I'm working with a data set from a multi-school data set and trying to model the relationship between a dichotomous Sleep Status (whether or not they were getting 8 or more hours of sleep per night) measured over two observation points (T1 & T2). Between T1 and T2 participants can change from a yes (≥8h) to a no (<8), vice versa, remain a yes, or remain a no.
There are also 2 conditions (ConditionA vs ConditionB) which applies to the entire school (e.g. schools 1-50 are ConditionA and schools 51-100 are all ConditionB) as part of a natural experiment (change in policy between T1 & T2, that affected some schools). I have some various other covariates to control for statistically (e.g. Sex, SES, etc) that I'm treating as time-invariant because I'm using measurements taken at baseline.
Fundamentally what I am interested in knowing is whether the individuals in Condition1 differ in Sleep Status from those in Condition2 at the follow up (T2) while accounting for their original Sleep Status (participants can go from meeting the status
In summary the key variables are:
- Sleep Status - Dependant variable (self-report ≥8h sleep/night), dichotomous yes (≥8h) or no (<8h) measured at both T1 & T2
- Time - T1 (Baseline) & T2 (Follow-up)
- SchoolID - clustering variable, approximately 100 clusters
- ParticipantID - arbitrary alphanumeric to link longitudinal data, participants are all nested within schools (students not included if they change schools)
- Condition - 2 factor variable, schools are all nested within one of the two conditions (ConditionA vs ConditionB) representing a change in policy that affected some schools but not others
- Sex - stand in for other control covariates that will be included in the model
I know I'm going to use some kind of mixed modelling approach (likely multilevel logistic regression) but am having some difficulty deciding on what variables should be included as an interaction term vs allowing the slopes to vary.
If I were to create a model for a cross sectional data set it would be something along the lines of:
Sleep Status ~ Sex + Condition + (1|SchoolID)
However to address with the longitudinal nature of the data I suspect I should instead be modelling something along the lines of:
Sleep Status.T2 ~ Sex + Sleep Status.T1*Condition + (1|SchoolID)
However, I think I've confused myself somewhat by also considering using a growth model approach or potentially using a nominal logistic regression to account for direction and type of change in the Sleep status (i.e. 4 possible outcomes: 01 (no-yes), 10 (yes-no), 00 (no-no), 11 (yes-yes)).
Any insight or help would be appreciated as it is my first time trying to model change on a dichotomous variable and it's further complicated by the clustered nature of the data.