1. Developing a Mixed Effects Model Using SAS PROC MIXED
Lauren Ackerman
Katherine Morgan
Rai Oshima

2. Purpose of the Pilot Study
How accurately can participants identify gender from a handwriting sample?
2. Does accuracy improve with feedback?

3. Demographic Information
Group
Feedback n = 13
No Feedback n=13
Waves
Wave 1
n = 21
Wave 2
n = 25
Wave 3
n = 24
Demographics
Age
Mean = 26.42
Std Dev = 5.07
Min = 17
Max = 40
Gender
M = 8
F = 18
Dominant Hand
R = 23
L = 1
Missing = 2
Satisfaction
Y = 20
N = 4
Predict
Y = 15
N = 9
Missing Data!!!

4. Writing Samples
1 – F
2 – M
3 – F
4 – F
5 – M
6 – F

5. 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;

6. 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;

7. OLS Assumptions
Normality
Homoscedasticity
Zero Correlation

8. Why PROC MIXED?

9. Modeling Covariance Structure
Unstructured Covariance Model
Independence Covariance Model
Compound Symmetry Covariance Model

10. Missing Data
PROC REG vs. PROC MIXED
MAR
Missing At Random

11. proc mixed data = hand_long method=ml;
model score = time / solution;
run;
proc reg data = hand_long;
model score = time;
run; quit;

12. General Multilevel Model

13. Independence vs. Multilevel Model

14. Unconditional Growth Model
PROC MIXED Output
PROC REG Output

15. Covariances and Correlations
Correlation Matrix

16. Multilevel Model with Group

17. Fixed Effects Model Analysis
Parameter
Model A
Model B
Model C
Model D
Model E
Model F
Initial Status Π0i
Intercept
γ00
(0.6917)***
(0.8362)***
(0.7767)***
(0.7893)***
(1.3379)***
(1.1584)***
Happy
(N = 1)
γ01
(1.9405)*
(1.7057)*
(1.4950)**
(1.4948)**
Centered Age
(Age – 17)
γ02
(0.1360)
(0.1112)*
Rate of Change Π1i
γ10
1.7341
(0.5303)**
1.5964
(0.5696)*
1.6681
(0.5295)**
1.4907
(0.9542)
1.6977
(0.5090)**
γ11
1.2414
(1.4141)
γ12
(0.1018)
Variance Components
Level 1
Within Person σε
(3.2023)***
(2.5832)***
(2.4676)***
(2.6187)***
(2.2713)***
(2.2724)***
Level 2
In Initial Status σ0
6.6775
(3.6172)*
5.6867
(5.9618)
0.5907
(4.1543)
0.9881
(4.8273)
Rate of Change σ1
Covariance
σ01
1.0373
(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
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

18. 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

19. Fit Statistics for Covariance Models
Independence
Standard
Unstructured
Compound
Symmetry
Heterogeneous
First-Order
Autoregressive
Toeplitz
-2RLL
369.1
366.5
364.6
365.3
368.2
357.3
AIC
371.1
370.5
368.6
373.3
373.1
376.2
363.3
AICC
372.2
370.7
368.8
374.0
376.9
363.7
BIC
373.2
372.9
371.0
378.0
375.4
380.9
366.8
Deviance Statistics

20. Pilot Study Results
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)

21. Conclusion Why SAS? Why PROC MIXED?
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