# Why use Linear Mixed Models instead of Repeated Measures ANOVA?

Well, here's some background before the question:

I have an experiment where I evaluate the heart rate of subjects in 4 different conditions (4 time points). The subjects also answer a psychometric scale divided in a factor with 2 levels (e.g. high and low).

What I want to see is: Does the heart rate change across conditions? Is there a difference in the heart rate between the low and high groups across the conditions?

Having this in mind, I've been told to use a repeated measures ANOVA to evaluate the change across conditions and to see if there's difference in the heart rate between the groups.

Question:

Is that the best approach?

I've been reading and people often use a linear mixed model to adress this type of problem. From what I've read linear mixed models are usually more accurate and flexbile than repeated measures ANOVA.

So, using the lme4 package in R to perform a linear mixed model, my dependet variable would be heart rate, the fixed effect would be the condition and the random effect would be the high and low group, right? Would this random effect be crossed?

Considering this example:

subject   hr     condition  symptoms
1        83.43    time1      high
1        90.32    time2      high
1        87.23    time3      high
1        84.45    time4      high
2        67.75    time1      low
2        78.24    time2      low
2        79.65    time3      low
2        70.12    time4      low


How would be the syntax using lmer?

• Repeated measures anova is a linear mixed model they are virtually synonymous...any differences "accuracy" is likely a result of the estimator function,(i.e., maximum likelihood, MCMC, ordinary least squares) and likely a limited data set. Mar 14, 2019 at 16:39
• At first, you should get a better understanding of what fixed and random effects are. See e.g. the answers to this question: stats.stackexchange.com/q/4700/136579 You seem to be interested in the interaction between condition and symptoms. So you should treat these two fixed factors as fixed effects and include the main effects and their interaction in your model. Your repeated measures are grouped by subjects. So subjects would be a random factor and thus you should consider including random intercepts and possibly random slopes (for condition) for this grouping factor. Mar 14, 2019 at 17:28
• If your data are balanced with regard to observations per subject per condition and there are scale data for every subject, then I see hardly any advantage of using linear mixed models (compared to a mixed factorial ANOVA) for your data if your interest is in the main effect of condition and the condition x symptoms interaction. Mar 14, 2019 at 17:35
• @EdM I'm still conducting the experiment, but the idea is to have a balanced group of high and low symptoms. The subjects always complete the 4 conditons (time 1, 2, 3, 4) and the symptoms scale is not related to the conditions. Subjects respond the scale after the end of last condition (time 4). Mar 14, 2019 at 18:33
• Group would be a fixed effect. The random effect would be person. Mar 16, 2019 at 13:08

As @statmerkur said in a comment:

If your data are balanced with regard to observations per subject per condition and there are scale data for every subject, then I see hardly any advantage of using linear mixed models (compared to a mixed factorial ANOVA) for your data if your interest is in the main effect of condition and the condition x symptoms interaction.

Linear mixed models can be helpful when you don't have well balanced data. They can in principle provide more flexibility, allowing for different types of experimental designs. In your case, with symptoms self-reported by each subject, you could then have an unbalanced design (different numbers of cases for each of the symptoms). It would still be possible to perform ANOVA in that case (taking the differences in numbers of cases into account), but a linear mixed model might be used and could be implemented quite simply. If you want to use a linear mixed model, here are some thoughts.

As @PeterFlom said in a comment:

Group [condition] would be a fixed effect. The random effect would be person [subject].

According to your presentation, you specifically want to model the main effect of condition, the main effect of symptoms, and their interaction, on HR. Those 3 have to be treated as fixed effects. The random effects are those that you wish to control for without modeling as individual fixed effects; in your case that is subject.

In principle you can use a linear mixed model to cover all sorts of random effects: random effects for intercepts (e.g., differences among subjects in baseline HR for condition=time1), random effects for slopes (e.g. differences among subjects in HR responses to conditions), and so on. A linear mixed model can handle many types of crossed or nested designs, and the syntax in the lme4 package, when used correctly, allows the software to figure out the appropriate analysis for the design.

In your case, however, you only have 1 instance of each condition and 1 symptoms value for each subject. So in your case you could account for an intercept of baseline HR for each of the subjects with a random effect, but as you don't have replicates your model might be over-specifed if you tried to incorporate additional random effects.

A few additional thoughts on the experimental design. From the labels it looks like the conditions are always presented in the same order in time, so there might be some ambiguity in terms of actual effects of condition versus the passage of time. The self-report of symptoms seems to be after condition=time4 in all cases, so the same ambiguity could arise in the condition by symptoms interaction. Also, the report of symptoms might be considered an outcome variable rather than a predictor per se. (My sense is that you are treating the sypmtoms as predictors based on a class of people who report either of the symptoms; that might be OK based on your knowledge of the subject matter.) If my interpretation of your design is correct, a reviewer or reader will be likely to note these issues, so you should be ready to address them.