Repeated-measures regression in single subject design

Question

I'm grateful for advice on which R analysis to choose for the following study:

I measured stress in one subject on 27 days in the night and in the morning.

Now I want to predict stress in the night via stress in the morning. All data stem from the same subject. There are 27 timepoints in total.

How do I account for the repeated measures in this?

A normal lm doesn't work since it's repeated. When i use lme4, R gives a warning: If i cluster within ID (always the same participant) the warning is: I have to have more than 1 observation. If I cluster within video (27 videos) R warns that the number of clusters has to be smaller than the number of observations.

I have thought about uSEM, lme4, gee or dynamic linear regression.

Do you have any ideas how I model this? I always want to predict the stress in the night by the stress the former day.

Any advice is very welcome and thank you so much for reading this far.

head(data)

dailystress nightstress dailystress.l1 Video

1 0.333 0.166 0.183 1
2 1 0.142 0.166 2
3 0 0.0741 0.142 3
4 NA 0.138 0.0741 4
5 1 0.0567 0.138 5
6 0.667 0.102 0.0567 6

str(data) is

dailystress: num [1:26] 0.333 1 0 NA 1
..- attr("format.spss")= chr "F8.2"
..- attr("display_width")= int 14
nightstress: num [1:26] 0.1658 0.1424 0.0741 0.138 0.0567
..- attr("format.spss")= chr "F20.8"
..- attr("display_width")= int 22
dailystress.l1: num [1:26] 0.1834 0.1658 0.1424 0.0741 0.138
..- attr("format.spss")= chr "F20.8"
..- attr("display_width")= int 25
Video: num [1:26] 1 2 3 4 5 6 7 8 9 10
..- attr(*, "format.spss")= chr "F8.0"

Answer 1

Consider a model like the following for your data

stress$_{td} \sim N(\mu_t+\pi_d, ~\sigma^2),~\pi_d \sim N(0,~\tau^2)$,

where $t$ codes the time (morning, afternoon) and $d$ indexes the 27 days. If Gaussianity is a reasonable assumption, you can analyze the data with the above model formulation using lme4 or nlme:

m1 <- lmer(stress ~ time+(1|day), data=...)
summary(m1)

m2 <- lme(stress ~ time, random=~1|day, data=...)
summary(m2)

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P.S.

The previous recommendation was based on the assumption that the primary focus is on comparing dailystress and nightstress, and this additional information has been incorporated following the OP's update.

Lacking direct access to the dataset, providing a specific recommendation is challenging. Instead, I offer a more general approach:

1. Theoretical Hypothesis: Clearly formulate your theoretical hypothesis regarding the relationship between dailystress and nightstress. Define the expected patterns or trends.

2. Data Visualization: Plot the data to gain insights. Visualization can reveal patterns, trends, or anomalies that align with or challenge your theoretical hypothesis. Tools like scatter plots, or time-series plots can be insightful.

3. Modeling: Consider employing an autoregressive model or its derivatives. In R, the ar function could be a good starting point. Such models can capture temporal dependencies in the data, which might be crucial when studying stress patterns over time.

This approach encourages a structured exploration of the data, ensuring that your analysis is guided by your theoretical expectations. Visualization aids in uncovering nuances, and an autoregressive model provides a statistical framework for capturing temporal dependencies, a common consideration in stress-related studies.