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My research is looking at ethnic differences in teenage mental health during the pandemic. Specifically I have 2 independent variables: ethnicity (categorical - 2 groups: white and non-white) and time point (categorical - 2 time points: before the pandemic and after the 1st UK lockdown). My dependent variable is a measure of mental health which is a continuous variable. This measure was repeated at both time points.

I am a bit confused on the analysis and whether I have done it correctly. My aim was to do multiple regression to see if the time point and ethnicity predicted changes in mental health scores. However I got a bit stuck as one of my predictors is independent (ethnicity) and the other is repeated measures (time point). I dummy coded the ethnicity variable but as time point was repeated measures I converted my dataset into long format and then dummy coded, but this led to double the amount of cases for the ethnicity variable. Would this be an issue? I'm not sure if you can even do a multiple regression with one independent measures predictor and one repeated measures predictor?

So I ran the regression and both of the predictors came out as highly significant (β =.157 and -.119, p = 0.000) but together they only account for 3.7% of the variance which I don't understand.

Any help would be much appreciated!

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  • $\begingroup$ Why would you use white and non-white over a more granular model? $\endgroup$
    – jbuddy_13
    Jan 5 at 16:44
  • $\begingroup$ Wouldn't the interaction between race and pandemic be the actual (only?) term of scientific interest here? I'm not sure why you are surprised that those two predictors explain very little variation. Surely there is more to teenage mental health than whether a teenager is white or not. You don't say anything about the dataset but you would be able to build a more meaningful model if you can include other variables that are (expected) to be predictive of the mental well-being of teenagers. (I'd guess a lot depends on the environment they are growing up in.) $\endgroup$
    – dipetkov
    Jan 5 at 17:05

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While your p-values suggest that both effects are highly significant, their effect sizes are rather small (I assume you are reporting standardized betas, in which case they can be directly interpreted as effect sizes). This is common in large datasets, even small effects can become highly significant. This is in line with your R squared. An R squared of 3.7% is, in my experience, very typical in studies like yours, as mental health is very much a multi-cause issue (you probably would not expect someone's ethnic background and the time of measurement to fully explain their level of mental health, right?).

Another issue is that you have a repeated measures design and you should somehow take into account that you measure same individuals twice. Regular regression may not be suitable because your observations are not independent. Therefore, you should probably use either repeated-measures ANOVA with time as a within-person factor or a linear mixed model regression with participant as random effect and ethnic background as predictor. Third option would be latent difference score model (also known as latent change score model).

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