.39 0.6966

UN(3,2) id 0.2272 0.08847 2.57 0.0102

UN(3,3) id 0.4790 0.08551 5.60 <.0001

UN(4,1) id -0.00489 0.002553 -1.92 0.0554

UN(4,2) id 0.1272 0.08845 1.44 0.1504

UN(4,3) id 0.2484 0.07028 3.53 0.0004

UN(4,4) id 0.5498 0.09223 5.96 <.0001

UN(5,1) id 0.006026 0.003945 1.53 0.1266

UN(5,2) id 0.3808 0.1451 2.62 0.0087

UN(5,3) id 0.3100 0.1058 2.93 0.0034

UN(5,4) id 0.1980 0.1118 1.77 0.0766

UN(5,5) id 0.9798 0.1589 6.16 <.0001

UN(6,1) id 0.000786 0.000869 0.90 0.3662

UN(6,2) id 0.06868 0.03312 2.07 0.0381

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Estimate Error Value Pr Z

UN(6,3) id 0.03304 0.02360 1.40 0.1615

UN(6,4) id -0.00201 0.02371 -0.08 0.9323

UN(6,5) id 0.09390 0.03800 2.47 0.0135

UN(6,6) id 0.06724 0.01168 5.76 <.0001

UN(7,1) id -0.00192 0.001485 -1.29 0.1963

UN(7,2) id -0.01312 0.04830 -0.27 0.7859

UN(7,3) id 0.05188 0.03709 1.40 0.1619

UN(7,4) id 0.03777 0.03614 1.05 0.2960

UN(7,5) id 0.004220 0.06473 0.07 0.9480

UN(7,6) id 0.01253 0.01419 0.88 0.3774

UN(7,7) id 0.1616 0.02667 6.06 <.0001

UN(8,1) id 0.001471 0.001859 0.79 0.4287

UN(8,2) id 0.01513 0.06443 0.23 0.8144

UN(8,3) id 0.05991 0.04706 1.27 0.2030

UN(8,4) id 0.1340 0.05014 2.67 0.0075

UN(8,5) id 0.02670 0.08283 0.32 0.7472

UN(8,6) id -0.01704 0.01752 -0.97 0.3308

UN(8,7) id -0.00584 0.02675 -0.22 0.8271

UN(8,8) id 0.2999 0.04909 6.11 <.0001

Null Model Likelihood Ratio Test

DF Chi-Square Pr > ChiSq

35 656.89 <.0001

Solution for Fixed Effects

Effect trait2 sex Estimate Error DF t Value Pr > |t|

trait2 grow -0.3306 0.03301 78 -10.02 <.0001

trait2 heart -1.8642 1.0857 78 -1.72 0.0900

trait2 intesti -6.1261 0.7638 78 -8.02 <.0001

trait2 liver -6.3726 0.8723 78 -7.31 <.0001

trait2 stomach -0.1802 0.1585 78 -1.14 0.2590

trait2 zsmr22 -2.4600 0.3043 78 -8.09 <.0001

trait2 zsmr27 -4.6424 0.5078 78 -9.14 <.0001

trait2 zsmr33 -4.8471 0.6761 78 -7.17 <.0001

mass*trait2 grow 0.3001 0.02096 78 14.32 <.0001

mass*trait2 heart 1.1026 0.6775 78 1.63 0.1077

mass*trait2 intesti 3.7744 0.4777 78 7.90 <.0001

mass*trait2 liver 3.9293 0.5466 78 7.19 <.0001

mass*trait2 stomach 0 . . . .

mass*trait2 zsmr22 1.0173 0.1931 78 5.27 <.0001

mass*trait2 zsmr27 2.7804 0.3205 78 8.68 <.0001

mass*trait2 zsmr33 3.7533 0.4238 78 8.86 <.0001

trait2*sex grow f -0.00298 0.006293 78 -0.47 0.6374

trait2*sex grow m 0 . . . .

trait2*sex heart f 0.1871 0.2172 78 0.86 0.3916

trait2*sex heart m 0 . . . .

trait2*sex intesti f 0.1763 0.1576 78 1.12 0.2667

trait2*sex intesti m 0 . . . .

trait2*sex liver f 0.1897 0.1697 78 1.12 0.2672

trait2*sex liver m 0 . . . .

trait2*sex stomach f 0.3604 0.2242 78 1.61 0.1119

trait2*sex stomach m 0 . . . .

trait2*sex zsmr22 f -0.07440 0.05960 78 -1.25 0.2157

trait2*sex zsmr22 m 0 . . . .

trait2*sex zsmr27 f 0.07966 0.09218 78 0.86 0.3902

trait2*sex zsmr27 m 0 . . . .

trait2*sex zsmr33 f -0.1719 0.1249 78 -1.38 0.1728

trait2*sex zsmr33 m 0 . . . .

