Growth Curve Model - of David A. Kenny

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 3

Picture of Linear Growth Curve Model for One Person 30

Outcome

25 20 15 10 5 0 0

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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. 6

• 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 8

• 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. 12

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? 13

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. 18

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 20

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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. 23

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 24

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 27

Convergence Issues: SPSS • Sometimes run will not converge and you get the message:

• What to do? – Theoretical Solutions – Computational Solutions 28

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. 29

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 31

Thanks! Debby Kashy

Tessa West

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More Webinars References (pdf) Programs Repeated Measures Two-Intercept Model Crossed Design Other Topics 33