1. When the Mean isn’t Enough
Methods for Assessing Individual Differences using SAS
Melissa McTernan, PhD -- CSU Sacramento

2. Talk Outline Introduction Common focus on population means
Costs of means-only analysis
Motivation to look beyond the mean
Methods for assessing individual differences in SAS
Preparing the data
Visualizing the individual
Mixed effects models

3. The Average Californian
Do you know her?
The average person in California*
Is 35 years old
Is Latinx
Is a woman
Is overweight
Is a democrat and a
Shares a household with 1.95 other people
Pays $1,851/mo for her mortgage
Has a 28 minute commute to work
Works 41.3 hours a week in a retail job
Has $11,760 of student debts
Drinks 4.8 alcoholic beverages a week
… and has spent $295 dollars on spontaneous purchases while under the influence
*Based on finder.com data and data from the US Census the Bureau of Labor Statistics

4. Common Focus on the Pop. Mean
Many commonly-used methods only produce mean estimates
T-tests
Is the mean for group A different than the mean for group B?
ANOVAs
Do groups A, B, and C have different means?
Linear (simple or multiple) Regression
How much does Y change based on a single unit change in X, for the average individual?

5. Limitations of Means-Only Methods
The mean may or may not be a good summary of the data
Even if the mean is a good summary, the mean still may not represent ANY individual in the population
Recall the example of the “average Californian”
For which of these distributions is the mean more representative of the group?

6. Limitations of Means-Only Methods
Implications
Overgeneralization can lead us down an ugly path…
Clinical and medical interventions may work well for the average person, but may actually be harmful for individuals in certain sub-groups
Focus on the “average” may hide disparities
Example: A longitudinal study may show that, on average, student performance is increasing. Without looking at the individual learning curves, we miss the important fact that some students’ performance is not increasing, or is declining.

7. Methods for Assessing Individual Differences
Using NLSY97 Data,
Variables: Overall outlook on life, whether the participant has health care coverage, and a continuous measure of general health

8. Preparing the Data
”Wide” format vs. “Long” format

9. PROC TRANSPOSE is more efficient, but limited to a single variable
Preparing the Data
ARRAY statements are a simple way to reshape the data, but inefficient for large datasets
PROC TRANSPOSE is more efficient, but limited to a single variable

10. Visualizing Individual Differences
PROC SGPLOT to visualize complex data
Allows you to build upon a base chart to add layers of chart components
Examples:
Build a histogram with a density plot overlay
Build a scatterplot, then overlay a line of best fit
Spaghetti Plots for Longitudinal Data
Plot a trajectory for each individual across time
Overlay the mean trajectory

11. Visualizing Individual Differences
Layer 1
Layer 2

12. Visualizing Individual Differences
What information would we be missing if we only plotted the red line?

13. Visualizing Individual Differences
PROC SGPANEL
Also takes advantage of layering
Allows you to compare two side-by-side plots with a “panelby” option
Now, we can look at individuals within subgroups, within the sample at large
… rather than a mean trajectory across all groups and all people

14. Visualizing Individual Differences

15. Visualizing Individual Differences

16. Accounting for Individual Differences with PROC MIXED
In longitudinal statistical analyses

17. Accounting for Individual Differences with PROC MIXED
Linear mixed effects models allow you to add random effects to account for individual differences in model parameters
Add a random intercept to account for variance in intercept across people
Add a random slope to account for variance in slope across individuals
First, let’s look at a model that only provides information about the typical person (i.e. a fixed effects model, or a model without any random effects)

18. Accounting for Individual Differences with PROC MIXED
First, let’s look at a model that only provides information about the typical person …

19. Accounting for Individual Differences with PROC MIXED
Add a REPEATED statement to add variance components for the growth parameters
Added statement

20. Accounting for Individual Differences with PROC NLMIXED
In longitudinal statistical analyses

21. Accounting for Individual Differences with PROC NLMIXED
PROC NLMIXED is more flexible than PROC MIXED
Non-linear mixed effects models
Outcome may be non-normally distributed (i.e. binary)
User-defined log-likelihood functions
Variance in random intercept

22. Accounting for Individual Differences with PROC GLIMMIX
In longitudinal statistical analyses

23. Accounting for Individual Differences with PROC GLIMMIX
PROC GLIMMIX is also very flexible
Generalized Linear Mixed Models
Outcome may be non-normally distributed (i.e. binary)

24. Comparing NLMIXED and GLIMMIX
PROC GLIMMIX defaults to a pseudolikelihood approach for selection model parameter estimates
PROC NLMIXED defaults to maximum likelihood (ML) using the adaptive Gaussian-Hermite quadrature method of approximation
Note: This is identical to the approach that would be used in PROC GLIMMIX if METHOD=QUAD in the GLIMMIX statement

25. What are the take-aways from this presentation?
Conclusions

26. Conclusions
Only visualizing average trends or estimating average parameters may provide information about the typical person, but that is often not useful
The ”typical” person may not even exist!
SAS Software offers many procedures for data management, data visualization, and data analysis, that preserve information about the individual
Making use of these procedures and incorporating them into practice can lead to more effective and informed interventions/responses

27. Contact Information
Name: Melissa McTernan, PhD Sac State University Sacramento, CA