• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
The Analysis Factor

The Analysis Factor

Statistical Consulting, Resources, and Statistics Workshops for Researchers

  • Home
  • About
    • Our Programs
    • Our Team
    • Our Core Values
    • Our Privacy Policy
    • Employment
    • Guest Instructors
  • Membership
    • Statistically Speaking Membership Program
    • Login
  • Workshops
    • Online Workshops
    • Login
  • Consulting
    • Statistical Consulting Services
    • Login
  • Free Webinars
  • Contact
  • Login

Examples for Writing up Results of Mixed Models

by Karen Grace-Martin 18 Comments

One question I always get in my Repeated Measures Workshop is:

“Okay, now that I understand how to run a linear mixed model for my study, how do I write up the results?”

This is a great question.

There are many pieces of the linear mixed models output that are identical to those of any linear model–regression coefficients, F tests, means.

But there is also a lot that is new, like intraclass correlations and information criteria.  And a lot of output we’re used to seeing, like R squared, isn’t there anymore.

And because the model is more complicated, you may need to include in your paper more information about how you set up the model.  For example, you usually need to say whether you included a random intercept or slope (and at which level) and which covariance structure you chose for the residuals.

The problem I have in answering this is how you write it up is very much dependent on who you’re writing for.

Writing for Journals and Committees

The first thing to consider is your field and how familiar readers from your field will be with mixed models.  I’ve worked with clients whose reviewers had never heard of them.

If you’re in a field like this, one of two things will happen.

1. reviewers will be suspicious that you were making up some hocus-pocus statistics to get significant p-values.  Or

2. reviewers will have no idea what you’re talking about and can’t evaluate what you’ve done.  Furthermore, they’ll insist you report statistics that aren’t available in mixed models, like eta-squared.

If that’s your situation, you’re going to have to write it up with a bit more detail than you otherwise would.  Confused reviewers won’t be inclined to accept your paper.  Educate your readers about the methods.  Explain not just what you did, but why it was necessary.

Be generous with citations of not only papers that used mixed models but also those that explain what they are.

If you’re in a field where mixed models are more familiar and most readers will understand them, you’ll need to give enough detail that someone who understands mixed models could evaluate the approach.  This means you will need to say which random effects you included and which covariance structure you chose.  But you won’t have to explain what a random effect does.

Writing for non-statistical audiences

What if your audience isn’t a research audience, but your company’s marketing managers or your agency’s clinical staff?  They likely never needed statistics classes and have no understanding at all of what you’re doing. They just want to understand whether the intervention worked and they’re counting on you to know what you’re doing statistically.

In that case, you want to eliminate as much statistical jargon as possible.  Do everything you can to explain anything you can in English.  You can always put the statistical details in an appendix in case some future researcher comes across it.

They may understand “I used a linear mixed model because it accounts for the fact that multiple responses from the same person are more similar than responses from other people.”  But they won’t want to know how or why this is true.

Use a model

The ideal situation is to use as a guide a published paper that used the same type of mixed model in the journal you’re submitting to.

I can’t usually supply that to researchers, because I work with so many in different fields.

So I thought I’d try this.  Here is a list of a few papers I’ve worked on personally that used mixed models.

Feel free to look them up, in case it helps.

  • J Tee Todd, Susan G Butler, Drew P Plonk, Karen Grace-Martin, Cathy A Pelletier. (2012). Effects of chemesthetic stimuli mixtures with barium on swallowing apnea duration. The Laryngoscope, 122(10):2248-51.
  • Catriona M Steele, Gemma L Bailey, Sonja M Molfenter, Erin M Yeates, Karen Grace-Martin. (2010). Pressure profile similarities between tongue resistance training tasks and liquid swallows.  The Journal of Rehabilitation Research and Development, 47(7):651-60.
  • Susan Butler, Karen Grace-Martin. (2010). The Effect of Chemesthesis on Swallowing Apnea Duration.  Otolaryngology-Head and Neck Surgery, 143(2).

One other suggestion I’ve found helpful.  Try googling:

“used a linear mixed model” .pdf field

Type that in exactly, with the quotes, but replace the word field with whatever your field is: nursing, sociology, etc.  You will be surprised what you may find.

