Say I have a data set of 32 study participants. The dependent variables are two different physiological reactions to stimuli. These are repeated measures, recorded over 16 trials. There are two different types of stimuli and there are four different experimental conditions relating to the order in which the stimuli are presented. Every participant's reactions are recorded in all trials and to all stimulus types, but only in one experimental condition per participant.
Due to the nature of the experiment I can be confident that the physiological reactions both decrease over time/trials. What I am interested in however are possible difference in the *pattern* of decrease due to reaction type, stimulus type and condition.
My first thought was "That sounds like random slopes in a linear mixed model", however I am unsure if this is actually applicable here. Because if in one condition participants have first very high values and later very low values in reaction measures and in another condition their values are decreasing steadily, they could still have the same regression slope. And while standard errors may be different between conditions, from that alone I couldn't infer anything about the nature of the difference between the two conditions.
Am I right with thinking this or are there possibilities within linear mixed models to analyse this type of research question?
If I am right, what would be an appropriate alternative? Repeated-measure MANOVA, maybe? Or something else altogether?
Thank you very much for your help.
Assuming that the outcome variable is continuous, the multivariable linear mixed-effect (LME) model will definitely work. If the outcome is binary/categorical, use the multivariable generalized linear mixed-effect model (GLMM). Your sample size is very small.
An alternative is using the generalized estimating equation (GEE) by assuming different correlation structures among clusters. Here, each individual is a cluster. You could try exchangeable, unstructured, independent, and AR1 correlation structures. Then compare the models with different correlation structures using QIC value. The smallest QIC indicates the best model. Note: Unlike the strong modelling assumption of LME or GLMM, the GEE is free from distributional assumption. So, you have more flexibility here compared to LME or GLMM.
- Badges
- Science topic