topic Re: How to interpret SE for lsmeans in Statistical Procedures

How to interpret SE for lsmeans

Ruhi — Mon, 21 Mar 2016 15:43:41 GMT

Hi All,

I am working on studying the variability of a new medical device. We took repeated measurements (12 on each of 30 subjects) on the device. Now I want to see the varaibility of measurements in gender groups, bmi groups etc. I ran a mixed model in sas with repeated measurements and got lsmeans for men, women, bmi groups and so on and their Standard errors. I am not sure how do I interpret the SE from LSMEANS in this case to PI? or do I get the Standard Deviation from SE's (SE*SQRT(N)), but my total sample size is 30 and here DF for gender is 350, so what is N in my case?

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

Any help is greatly appreciated.

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

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

Re: How to interpret SE for lsmeans

cici0017 — Tue, 29 Mar 2016 15:01:23 GMT

The approximate standard errors for the LS-mean is computed as the square root of L*(X'*(V_hat)^-1*X)^-1*L'. The standard error is appropriate statistic for the LSMEANS not standard deviation. The standard deviation is a characteristic of the data itself, not of estimates such as the LS-means. If you want a standard deviation of a group of data, use the PROC MEANS.

The default is the denominator degrees of freedom taken from the "Type III Tests of Fixed Effects" table corresponding to the LS-means effect, 350 is the denominator degrees of freedom for the tests of fixed effects resulting from the MODEL. The documentation points out -

"The DDFM=BETWITHIN option is the default for REPEATED statement specifications (with no RANDOM statements). It is computed by dividing the residual degrees of freedom into between-subject and within-subject portions. PROC MIXED then checks whether a fixed effect changes within any subject. If so, it assigns within-subject degrees of freedom to the effect; otherwise, it assigns the between-subject degrees of freedom to the effect (see Schluchter and Elashoff 1990). " Check the documentation of DDFM = option on the MODEL statement in PROC MIXED procedure.

Re: How to interpret SE for lsmeans

Ruhi — Tue, 29 Mar 2016 21:51:30 GMT

Ok, but I am not still not sure how do one explain SE from LSMEANS to a PI. They want to have an explanation about SE , because they understand std as how far a person is from the mean of the group. They try to understand SE in the same way.

Thanks

Re: How to interpret SE for lsmeans

Rick_SAS — Wed, 30 Mar 2016 13:19:07 GMT

Tell the PI that standard deviations are for data. It is associated to the mean in the sense that a standard deviation provides a measure of how close some random future observation will be to the mean estimate.

In a similar way, you can think of a standard error as a way to think about how widely the parameter estimates will be expected to vary if you collect new data. A SE gives you a sense for how accurate your parameter estimate is.

If that is too abstract, you can also use the more familiar notion of a confidence interval. A confidence interval says that, given the data, the true parameter is probably within a certain interval (with some confidence). Standard errors are often used to construct confidence intervals. A big standard error leads to a wide CI; a small SE leads to a small CI.