Transcript Growth Curve Models Latent Means Analysis

Multilevel Modeling:
Other Topics
David A. Kenny
January 7, 2014
Outline
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Centering and the Three Effects
Multiple Correlation
Convergence issues in SPSS
Tau matrix
Significance Testing
Non-normal outcomes
GEE
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Centering and
the Three Effects
• The Three Effects of X (a level 1
variable) on Y
–Within: effect of X on Y estimated for
each level 2 unit and then averaged
–Between: effect of mean X on Y
–Pooled: an “average” of the two
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Example: Effect of Daily
Stress on Mood
• Within: the effect of daily stress on
mood computed for each person and
then averaged
• Between: Stress is averaged for each
person and then average stress is used
to predict mood.
• Pooled: Stress is used to predict mood
using all people and all days.
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Types of Centering and the Effect
• Grand mean centering
– X effect: Pooled estimate
• Grand mean centering with mean X as a
predictor
– X effect: Within estimate
– Mean X effect: Between minus within
estimate
• Group (or person) mean
– X effect: Within estimate
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Multiple Correlation
• Not outputted by any MLM program.
• Estimate a second model without any fixed
effects besides the intercept, the empty
model.
• Measure the relative changes in variances
with predictors in and out of the model.
– sE2 from the empty model; sE2 from the model
– (sE2 - sM2)/sE2
– If negative, report as zero.
– Sometimes called pseudo R2.
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Illustration: Légaré
Variances
>
Terma Empty Model
Model
R2
DD
0.105
0.102
.040
DP
0.131
0.131
.004
PD
0.009
0.008
.054
PP
0.184
0.184
.000
aD implies that the respondent is the doctor
P
and that level is that of the patient.
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Tau Matrix
• Whenever there is more than one
random effect, there is a variancecovariance matrix of random
effects.
• That matrix is called the “tau matrix”
in the program HLM.
• Different programs make different
restriction on this matrix.
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Programs
• HLM: Unstructured only
• SPSS and R’s nlme: Allows
various possibilities but not any
matrix.
• SAS and MLwiN: User can enter
own matrix which gives maximal
flexibility.
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Example: Growth Curve Model with
Indistinguishable Dyad Members
Slope P1 (1)
Int. P1 (2)
Slope P2 (3)
Int. 2 (4)
a
c
b
d
e
a
e
f
c
b
(1)
(2)
(3)
(4)
Letters symbolize different elements of
the tau matrix, some of which are set
equal.
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Significance Testing
• SPSS uses the Wald test for
variances.
• The likelihood ratio test involving
deviance differences is used by
other programs and provides a
more powerful and accurate test of
significance.
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Non-normal Outcomes
• Types
–Dichotomous or binary outcomes
–Counts
• For these cases, the error variance is
not an additional parameter.
• Basic model is often multiplicative.
• Can access in SPSS: Mixed Models,
Generalized Linear
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GEE: Generalized
Estimating Equations
• An alternative to MLM
• Does not test variance components, but
rather using a “working model.”
• Weaker assumptions about the
distribution of random variables.
• Used often in medical research.
• Used also with non-normal outcomes.
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