Type 3 Tests of Fixed Effects

Num Den

Effect DF DF F Value Pr > F

trait2 8 78 48.26 <.0001

mass*trait2 7 78 70.86 <.0001

trait2*sex 8 78 1.49 0.1737

Now, unfortunately i'm at a bit of loss of whether i can interpret the R corr matrix like a G corr matrix in this instance. Is the diagonal of the R matrix effectively the across individual variances?

Re: multivariate mixed model issues - Y variables with and without residual variance

SteveDenham — Thu, 30 Oct 2014 18:48:41 GMT

Well almost. Since the RCORR and GCORR have 1's on the diagonal, I am going to assume you want RCOV and GCOV, and in this case, the diagonal elements of RCOV, starting with (1,1)=0.000748, is the variance of zsmr22, after removing all fixed effects in the model. So, I would interpret this as the inter-subject variability of zsmr22. You did say that all of these scores were standardized to (0, 1) variables, so I would say that at 22C there isn't much animal to animal variation in metabolic rate.

You may want to only scale the scores, so that they are all just zero centered, and re-run this. The diagonal values then should look like true variances.

Steve Denham

Re: multivariate mixed model issues - Y variables with and without residual variance

fishhead — Fri, 31 Oct 2014 03:32:19 GMT

thanks again. nearly there now. although you say 1,1 is the variance of zsmr22, didn't you mean to say grow? (SAS seems to order alphabetically). If SAS order this way, then the diagonal variances should be in same order as given in the fixed effects solution.

can mixed do a covtest of a particular covariance element, or do i have to go to glimmix to test whether particular covariances (correlations) are significant? like, say i wanna know if 8,2 is significant?

Re: multivariate mixed model issues - Y variables with and without residual variance

SteveDenham — Fri, 31 Oct 2014 13:39:53 GMT

You are right--it would be the variance due to grow not zsmr22, so throw out all that bs about metabolic rate at 22 that I had in a previous post.

Testing of individual variances or covariances is really tricky. The p value in the Covariance Parameter Estimates table (from the covtest option) is a Wald type test that is really sensitive to normality assumptions. You might be able to get after specific test by a likelihood ratio test. If you restricted the parameter value to zero (and now we are back at the very beginning of this thread) and looked at the difference in -2 log likelihood, you should have a single degree of freedom chi squared test.

Or as you bring up, it's off to GLIMMIX. Here is the code I would use to test if the variances are individually equal to zero:

proc glimmix ;

class id trait2 sex ;

where trait2 in ('zsmr22' 'zsmr27' 'zsmr33' 'grow' 'intesti' 'liver' 'stomach' 'heart' ) ;

model score = trait2 trait2*mass trait2*sex / noint solution ;

random trait2 /residual subject=id type=un rcorr ;

covtest 'v1' general 1;

covtest 'v2' general 0 0 1;

covtest 'v3' general 0 0 0 0 0 1;

covtest 'v4' general 0 0 0 0 0 0 0 0 0 1;

covtest 'v5' general 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1;

covtest 'v6' general 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1;

covtest 'v7' general 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1;

covtest 'v8' general 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1;;

run;

You may want to add an ESTIMATE option on the COVTEST statements to see what the covariance estimates are under the null that the specified variance is zero--good for sensitivity analysis.

Steve Denham

Re: multivariate mixed model issues - Y variables with and without residual variance

fishhead — Tue, 18 Nov 2014 05:55:15 GMT

Yes, I was aware that covtest in Mixed is not great.

i tried your covtest statement in glimmix but they dont work. i did successfully test covariances (not variances on the diagonal) using this 8x8 matrix and setting groups of covariances that logically cluster together to zero:

covtest

. .

. . .

. . . .

. . . . .

. . . . . .

. . . . . . .

. 0 0 0 0 . . .

;

BUT, if i test any of the variances (diagonal elements) setting them to zero, it returns me no test, as shown here below:

	Tests of Covariance Parameters
	Based on the Restricted Likelihood

Label

-2 Res Log Like

ChiSq

Pr > ChiSq

Note

Parameter list

Is this because a model without a given variance means any covariances with it must then also be zero, and so it screws with the test? in other words, i cant test this?

thanks!

Re: multivariate mixed model issues - Y variables with and without residual variance

SteveDenham — Tue, 18 Nov 2014 14:14:19 GMT

Not real sure on this one, but it may be worth trying the RESTART option on the COVTEST statements. That would set the variance to zero at the start of the process rather than trying to backfit a zero into place.

Steve Denham