Obsidian | Level 7

## Calculate SE for repeated measure data

Hi

We have got a new device to study some characteristics of the human back. We don't have much literature on that machine yet. So we are in the initial phases of learning about that machine and want to get some idea of varaibility, relaibility etc.

So the study data contains 12 observation (scans) on each human and 30 humans in total . We know gender, and BMI group info as well. We initially want to know the varaibility within 12 scans and then look that up for gender and bmi groups. Some of the previous literatutre has calculated CV's, ICC's and SE of teh mean. Their experiment setup were different but somewhat similar.  We are planning to do something similar.

I am thinking of running a mixed model with repeated statement on my data in long format. I actually ran with CS and AR(1) covaraince structures. Both seem to fit equally from AIC values. But I am not sure how do I get estimates of SE of the dependent variable. With CS I get two varaince components (error and cs). I am not sure how do I go about calculating SE's for the dependent varaible form the info at hand. Or I am running everything wrong ? I can calculate the icc' s but I am not sure how do I get Coefficient of varaition for male, female and bmi groups.

Any help is very appreciated.

Thanks a ton!!!!

3 REPLIES 3
Rhodochrosite | Level 12

## Re: Calculate SE for repeated measure data

You didn't show code, so it is not clear what you are asking. If you want SEs for means, put in LSMEANS statments, or use ESTIMATE or LSMESTIMATE statements to get SEs for contrasts of means. This is all automatic. If you want a SE for each predicted observation, then you use an output statement (in GLIMMIX), or an outp= or outm= option in the model statement of MIXED.

With a mixed model, there are multiple sources of variability (more than one variance). Thus, there is no such thing as a CV.

Obsidian | Level 7

## Re: Calculate SE for repeated measure data

Actually I am interested in accessing the varaibility in the instrument. So we calculated data on 30 humans and we have 12 scans(within 6seconds) on each human. Gender, BMI, body fat and skinfold are assumed to be sources of varaibility. I want to access the varaibility in :

1) measuring device (most imp)

2) gender

3) bmi

4) skinfold

4) bodyfat (bf)

I ran two different models, one with all predictors but skinfold was not significant , neither was interaction term with gender. so I removed the two. Below I pasted the results from both. The table just below is lsmeans from the second model. Sorry for bad formatting. So now atfirst I want the varaibility in the instrument. To get that I get the estimate of residual variance from the covariance parameter estimates. Also to look at the varaibility between male and females I will use the SE's form the LSMEANS table below. But I am not quite sure how do I get the varaibility in covaraites from SE's. Do I multiply each SE by sqrt(df).  Can you please provide your insights?

I really really appreciate your help.

Spoiler

Least Squares Means

Effect BMI gender BF Estimate Standard Error DF t Value Pr > |t|

gender        0              477.45  1.9367 350 246.53 <.0001

gender        1              438.69  2.5761 350 170.30 <.0001

BF                         1    484.45  2.4906 350 194.51 <.0001

BF                         2    468.57  2.8455 350 164.67 <.0001

BF                         3    421.19  4.2231 350 99.74   <.0001

BMI    1                        447.18  3.8360 350 116.57 <.0001

BMI    2                        444.38  2.8957 350 153.46 <.0001

BMI    3                        482.65  2.7025 350 178.60 <.0001

``````proc mixed data=icc; ;
class  pt bmi gender rater bf skinfold;
model vp_dl=gender bmi bf skinfold gender*bf gender*skinfold gender|bmi;
repeated pt/ type=cs;
lsmeans gender bf bmi skinfold;
run;``````

Covariance Parameter Estimates
Cov Parm Estimate
CS 468.58
Residual 0.4272

Fit Statistics
-2 Res Log Likelihood 3153.7
AIC (Smaller is Better) 3157.7
AICC (Smaller is Better) 3157.8
BIC (Smaller is Better) 3165.5

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 0.00 1.0000

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
gender 1 346 144.16 <.0001
SKINFOLD 2 346 0.05 0.9547
BMI 2 346 21.19 <.0001
BF 2 346 61.32 <.0001
gender*SKINFOLD 2 346 1.11 0.3295
gender*BF 2 346 5.52 0.0044
BMI*gender 2 346 15.47 <.0001

So I decided to remove skinfold and its iinteraction term.

Covariance Parameter Estimates
Cov Parm Estimate
CS 465.10
Residual 2.3113

Fit Statistics
-2 Res Log Likelihood 3179.6
AIC (Smaller is Better) 3183.6
AICC (Smaller is Better) 3183.6
BIC (Smaller is Better) 3191.4

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 0.00 1.0000

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
gender 1 350 144.60 <.0001
BMI 2 350 32.57 <.0001
BF 2 350 75.36 <.0001
gender*BF 2 350 5.38 0.0050
BMI*gender 2 350 18.10 <.0001
Rhodochrosite | Level 12

## Re: Calculate SE for repeated measure data

I still don't understand your question. Sorry. The SE is the measure of variability (uncertainty) for the estimated parameter of a covariable. It is printed right next to the parameter estimate in the solution table (just use the  "/ s" option on the model statement. You can use to get confidence intervals. One does not multiply the SE by anything related to df.

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