Developer Tutorial: Mixed Models Part 2: Handling Repeated Measures in Time and Space

[#1]

This technical presentation includes examples presented in JMP for Mixed Models. Data from the book used in the presentation is included. The video is over 90 minutes long with questions interspersed throughout. This tutorial and examples of regression, random coefficient and multi-level models all require JMP Pro. Part 3 will be scheduled for early 2022 and will cover assessing power and precision for mixed models.

Mixed Models are useful when you have multiple predictors, for example a factorial treatment with or without interactions, when there is curvature in the response over the predictor, and where multiple subjects are measured. 

See how to:

• Analyze repeated measures and longitudinal data in a pharmaceutical stability trial example

  • Address lack of independence of observations made on the same subject over time

  • Assess covariance and correlation between time points to select candidate structure

  • Compare Source and Degrees of Freedom for Experiment Design, Treatment design and Skeleton ANOVA
  • Understand the stats (model) behind the Skeleton ANOVA
  • Build the model and include interactions
  • Understand and evaluate Compound Symmetry, Auto-Regressive Correlation Matrix, Toeplitz and Antedependent Correlation Matrices
•  Model correlations in space (Spatial Models)
  • Understand spatial model terminology in a hazardous waste example

    • Variogram – graphical display of the semivariance as distance increases

    • Nugget – “jump” in semivariance at small distances

    • Sill – plateau of the semivariance

    • Range – distance to the Sill

Resources

• Also available is a video from Mixed Models Part 1: A Critical Tool When You Have More Than One Source of Variation
• JMP Pro documentation on fitting spatial structures mentioned in the session 
• Repeated Measures Add-In by Ruth Hummel that was mentioned in the session. NOTE: This functionality will be integrated into JMP Pro Version 17, at which point JMP 17 and later users will not require the add-in anymore.

[H2OSUP]

@eclaassen thank you for presenting on mixed models. I got a lot out of you presentations. I wanted to get your thoughts on how to handle a data set I am analyzing. I have 9 products which will be my treatment variable. Six parts were made from each product and weathered for up to 2500 hours. During the weathering separate parts are removed for testing at 500, 800, 1100, 1400 & 2500 hours. A part is also tested at 0 hours. I am planning to analyze the hours as a categorical factor. I am thinking the hours should be treated as split-plot in structure and not repeated measures as the same part was not tested throughout the weathering time. Three measurements are done on each part at different positions (A, B, C). I am thinking the positions could be treated as spatial in structure. Can you have a mixed model with a combination of split-plot and spatial structures? Thanks, Mike Morrow

[eclaassen]

Hi, Mike @H2OSUP . I'm glad you found the presentations beneficial.

It is possible to fit both a split-plot structure and a spatial correlation structure. Depending on the size of the data set and which spatial structure you try, you may run into convergence issues, as that often occurs when combining the two types of models. There is an example in the PROC MIXED documentation for SAS that does essentially this. Example 81.6 Line-Source Sprinkler Irrigation For anyone who might read this who is unfamiliar with SAS syntax, the "conversion" to JMP is like this: class statement variables would be designated Nominal columns in the JMP data table, the model statement is the Fixed Effect structure (in this case a factorial up to degree 2), the random statement is the random effects (Random tab in the Mixed personality in JMP), and the repeated statement the spatial structure designation (Repeated tab in the Mixed personality).

[H2OSUP]

Thanks, Elizabeth @eclaassen . I was able to get it to work. Is there a way to specify a LSMeans contrast in the Mixed Model platform? 

[eclaassen]

In the Multiple Comparisons red triangle menu option, you can either get all of the LSMeans and pairwise comparisons (with various adjustments like ANOM, Dunnett (for comparisons with a control), Tukey), or there's an option for User Specified estimates. The User Specified is still pairwise, but you can limit which comparisons you're looking for. There's an open request for more "freeform" contrasts, such as for interactions or average of these two vs one other. 

[H2OSUP]

Thanks Elizabeth @eclaassen . I am trying to get a specific comparison that would require a contrast statement.

[eclaassen]

I'll add your name (Mike @H2OSUP ) to track the request, so we can show the demand for the feature to allocate the resources to making it happen. I can't promise anything, but I hope that we can work on it soon.