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Developing a Mixed Effects Model Using SAS PROC
MIXED
Lauren Ackerman Katherine Morgan
Rai Oshima
Purpose of the Pilot Study
1. How accurately can participants identify gender from a handwriting sample?
2. Does accuracy improve with feedback?
Demographic Information
Group Feedbackn = 13
No Feedbackn=13
Waves Wave 1n = 21
Wave 2n = 25
Wave 3n = 24
Demographics AgeMean = 26.42Std Dev = 5.07Min = 17Max = 40
GenderM = 8F = 18
Dominant HandR = 23L = 1Missing = 2
SatisfactionY = 20N = 4Missing = 2
PredictY = 15N = 9Missing = 2
Missing Data!!!
Writing Samples
1. 2.
3. 4.
5. 6.
Why SAS:PROC SGPANEL
• Visualize change over time for each subject
proc sgpanel data = data_long;title 'Empirical Growth Plots of Score for Participants';label score = 'Score (# Correct out of 44)’ time = 'Time’;panelby id / columns = 3 rows = 5;reg y = score x = time;run;
PROC SGPLOT
proc sgplot data = data_long noautolegend;title 'OLS Trajectories Across Participants';yaxis min=0 max=50;reg x = time y = score / group = id
nomarkers lineattrs = (color = gray pattern = 1 thickness=1);
reg x = time y = score / nomarkers lineattrs = (color = red
pattern = 1 thickness=3);run;quit;
OLS Assumptions
1. Normality2. Homoscedasticity3. Zero Correlation
Why PROC MIXED?
Modeling Covariance Structure
Unstructured Covariance Model
Independence Covariance Model
cs20
220
20
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20
20
20
2
Compound Symmetry Covariance Model
in
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un
232313
232212
131221
Missing Data
PROC REG vs. PROC MIXED
MAR
Missing At Random
proc mixed data = hand_long method=ml;model score = time / solution;
run;
proc reg data = hand_long;model score = time;
run; quit;
TimeS 78.122.29ˆ
General Multilevel Model
)(
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101000
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1101
0000
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ijiiijijij
i
iij
ii
ii
ijijiiij
TimeTimeS
NandNwhere
TimeS
Independence vs. Multilevel Model
0: 0121
200 H
Unconditional Growth Model
PROC MIXED Output
PROC REG Output
Covariances and Correlations
000.1
579.0000.1
553.0512.0000.1
273.16
199.14
124.12
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2Re
2Re
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2Re
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sidualsidual
jjjjsidualsidual
jjsidual
TimeTimeTimeTime
TimeTime
Covariances Correlation Matrix
Multilevel Model with Group
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ijiiijijiijiij
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ijijiiij
TimeTimeGroupTimeGroupS
nandNwhere
Group
Group
TimeS
Fixed Effects Model AnalysisFixed Effects Parameter Model A Model B Model C Model D Model E Model F
Initial Status Π0i Intercept γ0031.0695
(0.6917)***
29.2597(0.8362)***
30.2060(0.7767)***
30.1538(0.7893)***
32.3241(1.3379)***
32.1517(1.1584)***
Happy(N = 1)
γ01 -5.3523(1.9405)*
-4.4149(1.7057)*
-4.5501(1.4950)**
-4.5436(1.4948)**
Centered Age(Age – 17)
γ02 -0.2769(0.1360)
-0.2568(0.1112)*
Rate of Change Π1i Interceptγ10 1.7341
(0.5303)**
1.5964(0.5696)*
1.6681(0.5295)**
1.4907(0.9542)
1.6977(0.5090)**
Happyγ11 1.2414
(1.4141)
Centered Age(Age – 17)
γ12 0.02611(0.1018)
Variance Components
Level 1 Within Person σε15.0951
(3.2023)***
12.1240(2.5832)***
11.6501(2.4676)***
12.1747(2.6187)***
11.0328(2.2713)***
11.0500(2.2724)***
Level 2In Initial Status
σ06.6775
(3.6172)*
5.6867(5.9618)
0.5907(4.1543)
0.9881(4.8273) 0 0
Rate of Change
σ1 0 0 0 0 0
Covariance σ011.0373
(3.0032)2.0230
(2.2735)2.3530
(3.1340)1.8423
(1.3173)1.8375
(1.3107)Ry,y 0.0930 0.2643 0.2037 0.2862 0.2857
Rε 0.1968 0.2282 0.1935 0.2691 0.2678
R0 0.1484 0.9115 0.8520 1.0000 1.0000
Deviance 408.9 399.0 387.7 393.0 365.9 366.0
AIC 414.9 409.0 405.7 407.0 379.9 378.0
BIC 418.6 415.3 417.0 415.8 388.2 385.1
2
2
2
2
2
2
Final Model
• Model F provided the best deviance statistic– Satisfaction with handwriting and age were the
only significant predictors for intercept– No significant predictor for slope besides time
ijiiij TimeAgeUnhappyS 70.1)17(26.054.415.32ˆ
Fit Statistics for Covariance Models
Independence
Standard
Unstructured
Compound Symmetry
Heterogeneous
CompoundSymmetry
First-OrderAutoregressi
ve
Heterogeneous
Autoregressive
Toeplitz
-2RLL 369.1 366.5 364.6 366.5 365.3 369.1 368.2 357.3
AIC 371.1 370.5 368.6 370.5 373.3 373.1 376.2 363.3
AICC 372.2 370.7 368.8 370.7 374.0 373.3 376.9 363.7
BIC 373.2 372.9 371.0 372.9 378.0 375.4 380.9 366.8Devia
nce
Sta
tisti
cs
20
220
20
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Pilot Study Results
1. How accurately can participants identify gender from a handwriting sample?
Baseline 69.91% accuracy; 95% CI (65.60%,74.23%)
Time important predictor (Estimate 1.73, p<0.01)
2. Does accuracy improve with feedback?
Group not significant (Estimate 0.37, p = 0.79)
ConclusionWhy SAS?• Graphical and mixed effects modeling
capability
Why PROC MIXED?• Allows autocorrelation and
homoscedasticity• Flexibility in modeling the within subject
variability • Handles missing data• Inclusion of time-varying predictors