My request to you

If you have worked on or know of a paper that used mixed models, please give us the reference in the comments.  Links to online versions are great too, if you have one.

Trust me, many people in your field are looking for an example and will be happy to cite it.

Fixed and Random Factors in Mixed Models
One of the hardest parts of mixed models is understanding which factors to make fixed and which to make random. Learn the important criteria to help you decide.

Tagged With: mixed model, Writing Results

Related Posts

  • The Difference Between Random Factors and Random Effects
  • The Difference Between Crossed and Nested Factors
  • The Intraclass Correlation Coefficient in Mixed Models
  • Multilevel Models with Crossed Random Effects

Reader Interactions

Comments

  1. irem says

    February 18, 2021 at 9:38 am

    a psych example:

    Improvement in hypersomnia with high frequency repetitive transcranial magnetic stimulation in depressed adolescents: Preliminary evidence from an open-label study
    A Irem Sonmez 1, M Utku Kucuker 1, Charles P Lewis 1, Bhanu Prakash Kolla 2, Deniz Doruk Camsari 1, Jennifer L Vande Voort 1, Kathryn M Schak 1, Simon Kung 1, Paul E Croarkin 3

    https://pubmed.ncbi.nlm.nih.gov/31634515/

    Reply
  2. Immunologist says

    October 15, 2020 at 9:28 pm

    Found this example in tumor immunology (just an example, writeup is minimal): https://www.cell.com/immunity/fulltext/S1074-7613(18)30261-9

    Reply
  3. Jennifer K says

    July 19, 2020 at 11:17 am

    Here’s an example of a mixed model in an applied psychology journal

    Kim, Block, & Nguyen (2019). What’s visible is my race, what’s invisible is my contribution: Understanding the effects of race and color-blind racial attitudes on the perceived impact of microaggressions toward Asians in the workplace. Journal of Vocational Behavior. 113, 75-87. https://doi.org/10.1016/j.jvb.2018.08.011

    Reply
  4. Sarah says

    October 17, 2018 at 2:02 pm

    Thank you so much!!
    Here are two papers in linguistics
    Lukyanenko, C., & Fisher, C. (2016). Where are the cookies? Two-and three-year-olds use number-marked verbs to anticipate upcoming nouns. Cognition, 146, 349-370.
    Kwon, H. (2017). Language experience, speech perception and loanword adaptation: Variable adaptation of English word-final plosives into Korean. Journal of Phonetics, 60, 1-19.

    Reply
    • Jill says

      July 30, 2020 at 10:55 am

      Thank you Sarah for posting these linguistics examples!

      Reply
  5. Candace Loy says

    August 17, 2017 at 11:57 pm

    Found a marine biology and ecology paper that has a useful way of reporting mixed models. https://www.nature.com/articles/srep28875#t2

    Reply
    • nadia says

      January 26, 2019 at 9:46 am

      thank you Candace

      Reply
  6. Emily says

    August 4, 2017 at 6:00 pm

    Thanks so much for this, Karen. You made the work of researching how to report this specific for my audience seems much less daunting!

    Here is a behavioral ecology paper that reports LMM

    http://homepages.abdn.ac.uk/julienmartin/pages/content/uploads/Martin-Réale-2008-AB.pdf

    Reply
    • Emily says

      August 4, 2017 at 6:11 pm

      Forgot to include a link to helpful tutorials I found (which include a little bit about how to report LMM) by Bodo Winter:

      http://www.bodowinter.com/tutorials.html

      Reply
  7. Kristina Mathiasen says

    February 10, 2017 at 2:45 pm

    Thank you very much for this. I have just been introduced to R to analyse my data for my final year BSc research project so this is very helpful. Thank you.

    Reply
  8. Christina says

    December 7, 2016 at 4:33 pm

    Thank you for the clear explanation, and for links to related topics. And, I appreciate the citations listed by other readers.

