Date: Thu, 3 May 2007 10:41:43 +0200
Reply-To: russell <russel@idasact.org.za>
Sender: "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From: russell <russel@idasact.org.za>
Subject: Re: strange multilevel model problem
In-Reply-To: <a809aab30705021509k2e2902b2mb976de2d9dabf5e1@mail.gmail.com>
Content-Type: text/plain; charset="iso-8859-1"
Hi there Kathy,
The best sources that will answer YOUR specific questions are
Snijders TAB and Bosker RJ (1994) Modeled variance in two-level models.
Sociological Methods and Research, 22: 342-363
You can also find very compelling explanations in a book by the same
authors-Multilevel analysis: an introduction to basic and advanced modelling
(1999).
Furthermore, Kreft and de Leeuw (1998) have the same (although less
"technical") discussion in one of their later chapters. Interestingly, both
Raudenbusch and Bryk (2002) and Singer and Willet (2003) touch on these same
issues.
In a nutshell: while the population within-variance is approximated well by
the within-variance in samples, the population between-variance component is
more complicated because it includes both between variance as measured in
samples and a bit of within-sampling variance (or more broadly sampling
error). This means that there is a fair bit of confounding in the estimation
of the between-variance. Thus, if you introduce a level 2 variable, it will
not impact on the residual level 1 variance but will reduce the (intercept
and slope) variances if your model is so specified. This is logical and will
lead to a reduction of level 2 variance(s). However, if you introduce a
variable at level 1 of your model, which does not have a between-variance
component, your level 1 residual variance should decrease (which is
logical), but your level 2 variance will increase. The level 2 variance is
unaffected by the introduction of a pure level 1 variable BUT BECAUSE THE
LEVEL 1 VARIANCE IS DECREASED , the level 2 variance is forced to increase
precisely because of the confounding that I have alluded to (if a quantity
stays unchanged and you decrease one of its components, by definition the
other component must increase).
Very clumsy explanation, but I cannot do better right now as I am still
digesting all this literature myself. So I am sure there are others who can
offer better (and perhaps more technically correct) explanations and ones
couched in clearer language. But I have tried-hope this does more good than
harm.
Thanks,
Russell
-----Original Message-----
From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of
Kathy McKnight
Sent: 03 May 2007 12:09
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: strange multilevel model problem
HI all,
I am having trouble running a multilevel model using "mixed linear models"
in SPSS v14, and I'm wondering if someone might have some insight into the
problem.
I used the following syntax to test an unconditional multilevel model in
which individuals are nested within cases (the cases are conflict resolution
processes facilitated by at least one "neutral"), as noted in
SUBJECT(CASEID) below. The outcome variable is a measure of the quality of
the final agreement reached during the process:
MIXED QUALITY
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = | SSTYPE(1)
/RANDOM = INTERCEPT | SUBJECT(CASEID) COVTYPE(UN).
The output gives me the following:
*Estimates of Covariance Parameters(a)*
* *
Parameter
Estimate
Std. Error
Wald Z
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
Residual
.180410
.012723
14.180
.000
.157121
.207152
Intercept [subject = CASEID]
Variance
.276698
.063378
4.366
.000
.176619
.433486
a Dependent Variable: QUALITY.
As I understand it, the Residual estimate gives me the explainable within
case variance, and the Intercept estimate gives me the explainable between
case variance for this outcome variable. In Judith Singer's paper in which
she discusses the output from a multilevel model using PROC MIXED in SAS,
she states that this between group variance should function as the ceiling
of explainable between group variance for this outcome.
So here's my problem. When I specify the "full model," in which 12
predictors are entered as FIXED EFFECTS ONLY (the only random effect in the
model is still the intercept), the between groups variance parameter
estimate INCREASES substantially (from .277 in the above table to .587 in
the full fixed effects model, as pasted below). This baffles me, because as
I add explanatory variables to the model, the explainable between groups
variance estimate ought to be DECREASING, or if it's an awful model, ought
to remain unchanged. So why would the between cases variance actually
increase in the conditional model when the unconditional model ought to be
giving me the ceiling estimate for that variance parameter?
Here's the syntax I used, and the output, for the full fixed effects model
(there are 12 predictors after the "with" statement):
MIXED QUALITY WITH M7 COMPLEX c_Q13A c_appro c_engage c_medskl c_relinf
c_effec
c_othrvw c_Q15E c_Q14G c_Q14H
/METHOD = REML
/PRINT = SOLUTION TESTCOV
/FIXED = M7 COMPLEX c_Q13A c_appro c_engage c_medskl c_relinf c_effec
c_othrvw
c_Q15E c_Q14G c_Q14H | SSTYPE(1)
/RANDOM = INTERCEPT | SUBJECT(CASEID) COVTYPE(UN).
The output that concerns me:
*Estimates of Covariance Parameters(a)*
* *
Parameter
Estimate
Std. Error
Wald Z
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
Residual
.107862
.010415
10.356
.000
.089264
.130336
Intercept [subject = CASEID]
Variance
.587327
.146167
4.018
.000
.360614
.956571
a Dependent Variable: QUALITY.
I appreciate any help anyone can offer!
Thanks very much,
Katherine McKnight
