Repeated Measures: Problems and Directions

Given that I have been doing a fair bit of physiological and repeated measure analyses lately, I have spent much time learning and experimenting with different ways to statistically model repeated measure designs. As an added note, these studies typically have a small sample size and comparisons are made between experimental blocks during a single testing session. Commonly, repeated measure studies use repeated measure ANOVAs or general linear modeling. This means that the assumptions of sphericity and compound symmetry are rarely met, requiring the usage of alternative methods. On a more practical level, there is another issue with the use of such methods in repeated measure phyiso studies, or in many repeated measure studies. This issue comes with individual differences. Individual differences can create crossovers where the change in response for some individuals is opposite of other individuals.

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Given that I have been doing a fair bit of physiological and repeated measure analyses lately, I have spent much time learning and experimenting with different ways to statistically model repeated measure designs.  As an added note, these studies typically have a small sample size and comparisons are made between experimental blocks during a single testing session.  Commonly, repeated measure studies use repeated measure ANOVAs or general linear modeling.  This means that the assumptions of sphericity and compound symmetry are rarely met, requiring the usage of alternative methods.  On a more practical level, there is another issue with the use of such methods in repeated measure phyiso studies, or in many repeated measure studies.  This issue comes with individual differences.  Individual differences can create crossovers where the change in response for some individuals is opposite of other individuals.

In a typical setup, a baseline reading is compared to 1 or more experimental blocks.  Individuals may not respond the same way to each of the experimental stimuli.  My typical task for boredom studies is a vowel counting task.  Some individuals, such as myself, find it incredibly boring, while other individuals may find this activity calming.  Additionally, personality factors can lead to differences in the baseline baseline readings and influence the way in which individuals respond to a stimulus.  These necessitate different approaches to analyzing the data.

The first alternative type of modeling is time- or cross-lagged correlations.  These measure two variables at two different times and then compare the correlation between all of the variables to determine what influences change between a variable over time.

Eron, Huesman, Lefkowitz & Walder (1972).

For one study that I am working on, I am administering two measures relating to boredom.  One measure is a personality measure that assesses boredom prone, while the other measure the frequency of the experience of boredom.  I realize it is not physio but it is much easier to explain from this example.  Traditionally, there is a strong, positive correlation between the measure of the frequency of boredom and the measure of boredom proneness.  However, I hypothesize that the correlation between two administrations of the measure of the frequency of the experience of boredom is not as strong as the relationship between either of these administrations of the measure of the frequency of boredom and the administrations of the boredom proneness scale.  This would suggest that the measure that assesses the frequency of boredom is more state dependent than the trait measure that assesses boredom proneness.  This method overcomes some of the limitations by better modeling the relationship between the change in one measure over time given the relationship that this measure has to another measure.

Along the same lines, structural equation modeling holds such promises in modeling these complex relationships.  I just have not had a sample size large enough to actually use it on this type of data before.

Another method to overcome some of the limitations previously discussed is to instead use mixed linear modeling.  Mixed linear modeling overcomes the problems of crossovers and differential responses by accounting for both fixed and random effects to produce predicted values for each participant.  These predicted values are then used in place of observed values in statistical comparisons.  Mixed linear modeling has the added advantage of being able to manipulate the covariance structure of the model to better account for the relationship between measurement blocks.  The changing of the covariance structure from the compound symmetry structure used in general linear modeling and ANOVAs can be theoretically motivated or empirically driven where the structure that provides the cleanest fit for the data is selected.  Mixed linear modeling minimizes the influence of individual differences on the comparisons made between multiple measurement blocks.  Mixed linear modeling also functions well with small sample sizes.  As a drawback, there are no well established methods for computing power and effect sizes.  Additionally, because the impact of individual differences, the random factor, is modeled out we no can no longer easily try to explain how or what individual differences led to such different responses.

I have been doing quite a bit of trying to model personality traits into mixed linear models of physiological functioning across multiple experimental blocks. While I am not certain it is the best approach statistically, I have been using a two step approach.  The first is to construct a preliminary set of mixed linear models.  Then, I use regression analysis or correlations to model the relationship between the change in autonomic function and a personality measure.  This gives me a set of related personality traits that influence physiological function.  If these are all strongly correlated in the same direction with each other and the change in autonomic tone, I use regression analysis to compute partial least squared correlations to find the strongest predictor of change in autonomic tone.  I then split my sample into groups around the personality variable of interest and rerun the mixed linear model with this additional grouping variable to characterize the different observed types of physiological responses.

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