    Reply
  9. K says

    September 13, 2016 at 12:12 am

    Another example Relationship Between Drug Dreams, Affect, and Craving
    During Treatment for Substance Dependence
    Hel´ ene Tanguay, MSc, Antonio Zadra, PhD, Daniel Good, BA, and Francesco Leri, PhD

    Reply
  10. Juliane Burghardt says

    April 15, 2016 at 5:21 am

    These authors now explain mixed models to social psychologists:
    Judd, C. M., Westfall, J., & Kenny, D. A. (2012). Treating stimuli as a random factor in social psychology: A new and comprehensive solution to a pervasive but largely ignored problem. Journal of personality and social psychology, 103(1), 54-69.

    Reply
  11. Erin Snook says

    March 29, 2016 at 10:57 am

    For the ecology field, the following paper uses linear mixed models:

    XU, C., LETCHER, B. H. and NISLOW, K. H. (2010), Context-specific influence of water temperature on brook trout growth rates in the field. Freshwater Biology, 55: 2253–2264. doi:10.1111/j.1365-2427.2010.02430.x

    Reply
    • C says

      June 27, 2016 at 10:25 pm

      Saviour!

      Reply
  12. Karen says

    February 10, 2016 at 6:53 pm

    Here is another one, from one of my clients:
    http://www.tandfonline.com/doi/full/10.1080/1754730X.2015.1110495

    Reply
  13. Gavin Northey says

    May 9, 2015 at 7:51 am

    Here’s a couple of articles using linear mixed models:

    Schiefer, J. and Fischer C. (2008). The gap between wine expert ratings and consumer preferences: Measures, determinants and marketing implications. International Journal of Wine Business Research, Vol. 20, No. 4, 335 – 351.

    Tainsky, S. (2009). “Television broadcast demand for National Football League contests.” Journal of Sports Economics 11(6): 629-640.

    Sulmont-Rossé, C., et al. (2008). “Impact of the arousal potential of uncommon drinks on the repeated exposure effect.” Food Quality and Preference 19(4): 412-420.

    Reply
  14. Catherine Ortner says

    December 16, 2014 at 3:46 pm

    Here are a couple of examples of mixed models used in articles in an APA journal, Emotion:
    Denny, B. T., & Ochsner, K. N. (2014). Behavioral effects of longitudinal training in cognitive reappraisal. Emotion, 14(2), 425–33. doi:10.1037/a0035276
    Crane, C. A., & Testa, M. (2014). Daily Associations Among Anger Experience and Intimate Partner Aggression Within Aggressive and Nonaggressive Community Couples. Emotion, 14(5), 985–994.

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Please note that, due to the large number of comments submitted, any questions on problems related to a personal study/project will not be answered. We suggest joining Statistically Speaking, where you have access to a private forum and more resources 24/7.

Primary Sidebar

Free Webinars

Binary, Ordinal, and Multinomial Logistic Regression for Categorical Outcomes (Signup)

This Month’s Statistically Speaking Live Training

  • April Member Training: Statistical Contrasts

Upcoming Workshops

  • Logistic Regression for Binary, Ordinal, and Multinomial Outcomes (May 2021)
  • Introduction to Generalized Linear Mixed Models (May 2021)

Read Our Book



Data Analysis with SPSS
(4th Edition)

by Stephen Sweet and
Karen Grace-Martin

Statistical Resources by Topic

  • Fundamental Statistics
  • Effect Size Statistics, Power, and Sample Size Calculations
  • Analysis of Variance and Covariance
  • Linear Regression
  • Complex Surveys & Sampling
  • Count Regression Models
  • Logistic Regression
  • Missing Data
  • Mixed and Multilevel Models
  • Principal Component Analysis and Factor Analysis
  • Structural Equation Modeling
  • Survival Analysis and Event History Analysis
  • Data Analysis Practice and Skills
  • R
  • SPSS
  • Stata

Copyright © 2008–2021 The Analysis Factor, LLC. All rights reserved.
877-272-8096   Contact Us

The Analysis Factor uses cookies to ensure that we give you the best experience of our website. If you continue we assume that you consent to receive cookies on all websites from The Analysis Factor.
Continue Privacy Policy
Privacy & Cookies Policy

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Necessary
Always Enabled

Necessary cookies are absolutely essential for the website to function properly. This category only includes cookies that ensures basic functionalities and security features of the website. These cookies do not store any personal information.

Non-necessary

Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. It is mandatory to procure user consent prior to running these cookies on your website.

SAVE & ACCEPT