Growth Curve Models Using
Multilevel Modeling with SPSS
David A. Kenny
January 23, 2014
Presumed Background
• Multilevel Modeling
• Nested
• Used to examine linear and nonlinear
changes over time
• Time the key predictor variable in
growth models
• Need at least three time points to
model growth
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Picture of Linear Growth Curve
Model for One Person
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Outcome
25
20
15
10
5
0
0
2
4
6
8
10
Time
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• Levels
– Level 1: Times
– Level 2: Persons
• Spacing of time points
– Each individual need not have the same
number of time points
– Difference between time points need be the
same
– Time points can be different for each
person
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• A person period dataset
• Each record is one time for each
person
• Sometimes called a “narrow”
format as opposed to a “wide”
format which has all the person’s
times on one record.
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• Campbell, L., Simpson, J. A., Boldry, J. G., & Kashy, D.
A. (2005). Perceptions of Conflict and Support in
Romantic Relationships: The Role of Attachment
Anxiety. Journal of Personality and Social Psychology,
88, 510-531.
• 103 Dating Couples completing a 14-day daily diary
study
• Consider only the males
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Download
Data
Syntax
Output
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• satisf: Satisfaction with the Relationship, measured
on a 1 to 7 scale
• day: Day of survey from 1 to 14
• time: measured in weeks and centered;
equals (day – 7.5)/7
• avoidc: attachment avoidance centered (grand mean
across both men and women subtracted)
• Missing cases
– One person and his partner is missing the
Attachment measure
– There are 11 missing satisfaction scores.
– Total number of cases: 103 x 14 – 25 = 1417
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• The intercept refers to the predicted score when
time equals zero.
• Thus, the scaling of time affects the intercept’s
meaning.
• Some common options for modeling the intercept
– Initial measurement (the usual option)
– Study midpoint
– Time of intervention
– Study endpoint
• In the Kashy data set, 7.5 is subtracted off of
each time since there are 14 time points
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satisfaction = intercept + b(time) + c(avoidc) + d(time*avoidc) + error
Intercept = predicted satisfaction score at the study midpoint (when
time = 0)
b = the predicted change in satisfaction as time for a week
If the main effect of time is positive then satisfaction is
increasing over time and if it is negative then satisfaction is
decreasing.
c = effect of avoidance attachment on satisfaction
d = Does the effect of time on satisfaction change as a function of
avoidance attachment?
Error = the part of satisfaction that is not predicted by time and
avoidant attachment.
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Random Effects
Variance of the intercepts
– based on the variance of how much men
vary in satisfaction at study midpoint
Variance of the slopes
– How much men vary in their rate of linear
change in satisfaction
Covariance between the intercept and slope
– Do individuals who have higher satisfaction
scores at the study midpoint change more
rapidly (or slowly) than those with lower
satisfaction scores at midpoint?
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MIXED satisf WITH time avoidc
/FIXED=time avoidc time*avoidc
/PRINT=SOLUTION TESTCOV
/RANDOM=INTERCEPT time | SUBJECT(personid)
COVTYPE(UNR).
“RANDOM INTERCEPT time” Estimates a random intercept and
slope variance.
UNR provides a correlation between slope and intercept.
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Satisfaction = 6.26 + 0.134(Time) +
-0.140(Avoid) + 0.032(Time*Avoid)
• Intercept = 6.26
– The average level of satisfaction at time = 0
• Coefficient for Time = 0.134
– Over time, satisfaction increases .134 units a week
– The slope is small, although it is statistically
significant. There is some evidence of an average
increase in satisfaction over time for men.
• Coefficient for Avoidance = -0.140
– More Avoidance less satisfaction
• No interaction of Time and Avoidance
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SPSS Output Random Effects
Random Effects
Variance of Intercepts:
Variance of Slopes:
Correlation Inter./Slope:
Var(1) = .460*
Var(2) = .124*
Corr(2,1) = -.032
/RANDOM INTERCEPT time | SUBJECT(personid) COVTYPE(UNR).
With SPSS, p values for variances (not correlations) must be
divided by two to make the p values one-sided.
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Random Effects
• Random effects:
– Variance in the intercepts
• some men were more satisfied than others at the
midpoint.
– Variance in the slopes
• some men are changing in satisfaction more than
others.
– Slope-intercept covariance
• Men with higher values at time 0 change more slowly
than those with lower values, but this correlation is not
significant and small.
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Autoregressive Errors
• Bolger, N., & Laurenceau, J.-P. (2013).
Intensive longitudinal methods: An
introduction to diary and experience
sampling research. New York: Guilford
Press.
• They suggest having errors that affect
one another:
e1  e2  e3
autoregressive errors
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MIXED satisf WITH time avoidc
/FIXED=time avoidc time*avoidc
/PRINT=SOLUTION TESTCOV
/RANDOM=INTERCEPT time | SUBJECT(personid)
COVTYPE(UNR)
/REPEATED day | SUBJECT(personid) COVTYPE(AR1).
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Changes
Half as much
slope variance
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Convergence Issues: SPSS
• Sometimes run will not converge and you get
the message:
• What to do?
– Theoretical Solutions
– Computational Solutions
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Theoretical
• Possibilities
–A variance component you want to
estimate is very small.
–Two variance components are too
highly correlated.
• Solution: Drop or combine component.
• Note if a variance component is
estimated as zero, you always get this
warning.
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Computational
• SPSS is poor at finding a solution: Use another
program.
• SPSS changes
– Change UNR to UN.
– If a predictor is random (e.g., time) increase
the size of its variance by decreasing the
variance of a predictor.
• That was why the units for “time” is
weeks not “days.”
– Make the following changes on the
“Estimation” screen:
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Increase
These are things
that work for me.
There may well be
better options.
Increase
Increase
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Thanks!
Debby Kashy
Tessa West
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More Webinars
References (pdf)
Programs
Repeated Measures
Two-Intercept Model
Crossed Design
Other Topics
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