Solving heterogeneous variance using mixed linear models

[jweedon]

Folks,

I'd like to set up a mixed linear model with one factor and one linear
covariate. No random factors or repeated measures, but residual
variance is to be estimated separately for each level of the factor.

I've fiddled with the Mixed point & click interface for a while trying
to fite this model, with no success.

Any pointers would be appreciated. I'm using V20 for Windows.

Jay Weedon

[David Marso]

Please define what model you are attempting to estimate.
How is it a mixed model when you state there are no repeated measures?
I always thought mixed models were appropriate for situations where one has a between subject factor and a within subject factor.  Don't know how to address the separate variance issue because you haven't provided sufficient/(any) information about your design!

---

jweedon wrote

Folks,

I'd like to set up a mixed linear model with one factor and one linear
covariate. No random factors or repeated measures, but residual
variance is to be estimated separately for each level of the factor.

I've fiddled with the Mixed point & click interface for a while trying
to fite this model, with no success.

Any pointers would be appreciated. I'm using V20 for Windows.

Jay Weedon

[jweedon]

I think I've given most of the relevant info. I want a linear model with independent normally-distributed residuals. If M is a fixed factor, Y is dependent, and X is a continuous covariate, then predict Y from an additive model containing M & X. In other words, this is ANCOVA, EXCEPT that model residuals have differing variances in different levels of factor M. In other words, a heteroskedasticity problem. The virtue of the mixed linear model strategy is that it allows residual variance (analogous to MSE in ANCOVA) to be estimated separately for each level of M. This is perfectly do-able in SAS, with PROC GLIMMIX or PROC MIXED. I just don't know how to do it in SPSS.

[Poes, Matthew Joseph]

Mixed model's don't require repeated measures, simply nesting.  They are designed to deal with failure to meet the IID assumption, which can fail for numerous reasons associated with nested data.

Matthew J Poes
Research Data Specialist
Center for Prevention Research and Development
University of Illinois
510 Devonshire Dr.
Champaign, IL 61820
Phone: [phone]
email: [hidden email]



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of David Marso
Sent: Thursday, April 19, 2012 1:57 PM
To: [hidden email]
Subject: Re: Solving heterogeneous variance using mixed linear models

Please define what model you are attempting to estimate.
How is it a mixed model when you state there are no repeated measures?
I always thought mixed models were appropriate for situations where one has a between subject factor and a within subject factor.  Don't know how to address the separate variance issue because you haven't provided
sufficient/(any) information about your design!

---

jweedon wrote

>
> Folks,
>
> I'd like to set up a mixed linear model with one factor and one linear
> covariate. No random factors or repeated measures, but residual
> variance is to be estimated separately for each level of the factor.
>
> I've fiddled with the Mixed point & click interface for a while trying
> to fite this model, with no success.
>
> Any pointers would be appreciated. I'm using V20 for Windows.
>
> Jay Weedon
>

--
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Sent from the SPSSX Discussion mailing list archive at Nabble.com.

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[Jo Fennessey]

I will be out of the office Friday 4/20/2012 and will check and respond to email Monday morning.

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[Ryan]

Jay,

Take a gander at this message I posted a while back:

http://listserv.uga.edu/cgi-bin/wa?A2=ind1108&L=spssx-l&P=R50929

Ryan

On Apr 19, 2012, at 3:25 PM, jweedon <[hidden email]> wrote:

> I think I've given most of the relevant info. I want a linear model with
> independent normally-distributed residuals. If M is a fixed factor, Y is
> dependent, and X is a continuous covariate, then predict Y from an additive
> model containing M & X. In other words, this is ANCOVA, EXCEPT that model
> residuals have differing variances in different levels of factor M. In other
> words, a heteroskedasticity problem. The virtue of the mixed linear model
> strategy is that it allows residual variance (analogous to MSE in ANCOVA) to
> be estimated separately for each level of M. This is perfectly do-able in
> SAS, with PROC GLIMMIX or PROC MIXED. I just don't know how to do it in
> SPSS.
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Solving-heterogeneous-variance-using-mixed-linear-models-tp5652270p5652578.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

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[jweedon]

Many thanks Ryan, that's just the ticket!

Jay

[Bruce Weaver]

For that particular model, the unequal variances t-test yields the same results.  Change to a fixed font if the following does not line up nicely.

Estimate    SE       df          t       p        Lower   Upper
-0.5126  0.0536   913.3551  -9.5676   0.0000 -0.6178 -0.4075  [1]
-0.5126  0.0536   913.3551  -9.5676   0.0000   -0.6178 -0.4075  [2]

[1] - Fixed effect test for Group from Ryan's MIXED analysis
[2] - Unequal variances t-test

For situations with more than 2 groups, I expect that the Welch or Brown-Forsythe F-tests available via ONEWAY would give the same (or very similar) results that you get with MIXED.

HTH.

jweedon wrote

Many thanks Ryan, that's just the ticket!

Jay